MAYBE
Rewrite Rules:
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x,?xs)) -> ?x,
     tl(nil) -> nil,
     tl(cons(?x,?xs)) -> ?xs,
     inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     if(true,?ys,?zs) -> ?ys,
     if(false,?ys,?zs) -> ?zs,
     nil -> inc(nil),
     inc(cons(?x,?xs)) -> cons(s(?x),inc(?xs)) ]
Apply Direct Methods...
Inner CPs:
   [ null(inc(nil)) = true,
     hd(inc(nil)) = 0,
     tl(inc(nil)) = nil ]
Outer CPs:
   [ if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6))))) = cons(s(?x_6),inc(?xs_6)) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Left-Linear, not Right-Linear
unknown Development Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ null(inc(nil)) = true,
     hd(inc(nil)) = 0,
     tl(inc(nil)) = nil,
     cons(s(?x_6),inc(?xs_6)) = if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6))))),
     true = null(inc(nil)),
     0 = hd(inc(nil)),
     nil = tl(inc(nil)),
     if(null(cons(?x,?xs)),nil,cons(s(hd(cons(?x,?xs))),inc(tl(cons(?x,?xs))))) = cons(s(?x),inc(?xs)) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <null(inc(nil)), true> by Rules <9, 0> preceded by [(null,1)]
 joinable by a reduction of rules <[([(null,1)],6),([(null,1),(if,1)],0),([(null,1)],7),([],0)], []>
Critical Pair <hd(inc(nil)), 0> by Rules <9, 2> preceded by [(hd,1)]
 joinable by a reduction of rules <[([(hd,1)],6),([(hd,1),(if,1)],0),([(hd,1)],7),([],2)], []>
Critical Pair <tl(inc(nil)), nil> by Rules <9, 4> preceded by [(tl,1)]
 joinable by a reduction of rules <[([(tl,1)],6),([(tl,1),(if,1)],0),([(tl,1)],7),([],4)], []>
Critical Pair <cons(s(?x_6),inc(?xs_6)), if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6)))))> by Rules <10, 6> preceded by []
 joinable by a reduction of rules <[], [([(if,3),(cons,2),(inc,1)],5),([(if,3),(cons,1),(s,1)],3),([(if,1)],1),([],8)]>
 joinable by a reduction of rules <[], [([(if,3),(cons,2),(inc,1)],5),([(if,1)],1),([(if,3),(cons,1),(s,1)],3),([],8)]>
 joinable by a reduction of rules <[], [([(if,3),(cons,2),(inc,1)],5),([(if,1)],1),([],8),([(cons,1),(s,1)],3)]>
 joinable by a reduction of rules <[], [([(if,3),(cons,1),(s,1)],3),([(if,3),(cons,2),(inc,1)],5),([(if,1)],1),([],8)]>
 joinable by a reduction of rules <[], [([(if,3),(cons,1),(s,1)],3),([(if,1)],1),([(if,3),(cons,2),(inc,1)],5),([],8)]>
 joinable by a reduction of rules <[], [([(if,3),(cons,1),(s,1)],3),([(if,1)],1),([],8),([(cons,2),(inc,1)],5)]>
 joinable by a reduction of rules <[], [([(if,1)],1),([(if,3),(cons,2),(inc,1)],5),([(if,3),(cons,1),(s,1)],3),([],8)]>
 joinable by a reduction of rules <[], [([(if,1)],1),([(if,3),(cons,2),(inc,1)],5),([],8),([(cons,1),(s,1)],3)]>
 joinable by a reduction of rules <[], [([(if,1)],1),([(if,3),(cons,1),(s,1)],3),([(if,3),(cons,2),(inc,1)],5),([],8)]>
 joinable by a reduction of rules <[], [([(if,1)],1),([(if,3),(cons,1),(s,1)],3),([],8),([(cons,2),(inc,1)],5)]>
 joinable by a reduction of rules <[], [([(if,1)],1),([],8),([(cons,2),(inc,1)],5),([(cons,1),(s,1)],3)]>
 joinable by a reduction of rules <[], [([(if,1)],1),([],8),([(cons,1),(s,1)],3),([(cons,2),(inc,1)],5)]>
unknown Diagram Decreasing
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x_1,?xs_1)) -> ?x_1,
     tl(nil) -> nil,
     tl(cons(?x_2,?xs_2)) -> ?xs_2,
     inc(?xs_3) -> if(null(?xs_3),nil,cons(s(hd(?xs_3)),inc(tl(?xs_3)))),
     if(true,?ys_4,?zs_4) -> ?ys_4,
     if(false,?ys_5,?zs_5) -> ?zs_5,
     nil -> inc(nil),
     inc(cons(?x_6,?xs_6)) -> cons(s(?x_6),inc(?xs_6)) ]
Sort Assignment:
 0 : =>15
 s : 15=>15
 hd : 35=>15
 if : 19*35*35=>35
 tl : 35=>35
 inc : 35=>35
 nil : =>35
 cons : 15*35=>35
 null : 35=>19
 true : =>19
 false : =>19
non-linear variables: {?xs_3}
non-linear types: {35}
types leq non-linear types: {35}
rules applicable to terms of non-linear types:
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x_1,?xs_1)) -> ?x_1,
     tl(nil) -> nil,
     tl(cons(?x_2,?xs_2)) -> ?xs_2,
     inc(?xs_3) -> if(null(?xs_3),nil,cons(s(hd(?xs_3)),inc(tl(?xs_3)))),
     if(true,?ys_4,?zs_4) -> ?ys_4,
     if(false,?ys_5,?zs_5) -> ?zs_5,
     nil -> inc(nil),
     inc(cons(?x_6,?xs_6)) -> cons(s(?x_6),inc(?xs_6)) ]
Rnl:
0: {}
1: {}
2: {}
3: {}
4: {}
5: {}
6: {0,1,2,3,4,5,6,7,8,9,10}
7: {}
8: {}
9: {}
10: {}
unknown innermost-termination for terms of non-linear types
unknown Quasi-Linear & Linearized-Decreasing
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x_1,?xs_1)) -> ?x_1,
     tl(nil) -> nil,
     tl(cons(?x_2,?xs_2)) -> ?xs_2,
     inc(?xs_3) -> if(null(?xs_3),nil,cons(s(hd(?xs_3)),inc(tl(?xs_3)))),
     if(true,?ys_4,?zs_4) -> ?ys_4,
     if(false,?ys_5,?zs_5) -> ?zs_5,
     nil -> inc(nil),
     inc(cons(?x_6,?xs_6)) -> cons(s(?x_6),inc(?xs_6)) ]
Sort Assignment:
 0 : =>15
 s : 15=>15
 hd : 35=>15
 if : 19*35*35=>35
 tl : 35=>35
 inc : 35=>35
 nil : =>35
 cons : 15*35=>35
 null : 35=>19
 true : =>19
 false : =>19
non-linear variables: {?xs_3}
non-linear types: {35}
types leq non-linear types: {35}
rules applicable to terms of non-linear types:
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x_1,?xs_1)) -> ?x_1,
     tl(nil) -> nil,
     tl(cons(?x_2,?xs_2)) -> ?xs_2,
     inc(?xs_3) -> if(null(?xs_3),nil,cons(s(hd(?xs_3)),inc(tl(?xs_3)))),
     if(true,?ys_4,?zs_4) -> ?ys_4,
     if(false,?ys_5,?zs_5) -> ?zs_5,
     nil -> inc(nil),
     inc(cons(?x_6,?xs_6)) -> cons(s(?x_6),inc(?xs_6)) ]
unknown innermost-termination for terms of non-linear types
unknown Strongly Quasi-Linear & Hierarchically Decreasing
check Non-Confluence...
obtain 17 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
check by Ordering(rpo), check by Tree-Automata Approximation   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
check by Interpretation(mod2)   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
check by Descendants-Approximation, check by Ordering(poly)   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ null(nil) -> true,
     null(cons(?x:Nat,?xs:List)) -> false,
     hd(nil) -> 0,
     hd(cons(?x:Nat,?xs:List)) -> ?x:Nat,
     tl(nil) -> nil,
     tl(cons(?x:Nat,?xs:List)) -> ?xs:List,
     inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     if(true,?ys:List,?zs:List) -> ?ys:List,
     if(false,?ys:List,?zs:List) -> ?zs:List,
     nil -> inc(nil),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (failure)
unknown Non-Confluence
unknown Huet (modulo AC)
check by Reduction-Preserving Completion...
failure(empty P)
unknown Reduction-Preserving Completion
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x,?xs)) -> ?x,
     tl(nil) -> nil,
     tl(cons(?x,?xs)) -> ?xs,
     inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     if(true,?ys,?zs) -> ?ys,
     if(false,?ys,?zs) -> ?zs,
     nil -> inc(nil),
     inc(cons(?x,?xs)) -> cons(s(?x),inc(?xs)) ]
Sort Assignment:
 0 : =>15
 s : 15=>15
 hd : 35=>15
 if : 19*35*35=>35
 tl : 35=>35
 inc : 35=>35
 nil : =>35
 cons : 15*35=>35
 null : 35=>19
 true : =>19
 false : =>19
maximal types: {15,19,35}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x,?xs)) -> ?x,
     tl(nil) -> nil,
     tl(cons(?x,?xs)) -> ?xs,
     inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     if(true,?ys,?zs) -> ?ys,
     if(false,?ys,?zs) -> ?zs,
     nil -> inc(nil),
     inc(cons(?x,?xs)) -> cons(s(?x),inc(?xs)) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ null(nil) -> true,
     null(cons(?x,?xs)) -> false,
     hd(nil) -> 0,
     hd(cons(?x,?xs)) -> ?x,
     tl(nil) -> nil,
     tl(cons(?x,?xs)) -> ?xs,
     inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     if(true,?ys,?zs) -> ?ys,
     if(false,?ys,?zs) -> ?zs,
     nil -> inc(nil),
     inc(cons(?x,?xs)) -> cons(s(?x),inc(?xs)) ]
Outside Critical Pair: <cons(s(?x_6),inc(?xs_6)), if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6)))))> by Rules <10, 6>
develop reducts from lhs term...
<{6}, cons(s(?x_6),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6)))))>
<{}, cons(s(?x_6),inc(?xs_6))>
develop reducts from rhs term...
<{1,3,5,6,9}, if(false,inc(nil),cons(s(?x_6),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{1,3,6,9}, if(false,inc(nil),cons(s(?x_6),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{1,3,5,9}, if(false,inc(nil),cons(s(?x_6),inc(?xs_6)))>
<{1,3,9}, if(false,inc(nil),cons(s(?x_6),inc(tl(cons(?x_6,?xs_6)))))>
<{1,5,6,9}, if(false,inc(nil),cons(s(hd(cons(?x_6,?xs_6))),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{1,6,9}, if(false,inc(nil),cons(s(hd(cons(?x_6,?xs_6))),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{1,5,9}, if(false,inc(nil),cons(s(hd(cons(?x_6,?xs_6))),inc(?xs_6)))>
<{1,9}, if(false,inc(nil),cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6)))))>
<{1,3,5,6}, if(false,nil,cons(s(?x_6),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{1,3,6}, if(false,nil,cons(s(?x_6),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{1,3,5}, if(false,nil,cons(s(?x_6),inc(?xs_6)))>
<{1,3}, if(false,nil,cons(s(?x_6),inc(tl(cons(?x_6,?xs_6)))))>
<{1,5,6}, if(false,nil,cons(s(hd(cons(?x_6,?xs_6))),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{1,6}, if(false,nil,cons(s(hd(cons(?x_6,?xs_6))),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{1,5}, if(false,nil,cons(s(hd(cons(?x_6,?xs_6))),inc(?xs_6)))>
<{1}, if(false,nil,cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6)))))>
<{3,5,6,9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(?x_6),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{3,6,9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(?x_6),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{3,5,9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(?x_6),inc(?xs_6)))>
<{3,9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(?x_6),inc(tl(cons(?x_6,?xs_6)))))>
<{5,6,9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(hd(cons(?x_6,?xs_6))),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{6,9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(hd(cons(?x_6,?xs_6))),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{5,9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(hd(cons(?x_6,?xs_6))),inc(?xs_6)))>
<{9}, if(null(cons(?x_6,?xs_6)),inc(nil),cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6)))))>
<{3,5,6}, if(null(cons(?x_6,?xs_6)),nil,cons(s(?x_6),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{3,6}, if(null(cons(?x_6,?xs_6)),nil,cons(s(?x_6),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{3,5}, if(null(cons(?x_6,?xs_6)),nil,cons(s(?x_6),inc(?xs_6)))>
<{3}, if(null(cons(?x_6,?xs_6)),nil,cons(s(?x_6),inc(tl(cons(?x_6,?xs_6)))))>
<{5,6}, if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),if(null(?xs_6),nil,cons(s(hd(?xs_6)),inc(tl(?xs_6))))))>
<{6}, if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),if(null(tl(cons(?x_6,?xs_6))),nil,cons(s(hd(tl(cons(?x_6,?xs_6)))),inc(tl(tl(cons(?x_6,?xs_6))))))))>
<{5}, if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),inc(?xs_6)))>
<{}, if(null(cons(?x_6,?xs_6)),nil,cons(s(hd(cons(?x_6,?xs_6))),inc(tl(cons(?x_6,?xs_6)))))>
Inside Critical Pair: <null(inc(nil)), true> by Rules <9, 0>
develop reducts from lhs term...
<{6,9}, null(if(null(inc(nil)),nil,cons(s(hd(inc(nil))),inc(tl(inc(nil))))))>
<{6}, null(if(null(nil),nil,cons(s(hd(nil)),inc(tl(nil)))))>
<{9}, null(inc(inc(nil)))>
<{}, null(inc(nil))>
develop reducts from rhs term...
<{}, true>
Inside Critical Pair: <hd(inc(nil)), 0> by Rules <9, 2>
develop reducts from lhs term...
<{6,9}, hd(if(null(inc(nil)),nil,cons(s(hd(inc(nil))),inc(tl(inc(nil))))))>
<{6}, hd(if(null(nil),nil,cons(s(hd(nil)),inc(tl(nil)))))>
<{9}, hd(inc(inc(nil)))>
<{}, hd(inc(nil))>
develop reducts from rhs term...
<{}, 0>
Inside Critical Pair: <tl(inc(nil)), nil> by Rules <9, 4>
develop reducts from lhs term...
<{6,9}, tl(if(null(inc(nil)),nil,cons(s(hd(inc(nil))),inc(tl(inc(nil))))))>
<{6}, tl(if(null(nil),nil,cons(s(hd(nil)),inc(tl(nil)))))>
<{9}, tl(inc(inc(nil)))>
<{}, tl(inc(nil))>
develop reducts from rhs term...
<{9}, inc(nil)>
<{}, nil>
Try A Minimal Decomposition {6,10}{4,2,0,9}{1}{3}{5}{7}{8}
{6,10}
(cm)Rewrite Rules:
   [ inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     inc(cons(?x,?xs)) -> cons(s(?x),inc(?xs)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ if(null(cons(?x_1,?xs_1)),nil,cons(s(hd(cons(?x_1,?xs_1))),inc(tl(cons(?x_1,?xs_1))))) = cons(s(?x_1),inc(?xs_1)) ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth & Bendix
Left-Linear, not Right-Linear
unknown Development Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ cons(s(?x_1),inc(?xs_1)) = if(null(cons(?x_1,?xs_1)),nil,cons(s(hd(cons(?x_1,?xs_1))),inc(tl(cons(?x_1,?xs_1))))),
     if(null(cons(?x,?xs)),nil,cons(s(hd(cons(?x,?xs))),inc(tl(cons(?x,?xs))))) = cons(s(?x),inc(?xs)) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <cons(s(?x_1),inc(?xs_1)), if(null(cons(?x_1,?xs_1)),nil,cons(s(hd(cons(?x_1,?xs_1))),inc(tl(cons(?x_1,?xs_1)))))> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
   [ inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     inc(cons(?x_1,?xs_1)) -> cons(s(?x_1),inc(?xs_1)) ]
Sort Assignment:
 s : 4=>4
 hd : 22=>4
 if : 8*9*22=>22
 tl : 22=>22
 inc : 22=>22
 nil : =>9
 cons : 4*22=>22
 null : 22=>8
non-linear variables: {?xs}
non-linear types: {22}
types leq non-linear types: {22}
rules applicable to terms of non-linear types:
   [ inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     inc(cons(?x_1,?xs_1)) -> cons(s(?x_1),inc(?xs_1)) ]
Rnl:
0: {0,1}
1: {}
unknown innermost-termination for terms of non-linear types
unknown Quasi-Linear & Linearized-Decreasing
   [ inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     inc(cons(?x_1,?xs_1)) -> cons(s(?x_1),inc(?xs_1)) ]
Sort Assignment:
 s : 4=>4
 hd : 22=>4
 if : 8*9*22=>22
 tl : 22=>22
 inc : 22=>22
 nil : =>9
 cons : 4*22=>22
 null : 22=>8
non-linear variables: {?xs}
non-linear types: {22}
types leq non-linear types: {22}
rules applicable to terms of non-linear types:
   [ inc(?xs) -> if(null(?xs),nil,cons(s(hd(?xs)),inc(tl(?xs)))),
     inc(cons(?x_1,?xs_1)) -> cons(s(?x_1),inc(?xs_1)) ]
unknown innermost-termination for terms of non-linear types
unknown Strongly Quasi-Linear & Hierarchically Decreasing
check Non-Confluence...
obtain 6 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
   [ inc(?xs:List) -> if(null(?xs:List),nil,cons(s(hd(?xs:List)),inc(tl(?xs:List)))),
     inc(cons(?x:Nat,?xs:List)) -> cons(s(?x:Nat),inc(?xs:List)) ]
 (success)
Witness for Non-Confluence: <if(null(cons(c_1,c_2)),nil,cons(s(hd(cons(c_1,c_2))),inc(tl(cons(c_1,c_2))))) <- inc(cons(c_1,c_2)) -> cons(s(c_1),inc(c_2))>
Direct Methods: not CR
{4,2,0,9}
(cm)Rewrite Rules:
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
Apply Direct Methods...
Inner CPs:
   [ tl(inc(nil)) = nil,
     hd(inc(nil)) = 0,
     null(inc(nil)) = true ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
inner CP cond (upside-parallel)
innter CP Cond (outside)
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ tl(inc(nil)) = nil,
     hd(inc(nil)) = 0,
     null(inc(nil)) = true,
     nil = tl(inc(nil)),
     0 = hd(inc(nil)),
     true = null(inc(nil)) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <tl(inc(nil)), nil> by Rules <3, 0> preceded by [(tl,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 95 candidates for checking non-joinability
check by TCAP-Approximation   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
   [ tl(nil) -> nil,
     hd(nil) -> 0,
     null(nil) -> true,
     nil -> inc(nil) ]
 (success)
Witness for Non-Confluence: <hd(inc(nil)) <- hd(tl(nil)) -> 0>
Direct Methods: not CR
{1}
(cm)Rewrite Rules:
   [ null(cons(?x,?xs)) -> false ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
{3}
(cm)Rewrite Rules:
   [ hd(cons(?x,?xs)) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
{5}
(cm)Rewrite Rules:
   [ tl(cons(?x,?xs)) -> ?xs ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
{7}
(cm)Rewrite Rules:
   [ if(true,?ys,?zs) -> ?ys ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
{8}
(cm)Rewrite Rules:
   [ if(false,?ys,?zs) -> ?zs ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
Commutative Decomposition failed: Can't judge
No further decomposition possible


Final result: Can't judge
new/inc2.trs: Failure(unknown)
(11030 msec.)