NO
Rewrite Rules:
   [ sum(leaf(?x)) -> ?x,
     sum(node(?x,?yt,?zt)) -> +(?x,+(sum(?yt),sum(?zt))),
     +(?x,0) -> ?x,
     +(?x,s(?y)) -> s(+(?x,?y)),
     node(?x,?yt,?zt) -> node(?x,?zt,?yt) ]
Apply Direct Methods...
Inner CPs:
   [ sum(node(?x_4,?zt_4,?yt_4)) = +(?x_4,+(sum(?yt_4),sum(?zt_4))) ]
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:
   [ sum(node(?x,?zt,?yt)) = +(?x,+(sum(?yt),sum(?zt))),
     +(?x,+(sum(?yt),sum(?zt))) = sum(node(?x,?zt,?yt)) ]
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 <sum(node(?x_4,?zt_4,?yt_4)), +(?x_4,+(sum(?yt_4),sum(?zt_4)))> by Rules <4, 1> preceded by [(sum,1)]
 joinable by a reduction of rules <[([(sum,1)],4),([],1)], []>
unknown Diagram Decreasing
check Non-Confluence...
obtain 8 rules by 3 steps unfolding
obtain 5 candidates for checking non-joinability
check by TCAP-Approximation   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
   [ sum(leaf(?x:Nat)) -> ?x:Nat,
     sum(node(?x:Nat,?yt:Tree,?zt:Tree)) -> +(?x:Nat,+(sum(?yt:Tree),sum(?zt:Tree))),
     +(?x:Nat,0) -> ?x:Nat,
     +(?x:Nat,s(?y:Nat)) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Nat,?yt:Tree,?zt:Tree) -> node(?x:Nat,?zt:Tree,?yt:Tree) ]
 (success)
Witness for Non-Confluence: <+(c_1,+(sum(c_2),sum(c_3))) <- sum(node(c_1,c_2,c_3)) -> +(c_1,+(sum(c_3),sum(c_2)))>
Direct Methods: not CR

Final result: not CR
new/tree5.trs: Success(not CR)
(48 msec.)