NO
Rewrite Rules:
   [ size(leaf) -> s(0),
     size(node(?x,?y)) -> +(size(?x),size(?y)),
     +(0,?y) -> ?y,
     +(s(?x),?y) -> s(+(?x,?y)),
     node(?x,?y) -> node(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [ size(node(?y_3,?x_3)) = +(size(?x_3),size(?y_3)) ]
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:
   [ size(node(?y,?x)) = +(size(?x),size(?y)),
     +(size(?x),size(?y)) = size(node(?y,?x)) ]
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 <size(node(?y_3,?x_3)), +(size(?x_3),size(?y_3))> by Rules <4, 1> preceded by [(size,1)]
 joinable by a reduction of rules <[([(size,1)],4),([],1)], []>
unknown Diagram Decreasing
check Non-Confluence...
obtain 9 rules by 3 steps unfolding
obtain 9 candidates for checking non-joinability
check by TCAP-Approximation   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
   [ size(leaf) -> s(0),
     size(node(?x:Tree,?y:Tree)) -> +(size(?x:Tree),size(?y:Tree)),
     +(0,?y:Nat) -> ?y:Nat,
     +(s(?x:Nat),?y:Nat) -> s(+(?x:Nat,?y:Nat)),
     node(?x:Tree,?y:Tree) -> node(?y:Tree,?x:Tree) ]
 (success)
Witness for Non-Confluence: <+(size(c_1),size(c_2)) <- size(node(c_1,c_2)) -> +(size(c_2),size(c_1))>
Direct Methods: not CR

Final result: not CR
new/tree1.trs: Success(not CR)
(22 msec.)