YES
(ignored inputs)COMMENT from the collection of \cite{AT2012}
Rewrite Rules:
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [ +(+(?y_1,?x_1),?z) = +(?x_1,+(?y_1,?z)),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)) ]
Outer CPs:
   [ +(?x,+(?y,?z)) = +(?z,+(?x,?y)) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly 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:
   [ +(?z,+(?x_1,+(?y_1,?y))) = +(+(?x_1,?y_1),+(?y,?z)),
     +(?z,+(?y,?x)) = +(?x,+(?y,?z)),
     +(?z,+(?x,?y)) = +(?x,+(?y,?z)),
     +(+(?x_1,+(?y_1,?y)),?z) = +(+(?x_1,?y_1),+(?y,?z)),
     +(+(?y,?x),?z) = +(?x,+(?y,?z)),
     +(+(?x_2,+(?y_2,?y)),+(?z,?z_1)) = +(+(+(?x_2,?y_2),+(?y,?z)),?z_1),
     +(+(?y,?x),+(?z,?z_1)) = +(+(?x,+(?y,?z)),?z_1),
     +(+(?x,?y),+(?z,?z_1)) = +(+(?x,+(?y,?z)),?z_1),
     +(?x_1,+(?y_1,?y)) = +(?y,+(?x_1,?y_1)),
     +(?x,+(?y,?z_2)) = +(+(?y,?x),?z_2) ]
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 <+(+(?y_1,?x_1),?z), +(?x_1,+(?y_1,?z))> by Rules <1, 0> preceded by [(+,1)]
 joinable by a reduction of rules <[([(+,1)],1),([],0)], []>
 joinable by a reduction of rules <[([],0),([(+,2)],1)], [([],1),([],0)]>
Critical Pair <+(+(?x,+(?y,?z)),?z_1), +(+(?x,?y),+(?z,?z_1))> by Rules <0, 0> preceded by [(+,1)]
 joinable by a reduction of rules <[([],0),([(+,2)],0)], [([],0)]>
Critical Pair <+(?y_1,+(?x,?y)), +(?x,+(?y,?y_1))> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[([],1),([],0)], []>
unknown Diagram Decreasing
check Non-Confluence...
obtain 12 rules by 3 steps unfolding
strenghten +(?x_3,?y_3) and +(?y_3,?x_3)
strenghten +(?x,+(?y,?x_4)) and +(?x_4,+(?x,?y))
strenghten +(?x,+(?y,?x_5)) and +(+(?x,?y),?x_5)
strenghten +(?x_1,+(?x_10,?y_1)) and +(?x_10,+(?y_1,?x_1))
strenghten +(?x_1,+(?y_1,?x_12)) and +(?x_12,+(?y_1,?x_1))
strenghten +(?x_1,+(?y_1,?z)) and +(+(?y_1,?x_1),?z)
strenghten +(?x_2,+(?x_10,?y_2)) and +(?x_10,+(?x_2,?y_2))
strenghten +(?x_6,+(?x_1,?y_1)) and +(?x_6,+(?y_1,?x_1))
strenghten +(+(?x_7,?y_7),?x_6) and +(?x_6,+(?x_7,?y_7))
strenghten +(+(?x_9,?y_9),?x_8) and +(?x_8,+(?y_9,?x_9))
strenghten +(+(?x_11,?y_11),?x_10) and +(?x_11,+(?x_10,?y_11))
strenghten +(+(?x_13,?y_13),?x_12) and +(?x_13,+(?y_13,?x_12))
strenghten +(+(?x_15,?y_15),?x_14) and +(?y_15,+(?x_14,?x_15))
strenghten +(+(?x_17,?y_17),?x_16) and +(?y_17,+(?x_17,?x_16))
strenghten +(?x,+(?x_2,+(?x_1,?y_1))) and +(?x_2,+(?x_1,+(?x,?y_1)))
strenghten +(?x,+(?y,+(?x_7,?y_7))) and +(+(?x,?y),+(?x_7,?y_7))
strenghten +(?x,+(?y,+(?x_9,?y_9))) and +(+(?x,?y),+(?y_9,?x_9))
strenghten +(?x,+(?y,+(?x_11,?y_11))) and +(?x_11,+(+(?x,?y),?y_11))
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Root-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
unknown Non-Confluence
Check relative termination:
   [ ]
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
relatively terminating
Huet (modulo AC)
Direct Methods: CR

Final result: CR
211.trs: Success(CR)
(3487 msec.)