YES
(ignored inputs)COMMENT from the collection of \cite{AT2012}
Rewrite Rules:
   [ -(+(?x,?y)) -> +(-(?x),-(?y)),
     +(?x,?y) -> +(?y,?x),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)) ]
Apply Direct Methods...
Inner CPs:
   [ -(+(?y_1,?x_1)) = +(-(?x_1),-(?y_1)),
     -(+(?x_2,+(?y_2,?z_2))) = +(-(+(?x_2,?y_2)),-(?z_2)),
     +(+(?y_1,?x_1),?z_2) = +(?x_1,+(?y_1,?z_2)),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)) ]
Outer CPs:
   [ +(?y_1,+(?x_2,?y_2)) = +(?x_2,+(?y_2,?y_1)) ]
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:
   [ -(+(?y,?x)) = +(-(?x),-(?y)),
     -(+(?x_3,+(?y_3,?y))) = +(-(+(?x_3,?y_3)),-(?y)),
     +(?x_2,+(?y_2,?y)) = +(?y,+(?x_2,?y_2)),
     +(-(?x),-(?y)) = -(+(?y,?x)),
     +(?x,+(?y,?z_3)) = +(+(?y,?x),?z_3),
     +(?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_1,+(?y_1,?y))),-(?z)) = -(+(+(?x_1,?y_1),+(?y,?z))),
     +(-(+(?y,?x)),-(?z)) = -(+(?x,+(?y,?z))),
     +(+(?x,?y),+(?z,?z_1)) = +(+(?x,+(?y,?z)),?z_1),
     +(-(+(?x,?y)),-(?z)) = -(+(?x,+(?y,?z))) ]
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)), +(-(?x_1),-(?y_1))> by Rules <1, 0> preceded by [(-,1)]
 joinable by a reduction of rules <[([],0)], [([],1)]>
Critical Pair <-(+(?x_2,+(?y_2,?z_2))), +(-(+(?x_2,?y_2)),-(?z_2))> by Rules <2, 0> preceded by [(-,1)]
 joinable by a reduction of rules <[([],0),([(+,2)],0)], [([(+,1)],0),([],2)]>
Critical Pair <+(+(?y_1,?x_1),?z_2), +(?x_1,+(?y_1,?z_2))> by Rules <1, 2> preceded by [(+,1)]
 joinable by a reduction of rules <[([(+,1)],1),([],2)], []>
 joinable by a reduction of rules <[([],2),([(+,2)],1)], [([],1),([],2)]>
Critical Pair <+(+(?x,+(?y,?z)),?z_1), +(+(?x,?y),+(?z,?z_1))> by Rules <2, 2> preceded by [(+,1)]
 joinable by a reduction of rules <[([],2),([(+,2)],2)], [([],2)]>
Critical Pair <+(?x_2,+(?y_2,?z_2)), +(?z_2,+(?x_2,?y_2))> by Rules <2, 1> preceded by []
 joinable by a reduction of rules <[], [([],1),([],2)]>
unknown Diagram Decreasing
check Non-Confluence...
obtain 13 rules by 3 steps unfolding
strenghten +(?x_4,?y_4) and +(?y_4,?x_4)
strenghten +(-(?x_1),-(?y_1)) and -(+(?y_1,?x_1))
strenghten +(-(?x_3),-(?y_3)) and -(+(?x_3,?y_3))
strenghten +(?x_1,+(?y_1,?z_2)) and +(+(?y_1,?x_1),?z_2)
strenghten +(?x_2,+(?y_2,?x_5)) and +(?x_5,+(?x_2,?y_2))
strenghten +(?x_2,+(?y_2,?x_6)) and +(+(?x_2,?y_2),?x_6)
strenghten +(?z_2,+(?x_2,?y_2)) and +(?x_2,+(?y_2,?z_2))
strenghten +(-(?x_8),-(?y_8)) and +(-(?y_8),-(?x_8))
strenghten +(-(?z_2),-(+(?x_2,?y_2))) and -(+(?x_2,+(?y_2,?z_2)))
strenghten +(-(+(?x_2,?y_2)),-(?z_2)) and -(+(?x_2,+(?y_2,?z_2)))
strenghten +(+(?x,?y),+(?z,?z_1)) and +(+(?x,+(?y,?z)),?z_1)
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)) -> +(-(?x),-(?y)) ]
   [ +(?x,?y) -> +(?y,?x),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)) ]
Polynomial Interpretation:
  +:= (2)+(1)*x1+(1)*x2
  -:= (2)+(4)*x1+(8)*x1*x1
relatively terminating
Huet (modulo AC)
Direct Methods: CR

Final result: CR
147.trs: Success(CR)
(9967 msec.)