YES
(ignored inputs)COMMENT from the collection of \cite{AT2012}
Rewrite Rules:
   [ -(+(?x,?y)) -> +(-(?x),-(?y)),
     -(-(?x)) -> ?x,
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [ -(+(?x_2,+(?y_2,?z_2))) = +(-(+(?x_2,?y_2)),-(?z_2)),
     -(+(?y_3,?x_3)) = +(-(?x_3),-(?y_3)),
     -(+(-(?x),-(?y))) = +(?x,?y),
     +(+(?y_3,?x_3),?z_2) = +(?x_3,+(?y_3,?z_2)),
     -(?x) = -(?x),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)) ]
Outer CPs:
   [ +(?x_2,+(?y_2,?z_2)) = +(?z_2,+(?x_2,?y_2)) ]
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:
   [ -(+(?x_3,+(?y_3,?y))) = +(-(+(?x_3,?y_3)),-(?y)),
     -(+(?y,?x)) = +(-(?x),-(?y)),
     +(?x_3,+(?y_3,?y)) = -(+(-(+(?x_3,?y_3)),-(?y))),
     +(?y,?x) = -(+(-(?x),-(?y))),
     +(?x,?y) = -(+(-(?x),-(?y))),
     -(?x_1) = -(?x_1),
     -(+(-(?x_2),-(?y_2))) = +(?x_2,?y_2),
     ?x_1 = -(-(?x_1)),
     +(-(?x_2),-(?y_2)) = -(+(?x_2,?y_2)),
     +(?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))),
     +(?x_3,+(?y_3,?y)) = +(?y,+(?x_3,?y_3)),
     +(-(?x),-(?y)) = -(+(?y,?x)),
     +(?x,+(?y,?z_4)) = +(+(?y,?x),?z_4) ]
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 <-(+(?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_3,?x_3)), +(-(?x_3),-(?y_3))> by Rules <3, 0> preceded by [(-,1)]
 joinable by a reduction of rules <[([],0)], [([],3)]>
Critical Pair <-(+(-(?x),-(?y))), +(?x,?y)> by Rules <0, 1> preceded by [(-,1)]
 joinable by a reduction of rules <[([],0),([(+,2)],1),([(+,1)],1)], []>
 joinable by a reduction of rules <[([],0),([(+,1)],1),([(+,2)],1)], []>
Critical Pair <+(+(?y_3,?x_3),?z_2), +(?x_3,+(?y_3,?z_2))> by Rules <3, 2> preceded by [(+,1)]
 joinable by a reduction of rules <[([(+,1)],3),([],2)], []>
 joinable by a reduction of rules <[([],2),([(+,2)],3)], [([],3),([],2)]>
Critical Pair <-(?x), -(?x)> by Rules <1, 1> preceded by [(-,1)]
 joinable by a reduction of rules <[], []>
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 <+(?y_3,+(?x_2,?y_2)), +(?x_2,+(?y_2,?y_3))> by Rules <3, 2> preceded by []
 joinable by a reduction of rules <[([],3),([],2)], []>
unknown Diagram Decreasing
check Non-Confluence...
obtain 14 rules by 3 steps unfolding
strenghten -(-(?x_1)) and ?x_1
strenghten +(?x_6,?y_6) and +(?y_6,?x_6)
strenghten -(-(-(?x_1))) and -(?x_1)
strenghten +(-(?x_3),-(?y_3)) and -(+(?y_3,?x_3))
strenghten +(-(?x_5),-(?y_5)) and -(+(?x_5,?y_5))
strenghten -(+(-(?x),-(?y))) and +(?x,?y)
strenghten +(?x_2,+(?y_2,?x_7)) and +(?x_7,+(?x_2,?y_2))
strenghten +(?x_2,+(?y_2,?x_8)) and +(+(?x_2,?y_2),?x_8)
strenghten +(?x_3,+(?y_3,?z_2)) and +(+(?y_3,?x_3),?z_2)
strenghten -(-(-(+(-(?x),-(?y))))) and +(?x,?y)
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)) -> ?x ]
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
Polynomial Interpretation:
  +:= (2)+(1)*x1+(1)*x2
  -:= (6)*x1
retract -(+(?x,?y)) -> +(-(?x),-(?y))
Polynomial Interpretation:
  +:= (1)*x1+(1)*x2
  -:= (1)+(2)*x1
relatively terminating
Huet (modulo AC)
Direct Methods: CR

Final result: CR
132.trs: Success(CR)
(6186 msec.)