MAYBE
(ignored inputs)COMMENT doi:10.4230/LIPIcs.FSCD.2016.33 [36] Example 25 submitted by: Takahito Aoto and Yoshihito Toyama
Rewrite Rules:
   [ +(0,?x) -> ?x,
     +(?x,0) -> ?x,
     +(1,-(1)) -> 0,
     +(-(1),1) -> 0,
     -(0) -> 0,
     -(-(?x)) -> ?x,
     -(+(?x,?y)) -> +(-(?x),-(?y)),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [ -(0) = 0,
     -(+(-(?x_3),-(?y_3))) = +(?x_3,?y_3),
     -(?x) = +(-(0),-(?x)),
     -(?x_1) = +(-(?x_1),-(0)),
     -(0) = +(-(1),-(-(1))),
     -(0) = +(-(-(1)),-(1)),
     -(+(?x_4,+(?y_4,?z_4))) = +(-(+(?x_4,?y_4)),-(?z_4)),
     -(+(?y_5,?x_5)) = +(-(?x_5),-(?y_5)),
     +(?x,?z_4) = +(0,+(?x,?z_4)),
     +(?x_1,?z_4) = +(?x_1,+(0,?z_4)),
     +(0,?z_4) = +(1,+(-(1),?z_4)),
     +(0,?z_4) = +(-(1),+(1,?z_4)),
     +(+(?y_5,?x_5),?z_4) = +(?x_5,+(?y_5,?z_4)),
     -(?x) = -(?x),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)) ]
Outer CPs:
   [ 0 = 0,
     ?x = +(?x,0),
     +(?x_4,?y_4) = +(?x_4,+(?y_4,0)),
     ?x_1 = +(0,?x_1),
     0 = +(-(1),1),
     0 = +(1,-(1)),
     +(?x_4,+(?y_4,?z_4)) = +(?z_4,+(?x_4,?y_4)) ]
Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

Combined result: Can't judge
183.trs: Failure(unknown CR)
(2 msec.)