MAYBE
(ignored inputs)COMMENT doi:10.2168/LMCS-8 ( 1:31 ) 2012 [35] Example 3.34 ( R_5 )
Rewrite Rules:
   [ +(?x,0) -> ?x,
     +(?x,s(?y)) -> s(+(?x,?y)),
     +(0,?y) -> ?y,
     +(s(?x),?y) -> s(+(?x,?y)),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     s(s(?x)) -> s(?x),
     s(?x) -> s(s(?x)) ]
Apply Direct Methods...
Inner CPs:
   [ +(?x_1,s(?x_6)) = s(+(?x_1,s(?x_6))),
     +(?x_1,s(s(?x_7))) = s(+(?x_1,?x_7)),
     +(s(?x_6),?y_3) = s(+(s(?x_6),?y_3)),
     +(s(s(?x_7)),?y_3) = s(+(?x_7,?y_3)),
     +(?x,?z_4) = +(?x,+(0,?z_4)),
     +(s(+(?x_1,?y_1)),?z_4) = +(?x_1,+(s(?y_1),?z_4)),
     +(?y_2,?z_4) = +(0,+(?y_2,?z_4)),
     +(s(+(?x_3,?y_3)),?z_4) = +(s(?x_3),+(?y_3,?z_4)),
     +(+(?y_5,?x_5),?z_4) = +(?x_5,+(?y_5,?z_4)),
     s(s(s(?x_7))) = s(?x_7),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)),
     s(s(?x)) = s(s(?x)) ]
Outer CPs:
   [ 0 = 0,
     s(?x_3) = s(+(?x_3,0)),
     +(?x_4,?y_4) = +(?x_4,+(?y_4,0)),
     ?x = +(0,?x),
     s(+(0,?y_1)) = s(?y_1),
     s(+(s(?x_3),?y_1)) = s(+(?x_3,s(?y_1))),
     s(+(+(?x_4,?y_4),?y_1)) = +(?x_4,+(?y_4,s(?y_1))),
     s(+(?x_1,?y_1)) = +(s(?y_1),?x_1),
     ?y_2 = +(?y_2,0),
     s(+(?x_3,?y_3)) = +(?y_3,s(?x_3)),
     +(?x_4,+(?y_4,?z_4)) = +(?z_4,+(?x_4,?y_4)),
     s(?x_6) = s(s(s(?x_6))) ]
Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

Combined result: Can't judge
124.trs: Failure(unknown CR)
(0 msec.)