MAYBE
(ignored inputs)COMMENT doi:10.2168/LMCS-8 ( 1:31 ) 2012 [35] Example 3.36 ( R_7 )
Rewrite Rules:
   [ +(?x,0) -> ?x,
     +(?x,s(?y)) -> s(+(?x,?y)),
     +(0,?y) -> ?y,
     +(s(?x),?y) -> s(+(?x,?y)),
     dbl(?x) -> +(?x,?x),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     s(?x) -> s(s(?x)),
     s(s(?x)) -> s(?x) ]
Apply Direct Methods...
Inner CPs:
   [ +(?x_1,s(s(?x_7))) = s(+(?x_1,?x_7)),
     +(?x_1,s(?x_8)) = s(+(?x_1,s(?x_8))),
     +(s(s(?x_7)),?y_3) = s(+(?x_7,?y_3)),
     +(s(?x_8),?y_3) = s(+(s(?x_8),?y_3)),
     +(?x,?z_5) = +(?x,+(0,?z_5)),
     +(s(+(?x_1,?y_1)),?z_5) = +(?x_1,+(s(?y_1),?z_5)),
     +(?y_2,?z_5) = +(0,+(?y_2,?z_5)),
     +(s(+(?x_3,?y_3)),?z_5) = +(s(?x_3),+(?y_3,?z_5)),
     +(+(?y_6,?x_6),?z_5) = +(?x_6,+(?y_6,?z_5)),
     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_5,?y_5) = +(?x_5,+(?y_5,0)),
     ?x = +(0,?x),
     s(+(0,?y_1)) = s(?y_1),
     s(+(s(?x_3),?y_1)) = s(+(?x_3,s(?y_1))),
     s(+(+(?x_5,?y_5),?y_1)) = +(?x_5,+(?y_5,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_5,+(?y_5,?z_5)) = +(?z_5,+(?x_5,?y_5)),
     s(s(s(?x_8))) = s(?x_8) ]
Left-Linear, not Right-Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

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