MAYBE
(ignored inputs)COMMENT full experiments for [35] submitted by: Takahito Aoto and Yoshihito Toyama
Rewrite Rules:
   [ +(?x,0) -> ?x,
     +(?x,s(?y)) -> s(+(?x,?y)),
     +(0,?y) -> ?y,
     +(s(?x),?y) -> s(+(?x,?y)),
     inc(?x) -> s(?x),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     inc(+(?x,?y)) -> +(inc(?x),?y) ]
Apply Direct Methods...
Inner CPs:
   [ +(?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)),
     inc(?x) = +(inc(?x),0),
     inc(s(+(?x_1,?y_1))) = +(inc(?x_1),s(?y_1)),
     inc(?y_2) = +(inc(0),?y_2),
     inc(s(+(?x_3,?y_3))) = +(inc(s(?x_3)),?y_3),
     inc(+(?x_5,+(?y_5,?z_5))) = +(inc(+(?x_5,?y_5)),?z_5),
     inc(+(?y_6,?x_6)) = +(inc(?x_6),?y_6),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)) ]
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)),
     s(+(?x_7,?y_7)) = +(inc(?x_7),?y_7),
     +(?x_5,+(?y_5,?z_5)) = +(?z_5,+(?x_5,?y_5)) ]
Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

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