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)),
     *(?x,0) -> 0,
     *(?x,s(?y)) -> +(*(?x,?y),?x),
     *(0,?y) -> 0,
     *(s(?x),?y) -> +(*(?x,?y),?y),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     *(*(?x,?y),?z) -> *(?x,*(?y,?z)),
     *(?x,?y) -> *(?y,?x),
     *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)),
     *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)) ]
Apply Direct Methods...
Inner CPs:
   [ +(?x,?z_8) = +(?x,+(0,?z_8)),
     +(s(+(?x_1,?y_1)),?z_8) = +(?x_1,+(s(?y_1),?z_8)),
     +(?y_2,?z_8) = +(0,+(?y_2,?z_8)),
     +(s(+(?x_3,?y_3)),?z_8) = +(s(?x_3),+(?y_3,?z_8)),
     +(+(?y_9,?x_9),?z_8) = +(?x_9,+(?y_9,?z_8)),
     *(0,?z_10) = *(?x_4,*(0,?z_10)),
     *(+(*(?x_5,?y_5),?x_5),?z_10) = *(?x_5,*(s(?y_5),?z_10)),
     *(0,?z_10) = *(0,*(?y_6,?z_10)),
     *(+(*(?x_7,?y_7),?y_7),?z_10) = *(s(?x_7),*(?y_7,?z_10)),
     *(*(?y_11,?x_11),?z_10) = *(?x_11,*(?y_11,?z_10)),
     *(+(*(?x_12,?y_12),*(?x_12,?z_12)),?z_10) = *(?x_12,*(+(?y_12,?z_12),?z_10)),
     *(+(*(?x_13,?z_13),*(?y_13,?z_13)),?z_10) = *(+(?x_13,?y_13),*(?z_13,?z_10)),
     *(?x_12,?x) = +(*(?x_12,?x),*(?x_12,0)),
     *(?x_12,s(+(?x_1,?y_1))) = +(*(?x_12,?x_1),*(?x_12,s(?y_1))),
     *(?x_12,?y_2) = +(*(?x_12,0),*(?x_12,?y_2)),
     *(?x_12,s(+(?x_3,?y_3))) = +(*(?x_12,s(?x_3)),*(?x_12,?y_3)),
     *(?x_12,+(?x_8,+(?y_8,?z_8))) = +(*(?x_12,+(?x_8,?y_8)),*(?x_12,?z_8)),
     *(?x_12,+(?y_9,?x_9)) = +(*(?x_12,?x_9),*(?x_12,?y_9)),
     *(?x,?z_13) = +(*(?x,?z_13),*(0,?z_13)),
     *(s(+(?x_1,?y_1)),?z_13) = +(*(?x_1,?z_13),*(s(?y_1),?z_13)),
     *(?y_2,?z_13) = +(*(0,?z_13),*(?y_2,?z_13)),
     *(s(+(?x_3,?y_3)),?z_13) = +(*(s(?x_3),?z_13),*(?y_3,?z_13)),
     *(+(?x_8,+(?y_8,?z_8)),?z_13) = +(*(+(?x_8,?y_8),?z_13),*(?z_8,?z_13)),
     *(+(?y_9,?x_9),?z_13) = +(*(?x_9,?z_13),*(?y_9,?z_13)),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)),
     *(*(?x,*(?y,?z)),?z_1) = *(*(?x,?y),*(?z,?z_1)) ]
Outer CPs:
   [ 0 = 0,
     s(?x_3) = s(+(?x_3,0)),
     +(?x_8,?y_8) = +(?x_8,+(?y_8,0)),
     ?x = +(0,?x),
     s(+(0,?y_1)) = s(?y_1),
     s(+(s(?x_3),?y_1)) = s(+(?x_3,s(?y_1))),
     s(+(+(?x_8,?y_8),?y_1)) = +(?x_8,+(?y_8,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)),
     0 = 0,
     0 = +(*(?x_7,0),0),
     0 = *(?x_10,*(?y_10,0)),
     0 = *(0,?x_4),
     0 = +(*(?x_13,0),*(?y_13,0)),
     +(*(0,?y_5),0) = 0,
     +(*(s(?x_7),?y_5),s(?x_7)) = +(*(?x_7,s(?y_5)),s(?y_5)),
     +(*(*(?x_10,?y_10),?y_5),*(?x_10,?y_10)) = *(?x_10,*(?y_10,s(?y_5))),
     +(*(?x_5,?y_5),?x_5) = *(s(?y_5),?x_5),
     +(*(+(?x_13,?y_13),?y_5),+(?x_13,?y_13)) = +(*(?x_13,s(?y_5)),*(?y_13,s(?y_5))),
     0 = *(?y_6,0),
     0 = +(*(0,?y_12),*(0,?z_12)),
     +(*(?x_7,?y_7),?y_7) = *(?y_7,s(?x_7)),
     +(*(?x_7,+(?y_12,?z_12)),+(?y_12,?z_12)) = +(*(s(?x_7),?y_12),*(s(?x_7),?z_12)),
     +(?x_8,+(?y_8,?z_8)) = +(?z_8,+(?x_8,?y_8)),
     *(?x_10,*(?y_10,?z_10)) = *(?z_10,*(?x_10,?y_10)),
     *(?x_10,*(?y_10,+(?y_12,?z_12))) = +(*(*(?x_10,?y_10),?y_12),*(*(?x_10,?y_10),?z_12)),
     *(+(?y_12,?z_12),?x_11) = +(*(?x_11,?y_12),*(?x_11,?z_12)),
     *(?y_11,+(?x_13,?y_13)) = +(*(?x_13,?y_11),*(?y_13,?y_11)),
     +(*(+(?x_13,?y_13),?y_12),*(+(?x_13,?y_13),?z_12)) = +(*(?x_13,+(?y_12,?z_12)),*(?y_13,+(?y_12,?z_12))) ]
Left-Linear, not Right-Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

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