MAYBE
Rewrite Rules:
   [ +(0,?x) -> ?x,
     +(-(?x),?x) -> 0,
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     -(0) -> 0,
     -(-(?x)) -> ?x,
     -(+(?x,?y)) -> +(-(?x),-(?y)),
     *(1,?x) -> ?x,
     *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)),
     *(*(?x,?y),?z) -> *(?x,*(?y,?z)),
     *(?x,?y) -> *(?y,?x),
     *(?x,0) -> 0,
     *(?x,-(?y)) -> -(*(?x,?y)) ]
Apply Direct Methods...
Inner CPs:
   [ +(0,0) = 0,
     +(?x_4,-(?x_4)) = 0,
     +(+(-(?x_5),-(?y_5)),+(?x_5,?y_5)) = 0,
     +(?x,?z_2) = +(0,+(?x,?z_2)),
     +(0,?z_2) = +(-(?x_1),+(?x_1,?z_2)),
     +(+(?y_3,?x_3),?z_2) = +(?x_3,+(?y_3,?z_2)),
     -(0) = 0,
     -(+(-(?x_5),-(?y_5))) = +(?x_5,?y_5),
     -(?x) = +(-(0),-(?x)),
     -(0) = +(-(-(?x_1)),-(?x_1)),
     -(+(?x_2,+(?y_2,?z_2))) = +(-(+(?x_2,?y_2)),-(?z_2)),
     -(+(?y_3,?x_3)) = +(-(?x_3),-(?y_3)),
     *(?x_7,?x) = +(*(?x_7,0),*(?x_7,?x)),
     *(?x_7,0) = +(*(?x_7,-(?x_1)),*(?x_7,?x_1)),
     *(?x_7,+(?x_2,+(?y_2,?z_2))) = +(*(?x_7,+(?x_2,?y_2)),*(?x_7,?z_2)),
     *(?x_7,+(?y_3,?x_3)) = +(*(?x_7,?x_3),*(?x_7,?y_3)),
     *(?x_6,?z_8) = *(1,*(?x_6,?z_8)),
     *(+(*(?x_7,?y_7),*(?x_7,?z_7)),?z_8) = *(?x_7,*(+(?y_7,?z_7),?z_8)),
     *(*(?y_9,?x_9),?z_8) = *(?x_9,*(?y_9,?z_8)),
     *(0,?z_8) = *(?x_10,*(0,?z_8)),
     *(-(*(?x_11,?y_11)),?z_8) = *(?x_11,*(-(?y_11),?z_8)),
     *(?x_11,0) = -(*(?x_11,0)),
     *(?x_11,?x_4) = -(*(?x_11,-(?x_4))),
     *(?x_11,+(-(?x_5),-(?y_5))) = -(*(?x_11,+(?x_5,?y_5))),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)),
     -(?x) = -(?x),
     *(*(?x,*(?y,?z)),?z_1) = *(*(?x,?y),*(?z,?z_1)) ]
Outer CPs:
   [ ?x = +(?x,0),
     0 = +(?x_1,-(?x_1)),
     +(?x_2,+(?y_2,?z_2)) = +(?z_2,+(?x_2,?y_2)),
     +(?y_7,?z_7) = +(*(1,?y_7),*(1,?z_7)),
     ?x_6 = *(?x_6,1),
     0 = 0,
     -(?y_11) = -(*(1,?y_11)),
     +(*(*(?x_8,?y_8),?y_7),*(*(?x_8,?y_8),?z_7)) = *(?x_8,*(?y_8,+(?y_7,?z_7))),
     +(*(?x_7,?y_7),*(?x_7,?z_7)) = *(+(?y_7,?z_7),?x_7),
     *(?x_8,*(?y_8,?z_8)) = *(?z_8,*(?x_8,?y_8)),
     *(?x_8,*(?y_8,0)) = 0,
     *(?x_8,*(?y_8,-(?y_11))) = -(*(*(?x_8,?y_8),?y_11)),
     *(0,?x_9) = 0,
     *(-(?y_11),?x_9) = -(*(?x_9,?y_11)) ]
unknown Terminating
not Left-Linear, not Right-Linear
unknown Gomi&Oyamaguchi&Ohta
check Non-Confluence...Unknown
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ +(0,?x) -> ?x,
     +(-(?x),?x) -> 0,
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     -(0) -> 0,
     -(-(?x)) -> ?x,
     -(+(?x,?y)) -> +(-(?x),-(?y)),
     *(1,?x) -> ?x,
     *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)),
     *(*(?x,?y),?z) -> *(?x,*(?y,?z)),
     *(?x,?y) -> *(?y,?x),
     *(?x,0) -> 0,
     *(?x,-(?y)) -> -(*(?x,?y)) ]
Sort Assignment:
 * : 33*33=>33
 + : 33*33=>33
 - : 33=>33
 0 : =>33
 1 : =>33
maximal types: {33}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ +(0,?x) -> ?x,
     +(-(?x),?x) -> 0,
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     -(0) -> 0,
     -(-(?x)) -> ?x,
     -(+(?x,?y)) -> +(-(?x),-(?y)),
     *(1,?x) -> ?x,
     *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)),
     *(*(?x,?y),?z) -> *(?x,*(?y,?z)),
     *(?x,?y) -> *(?y,?x),
     *(?x,0) -> 0,
     *(?x,-(?y)) -> -(*(?x,?y)) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ +(0,?x) -> ?x,
     +(-(?x),?x) -> 0,
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     -(0) -> 0,
     -(-(?x)) -> ?x,
     -(+(?x,?y)) -> +(-(?x),-(?y)),
     *(1,?x) -> ?x,
     *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)),
     *(*(?x,?y),?z) -> *(?x,*(?y,?z)),
     *(?x,?y) -> *(?y,?x),
     *(?x,0) -> 0,
     *(?x,-(?y)) -> -(*(?x,?y)) ]
Commutative Decomposition failed: Can't judge
No further decomposition possible


Final result: Can't judge
77.trs: MAYBE (272 msec.)