The relative rewrite relation R/S is considered where R is the following TRS
0(0(0(0(2(2(0(1(3(1(2(3(1(0(2(0(3(3(x1)))))))))))))))))) | → | 0(0(2(2(3(3(0(0(3(0(0(2(2(0(1(1(1(3(x1)))))))))))))))))) | (1) |
0(0(0(3(1(2(3(1(2(0(1(1(3(2(3(1(1(2(x1)))))))))))))))))) | → | 0(3(0(1(3(1(1(1(0(0(2(2(1(1(3(2(2(3(x1)))))))))))))))))) | (2) |
0(0(1(1(2(2(3(0(1(3(1(3(3(1(3(3(0(3(x1)))))))))))))))))) | → | 0(3(1(1(0(2(3(1(0(0(1(2(3(3(3(1(3(3(x1)))))))))))))))))) | (3) |
0(0(1(2(1(3(1(2(0(1(2(0(3(3(3(1(1(2(x1)))))))))))))))))) | → | 2(3(2(3(1(1(1(1(3(0(2(1(0(3(1(0(0(2(x1)))))))))))))))))) | (4) |
0(0(1(2(3(2(1(2(1(2(1(3(0(2(1(1(2(2(x1)))))))))))))))))) | → | 2(2(0(2(2(1(1(1(2(0(0(3(1(1(1(3(2(2(x1)))))))))))))))))) | (5) |
0(0(1(3(0(1(3(1(1(0(3(0(1(3(0(3(0(3(x1)))))))))))))))))) | → | 0(0(0(0(3(1(3(0(1(1(3(3(3(0(1(1(3(0(x1)))))))))))))))))) | (6) |
0(0(1(3(1(3(2(3(3(1(2(0(1(3(3(0(1(1(x1)))))))))))))))))) | → | 2(3(3(1(1(3(0(3(0(1(3(0(0(1(3(2(1(1(x1)))))))))))))))))) | (7) |
0(1(0(3(0(2(0(1(3(0(3(0(1(2(2(0(0(3(x1)))))))))))))))))) | → | 0(3(0(0(0(2(2(1(0(0(3(0(2(3(3(1(1(0(x1)))))))))))))))))) | (8) |
0(1(1(3(3(1(3(3(1(2(1(1(3(0(2(0(1(2(x1)))))))))))))))))) | → | 0(3(2(1(2(1(1(1(1(1(0(3(0(2(3(3(1(3(x1)))))))))))))))))) | (9) |
0(1(2(0(1(1(1(2(1(1(2(1(0(3(0(1(0(1(x1)))))))))))))))))) | → | 1(2(0(0(0(2(1(0(2(1(1(1(1(3(1(1(0(1(x1)))))))))))))))))) | (10) |
0(1(2(1(2(0(3(3(1(2(1(3(1(2(1(3(1(0(x1)))))))))))))))))) | → | 2(3(2(1(1(1(1(0(2(2(1(1(0(3(3(1(0(3(x1)))))))))))))))))) | (11) |
0(1(2(2(1(2(2(0(0(1(0(3(0(1(1(3(3(1(x1)))))))))))))))))) | → | 0(1(0(3(1(0(2(1(3(2(3(0(2(2(1(1(0(1(x1)))))))))))))))))) | (12) |
0(1(2(3(1(0(1(0(2(1(3(2(1(2(0(1(0(1(x1)))))))))))))))))) | → | 0(2(0(1(1(2(3(3(1(2(0(2(0(1(1(1(0(1(x1)))))))))))))))))) | (13) |
0(2(1(2(3(1(3(0(2(0(3(2(3(1(3(3(2(0(x1)))))))))))))))))) | → | 2(3(3(0(2(3(3(2(0(0(3(2(1(1(1(3(2(0(x1)))))))))))))))))) | (14) |
0(2(1(3(1(2(3(0(1(3(2(2(3(1(1(1(0(1(x1)))))))))))))))))) | → | 2(0(3(1(0(2(3(2(1(2(3(0(1(1(1(1(3(1(x1)))))))))))))))))) | (15) |
0(3(0(1(3(1(3(0(2(3(0(1(2(2(1(0(1(0(x1)))))))))))))))))) | → | 0(3(3(1(2(3(0(0(3(0(0(1(1(1(1(2(2(0(x1)))))))))))))))))) | (16) |
0(3(0(2(1(2(1(3(3(0(0(0(3(1(2(3(0(1(x1)))))))))))))))))) | → | 0(2(3(0(1(0(0(3(3(3(1(0(0(2(3(2(1(1(x1)))))))))))))))))) | (17) |
0(3(1(0(0(1(3(3(3(2(0(0(3(1(3(3(1(3(x1)))))))))))))))))) | → | 0(3(3(3(3(2(3(0(1(3(0(1(1(0(1(0(3(3(x1)))))))))))))))))) | (18) |
0(3(2(1(3(1(2(2(0(0(0(3(2(0(1(0(1(3(x1)))))))))))))))))) | → | 2(3(0(3(2(1(1(1(1(0(3(0(2(0(0(0(3(2(x1)))))))))))))))))) | (19) |
0(3(3(0(2(3(0(1(2(1(1(3(3(2(0(3(0(2(x1)))))))))))))))))) | → | 0(3(2(3(3(0(3(2(3(3(1(1(0(0(2(1(0(2(x1)))))))))))))))))) | (20) |
0(3(3(3(2(1(3(1(1(2(2(2(0(2(0(1(1(1(x1)))))))))))))))))) | → | 0(2(0(2(2(3(1(1(1(1(3(2(3(2(3(0(1(1(x1)))))))))))))))))) | (21) |
1(0(1(2(3(1(1(3(3(0(3(1(3(1(1(0(1(1(x1)))))))))))))))))) | → | 1(1(1(1(0(2(3(0(0(1(1(3(3(1(3(3(1(1(x1)))))))))))))))))) | (22) |
1(0(2(1(0(3(2(3(1(3(0(1(1(0(2(3(0(2(x1)))))))))))))))))) | → | 1(2(1(1(0(2(2(1(1(0(3(3(3(0(3(0(0(2(x1)))))))))))))))))) | (23) |
1(0(2(2(2(2(3(3(0(0(3(0(3(2(0(1(3(0(x1)))))))))))))))))) | → | 1(1(3(2(0(2(3(3(0(2(0(0(2(3(2(3(0(0(x1)))))))))))))))))) | (24) |
1(0(3(2(2(3(2(0(1(3(3(1(1(3(1(0(1(0(x1)))))))))))))))))) | → | 1(1(0(3(0(0(3(2(1(0(1(1(3(3(2(1(2(3(x1)))))))))))))))))) | (25) |
1(1(0(0(1(0(2(2(1(0(1(0(1(3(1(1(3(3(x1)))))))))))))))))) | → | 1(1(1(3(0(1(3(0(2(1(1(2(1(1(0(0(3(0(x1)))))))))))))))))) | (26) |
1(1(0(3(3(3(1(2(1(2(3(1(0(1(0(0(1(2(x1)))))))))))))))))) | → | 1(1(1(0(1(1(1(1(3(3(0(2(2(2(3(3(0(0(x1)))))))))))))))))) | (27) |
1(1(2(0(0(1(3(0(1(3(0(3(2(0(1(2(0(0(x1)))))))))))))))))) | → | 1(1(0(0(3(2(0(1(3(0(2(3(2(0(1(1(0(0(x1)))))))))))))))))) | (28) |
1(1(3(1(2(0(0(2(1(0(0(0(1(3(3(1(2(3(x1)))))))))))))))))) | → | 1(1(1(1(2(2(0(3(3(1(3(0(3(1(0(0(0(2(x1)))))))))))))))))) | (29) |
1(1(3(3(1(0(0(1(0(2(3(3(0(1(3(1(0(1(x1)))))))))))))))))) | → | 1(3(0(0(3(0(3(3(1(2(3(0(1(1(1(1(0(1(x1)))))))))))))))))) | (30) |
1(2(0(0(1(2(0(1(1(2(1(3(1(1(0(3(1(2(x1)))))))))))))))))) | → | 1(1(1(1(0(1(1(2(0(2(1(2(1(0(3(0(2(3(x1)))))))))))))))))) | (31) |
1(2(0(3(0(1(1(3(0(0(0(1(2(1(0(2(0(3(x1)))))))))))))))))) | → | 1(3(2(2(1(0(0(0(0(3(3(2(1(0(1(1(0(0(x1)))))))))))))))))) | (32) |
1(2(1(3(1(0(3(2(2(2(3(3(2(1(2(1(3(3(x1)))))))))))))))))) | → | 1(2(2(1(3(2(2(2(3(3(1(3(2(0(3(1(1(3(x1)))))))))))))))))) | (33) |
1(2(2(2(3(3(0(2(1(3(1(2(2(1(1(0(1(1(x1)))))))))))))))))) | → | 1(2(2(2(3(0(1(3(1(2(2(0(3(2(1(1(1(1(x1)))))))))))))))))) | (34) |
1(2(3(2(0(1(3(3(1(2(0(1(3(2(2(3(3(3(x1)))))))))))))))))) | → | 1(2(0(3(3(2(1(2(0(3(3(3(2(1(1(3(2(3(x1)))))))))))))))))) | (35) |
1(3(0(3(3(2(3(1(3(2(3(0(1(3(1(3(3(0(x1)))))))))))))))))) | → | 1(3(0(1(1(3(0(2(2(3(3(3(1(3(3(3(3(0(x1)))))))))))))))))) | (36) |
1(3(1(2(1(1(0(1(0(2(2(3(1(0(3(1(2(1(x1)))))))))))))))))) | → | 1(1(0(0(1(2(3(3(1(1(3(0(1(1(2(2(2(1(x1)))))))))))))))))) | (37) |
1(3(1(2(2(1(3(0(3(1(2(3(3(1(0(0(3(3(x1)))))))))))))))))) | → | 1(3(0(2(1(0(1(2(3(0(3(3(3(1(1(2(3(3(x1)))))))))))))))))) | (38) |
1(3(2(1(3(2(0(1(1(1(3(1(1(2(1(3(2(2(x1)))))))))))))))))) | → | 1(1(3(1(0(2(1(1(3(2(1(1(1(3(2(2(3(2(x1)))))))))))))))))) | (39) |
1(3(2(3(0(2(2(1(2(0(0(3(1(3(2(0(1(3(x1)))))))))))))))))) | → | 1(3(0(0(2(1(2(3(3(1(1(0(3(2(0(2(2(3(x1)))))))))))))))))) | (40) |
1(3(3(0(1(0(0(2(0(0(1(3(1(3(1(0(1(3(x1)))))))))))))))))) | → | 1(1(3(0(3(0(0(1(1(3(2(0(3(3(1(0(1(0(x1)))))))))))))))))) | (41) |
2(0(2(0(2(0(3(1(2(0(1(3(1(1(0(1(1(0(x1)))))))))))))))))) | → | 2(1(1(1(0(0(2(3(0(0(1(1(1(3(2(2(0(0(x1)))))))))))))))))) | (42) |
2(1(0(1(2(1(1(0(2(3(1(1(2(1(0(1(1(2(x1)))))))))))))))))) | → | 2(1(0(0(1(2(2(1(1(0(1(1(1(2(1(3(1(2(x1)))))))))))))))))) | (43) |
2(1(2(2(1(0(1(2(3(3(1(0(1(1(2(0(1(1(x1)))))))))))))))))) | → | 2(1(3(0(0(1(3(0(2(2(1(2(1(1(1(2(1(1(x1)))))))))))))))))) | (44) |
2(1(3(1(2(1(1(0(0(1(0(2(1(2(2(1(1(2(x1)))))))))))))))))) | → | 2(1(1(2(1(1(0(0(1(1(2(0(3(2(2(1(1(2(x1)))))))))))))))))) | (45) |
2(1(3(1(2(1(3(3(0(2(0(2(1(2(2(3(0(2(x1)))))))))))))))))) | → | 2(1(2(2(1(1(2(3(3(2(0(2(2(0(1(3(0(3(x1)))))))))))))))))) | (46) |
2(2(0(2(2(2(1(2(1(3(0(0(1(0(3(3(0(0(x1)))))))))))))))))) | → | 2(0(2(0(1(3(2(2(2(1(0(0(3(2(1(3(0(0(x1)))))))))))))))))) | (47) |
2(2(0(2(2(3(2(0(3(3(0(3(0(0(3(2(2(3(x1)))))))))))))))))) | → | 2(3(2(3(2(0(3(3(2(0(3(0(0(2(0(2(2(3(x1)))))))))))))))))) | (48) |
2(2(1(2(3(1(1(1(0(2(3(3(3(0(1(0(2(3(x1)))))))))))))))))) | → | 2(2(1(1(1(1(2(2(1(3(0(3(0(0(3(3(2(3(x1)))))))))))))))))) | (49) |
2(2(2(2(0(3(2(2(0(3(1(0(1(3(3(1(0(2(x1)))))))))))))))))) | → | 2(2(2(2(1(0(2(2(1(0(3(1(0(3(0(3(3(2(x1)))))))))))))))))) | (50) |
2(2(3(1(3(0(0(3(1(3(2(0(1(1(3(3(3(0(x1)))))))))))))))))) | → | 3(0(0(2(2(3(2(3(1(1(1(1(3(3(3(0(3(0(x1)))))))))))))))))) | (51) |
2(3(1(0(1(3(3(1(2(1(3(0(2(0(3(3(1(0(x1)))))))))))))))))) | → | 3(1(1(1(0(3(2(1(3(0(3(1(0(2(0(2(3(3(x1)))))))))))))))))) | (52) |
2(3(1(2(0(0(3(2(2(2(2(0(0(0(1(0(1(3(x1)))))))))))))))))) | → | 2(2(0(2(2(2(0(0(3(0(3(3(0(1(1(0(1(2(x1)))))))))))))))))) | (53) |
2(3(2(3(2(3(0(2(3(0(3(0(1(0(2(3(3(3(x1)))))))))))))))))) | → | 2(3(0(3(3(2(3(2(1(0(0(3(2(0(3(2(3(3(x1)))))))))))))))))) | (54) |
2(3(3(1(2(1(3(0(0(3(1(3(0(3(1(0(1(2(x1)))))))))))))))))) | → | 2(2(2(3(3(1(0(3(3(1(1(3(0(0(3(1(1(0(x1)))))))))))))))))) | (55) |
2(3(3(2(3(3(1(3(2(3(2(3(3(2(1(3(2(3(x1)))))))))))))))))) | → | 2(3(2(3(2(2(1(3(2(1(3(3(3(3(3(3(2(3(x1)))))))))))))))))) | (56) |
3(0(0(0(1(0(2(2(1(2(3(2(3(0(1(0(0(2(x1)))))))))))))))))) | → | 3(0(1(0(0(2(2(3(3(2(0(1(1(0(0(2(0(2(x1)))))))))))))))))) | (57) |
3(0(0(3(0(2(3(1(2(0(0(1(2(3(0(0(0(1(x1)))))))))))))))))) | → | 3(0(1(0(0(0(0(2(1(0(2(2(0(3(3(0(3(1(x1)))))))))))))))))) | (58) |
3(0(1(0(0(1(1(3(1(1(3(0(0(1(3(1(3(3(x1)))))))))))))))))) | → | 3(3(0(1(3(1(1(0(1(1(1(3(0(3(3(0(1(0(x1)))))))))))))))))) | (59) |
3(0(1(2(0(0(2(0(0(1(3(0(1(1(1(0(1(1(x1)))))))))))))))))) | → | 0(2(1(1(1(1(0(0(1(0(3(0(3(0(2(0(1(1(x1)))))))))))))))))) | (60) |
3(0(1(3(3(1(1(3(1(2(1(1(3(2(3(1(0(1(x1)))))))))))))))))) | → | 3(1(1(3(3(1(3(3(0(1(2(1(1(3(2(1(0(1(x1)))))))))))))))))) | (61) |
3(0(2(3(2(0(3(1(0(3(3(1(1(2(3(1(3(1(x1)))))))))))))))))) | → | 3(2(3(2(3(3(1(1(1(3(0(0(3(0(2(1(3(1(x1)))))))))))))))))) | (62) |
3(0(3(0(1(1(2(1(2(3(3(1(0(2(2(3(1(2(x1)))))))))))))))))) | → | 2(0(1(3(3(3(2(3(2(0(1(1(1(2(0(2(1(3(x1)))))))))))))))))) | (63) |
3(1(0(0(2(0(1(1(2(1(3(2(2(2(2(0(0(0(x1)))))))))))))))))) | → | 2(3(2(1(0(2(3(1(0(0(1(1(2(2(2(0(0(0(x1)))))))))))))))))) | (64) |
3(1(0(2(0(3(1(0(2(2(2(3(1(2(2(3(1(3(x1)))))))))))))))))) | → | 2(2(3(1(2(3(0(2(3(2(3(0(0(3(1(1(1(2(x1)))))))))))))))))) | (65) |
3(1(0(3(1(2(2(3(1(3(3(3(2(1(1(3(0(1(x1)))))))))))))))))) | → | 2(3(2(1(2(3(3(1(1(3(3(1(1(0(3(3(0(1(x1)))))))))))))))))) | (66) |
3(1(2(1(3(0(0(2(1(2(3(2(0(1(3(1(3(3(x1)))))))))))))))))) | → | 3(1(1(3(0(3(1(3(2(3(0(2(1(3(2(2(1(0(x1)))))))))))))))))) | (67) |
3(1(2(3(2(2(2(2(2(1(0(1(0(2(0(0(0(3(x1)))))))))))))))))) | → | 3(2(3(2(0(1(0(2(1(0(2(2(1(2(2(0(0(3(x1)))))))))))))))))) | (68) |
3(1(3(1(2(1(0(1(0(3(3(1(2(3(3(3(0(3(x1)))))))))))))))))) | → | 3(3(3(1(1(0(3(0(2(1(1(3(1(3(3(2(0(3(x1)))))))))))))))))) | (69) |
3(1(3(1(2(3(0(2(3(3(1(3(1(1(2(1(0(0(x1)))))))))))))))))) | → | 2(0(3(1(3(1(2(1(3(3(3(1(1(3(2(1(0(0(x1)))))))))))))))))) | (70) |
3(1(3(2(1(3(1(0(1(2(2(3(3(0(3(3(1(1(x1)))))))))))))))))) | → | 3(3(3(1(2(0(2(1(3(2(3(3(3(0(1(1(1(1(x1)))))))))))))))))) | (71) |
3(1(3(2(2(2(2(3(2(0(3(0(0(3(2(2(2(2(x1)))))))))))))))))) | → | 2(2(1(0(3(2(2(2(3(0(0(2(3(3(3(2(2(2(x1)))))))))))))))))) | (72) |
3(2(2(2(1(0(1(3(1(1(2(3(1(0(1(1(3(3(x1)))))))))))))))))) | → | 3(1(2(3(1(1(1(3(0(2(2(2(3(1(1(1(0(3(x1)))))))))))))))))) | (73) |
3(3(0(2(1(2(2(3(1(2(0(2(0(1(3(0(0(1(x1)))))))))))))))))) | → | 2(1(3(2(3(3(2(3(0(0(0(2(0(0(2(1(1(1(x1)))))))))))))))))) | (74) |
3(3(1(0(2(1(2(1(3(3(1(3(1(2(3(2(1(0(x1)))))))))))))))))) | → | 3(3(2(1(1(1(1(1(3(3(3(2(0(3(1(2(0(2(x1)))))))))))))))))) | (75) |
3(3(1(0(3(0(3(2(2(2(3(1(1(2(3(2(1(3(x1)))))))))))))))))) | → | 2(1(1(1(3(0(3(2(0(2(3(3(3(2(1(2(3(3(x1)))))))))))))))))) | (76) |
3(3(1(1(2(3(2(1(2(1(2(3(0(0(2(2(1(1(x1)))))))))))))))))) | → | 3(2(1(2(1(2(3(0(2(3(3(2(0(2(1(1(1(1(x1)))))))))))))))))) | (77) |
3(3(2(1(0(2(3(1(2(2(2(2(1(3(3(0(3(2(x1)))))))))))))))))) | → | 3(2(3(0(2(2(1(1(3(3(2(1(0(3(2(2(3(2(x1)))))))))))))))))) | (78) |
3(3(2(2(3(0(3(1(2(3(3(0(1(2(1(2(0(2(x1)))))))))))))))))) | → | 3(2(1(1(2(3(2(2(1(3(3(3(0(0(3(0(2(2(x1)))))))))))))))))) | (79) |
3(3(3(1(0(2(1(0(1(3(3(1(3(3(3(0(1(2(x1)))))))))))))))))) | → | 3(3(0(3(3(2(1(0(2(3(3(3(1(0(1(1(1(3(x1)))))))))))))))))) | (80) |
and S is the following TRS.
0(1(2(3(x1)))) | → | 0(1(2(3(x1)))) | (81) |
{0(☐), 2(☐), 1(☐), 3(☐)}
We obtain the transformed TRSThere are 137 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRSThere are 548 ruless (increase limit for explicit display).
[00(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 + 1 |
[13(x1)] | = | 1 · x1 + 5 |
[31(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 + 5 |
[23(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 5 |
[03(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 + 1 |
[11(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
There are 496 ruless (increase limit for explicit display).
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 + 1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
22(22(22(20(03(32(22(20(03(31(10(01(13(33(31(10(02(20(x1)))))))))))))))))) | → | 22(22(22(21(10(02(22(21(10(03(31(10(03(30(03(33(32(20(x1)))))))))))))))))) | (322) |
22(22(22(20(03(32(22(20(03(31(10(01(13(33(31(10(02(22(x1)))))))))))))))))) | → | 22(22(22(21(10(02(22(21(10(03(31(10(03(30(03(33(32(22(x1)))))))))))))))))) | (323) |
22(22(22(20(03(32(22(20(03(31(10(01(13(33(31(10(02(21(x1)))))))))))))))))) | → | 22(22(22(21(10(02(22(21(10(03(31(10(03(30(03(33(32(21(x1)))))))))))))))))) | (324) |
22(22(22(20(03(32(22(20(03(31(10(01(13(33(31(10(02(23(x1)))))))))))))))))) | → | 22(22(22(21(10(02(22(21(10(03(31(10(03(30(03(33(32(23(x1)))))))))))))))))) | (325) |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 + 1 |
[33(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
13(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(00(x1))))))))))))))))))) | → | 12(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(00(x1))))))))))))))))))) | (602) |
13(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(02(x1))))))))))))))))))) | → | 12(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(02(x1))))))))))))))))))) | (603) |
13(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(01(x1))))))))))))))))))) | → | 12(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(01(x1))))))))))))))))))) | (604) |
13(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(03(x1))))))))))))))))))) | → | 12(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(03(x1))))))))))))))))))) | (605) |
13(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(20(x1))))))))))))))))))) | → | 12(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(20(x1))))))))))))))))))) | (666) |
13(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(22(x1))))))))))))))))))) | → | 12(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(22(x1))))))))))))))))))) | (667) |
13(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(21(x1))))))))))))))))))) | → | 12(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(21(x1))))))))))))))))))) | (668) |
13(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(23(x1))))))))))))))))))) | → | 12(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(23(x1))))))))))))))))))) | (669) |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 2 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 + 2 |
[20(x1)] | = | 1 · x1 + 2 |
[00(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 + 1 |
[32(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
21(10(01(12(21(11(10(02(23(31(11(12(21(10(01(11(12(20(x1)))))))))))))))))) | → | 21(10(00(01(12(22(21(11(10(01(11(11(12(21(13(31(12(20(x1)))))))))))))))))) | (294) |
21(10(01(12(21(11(10(02(23(31(11(12(21(10(01(11(12(22(x1)))))))))))))))))) | → | 21(10(00(01(12(22(21(11(10(01(11(11(12(21(13(31(12(22(x1)))))))))))))))))) | (295) |
21(10(01(12(21(11(10(02(23(31(11(12(21(10(01(11(12(21(x1)))))))))))))))))) | → | 21(10(00(01(12(22(21(11(10(01(11(11(12(21(13(31(12(21(x1)))))))))))))))))) | (296) |
21(10(01(12(21(11(10(02(23(31(11(12(21(10(01(11(12(23(x1)))))))))))))))))) | → | 21(10(00(01(12(22(21(11(10(01(11(11(12(21(13(31(12(23(x1)))))))))))))))))) | (297) |
30(01(13(33(31(11(13(31(12(21(11(13(32(23(31(10(01(10(x1)))))))))))))))))) | → | 31(11(13(33(31(13(33(30(01(12(21(11(13(32(21(10(01(10(x1)))))))))))))))))) | (354) |
30(01(13(33(31(11(13(31(12(21(11(13(32(23(31(10(01(12(x1)))))))))))))))))) | → | 31(11(13(33(31(13(33(30(01(12(21(11(13(32(21(10(01(12(x1)))))))))))))))))) | (355) |
30(01(13(33(31(11(13(31(12(21(11(13(32(23(31(10(01(11(x1)))))))))))))))))) | → | 31(11(13(33(31(13(33(30(01(12(21(11(13(32(21(10(01(11(x1)))))))))))))))))) | (356) |
30(01(13(33(31(11(13(31(12(21(11(13(32(23(31(10(01(13(x1)))))))))))))))))) | → | 31(11(13(33(31(13(33(30(01(12(21(11(13(32(21(10(01(13(x1)))))))))))))))))) | (357) |
33(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(00(x1))))))))))))))))))) | → | 32(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(00(x1))))))))))))))))))) | (606) |
33(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(02(x1))))))))))))))))))) | → | 32(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(02(x1))))))))))))))))))) | (607) |
33(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(01(x1))))))))))))))))))) | → | 32(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(01(x1))))))))))))))))))) | (608) |
33(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(03(x1))))))))))))))))))) | → | 32(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(03(x1))))))))))))))))))) | (609) |
33(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(20(x1))))))))))))))))))) | → | 32(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(20(x1))))))))))))))))))) | (670) |
33(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(22(x1))))))))))))))))))) | → | 32(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(22(x1))))))))))))))))))) | (671) |
33(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(21(x1))))))))))))))))))) | → | 32(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(21(x1))))))))))))))))))) | (672) |
33(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(23(x1))))))))))))))))))) | → | 32(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(23(x1))))))))))))))))))) | (673) |
[23(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 + 1 |
[03(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
31(12(23(32(22(22(22(22(21(10(01(10(02(20(00(00(03(30(x1)))))))))))))))))) | → | 32(23(32(20(01(10(02(21(10(02(22(21(12(22(20(00(03(30(x1)))))))))))))))))) | (366) |
31(12(23(32(22(22(22(22(21(10(01(10(02(20(00(00(03(32(x1)))))))))))))))))) | → | 32(23(32(20(01(10(02(21(10(02(22(21(12(22(20(00(03(32(x1)))))))))))))))))) | (367) |
31(12(23(32(22(22(22(22(21(10(01(10(02(20(00(00(03(31(x1)))))))))))))))))) | → | 32(23(32(20(01(10(02(21(10(02(22(21(12(22(20(00(03(31(x1)))))))))))))))))) | (368) |
31(12(23(32(22(22(22(22(21(10(01(10(02(20(00(00(03(33(x1)))))))))))))))))) | → | 32(23(32(20(01(10(02(21(10(02(22(21(12(22(20(00(03(33(x1)))))))))))))))))) | (369) |
[23(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 + 2 |
[13(x1)] | = | 1 · x1 + 1 |
[21(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 + 1 |
[20(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
23(33(32(23(33(31(13(32(23(32(23(33(32(21(13(32(23(30(x1)))))))))))))))))) | → | 23(32(23(32(22(21(13(32(21(13(33(33(33(33(33(32(23(30(x1)))))))))))))))))) | (338) |
23(33(32(23(33(31(13(32(23(32(23(33(32(21(13(32(23(32(x1)))))))))))))))))) | → | 23(32(23(32(22(21(13(32(21(13(33(33(33(33(33(32(23(32(x1)))))))))))))))))) | (339) |
23(33(32(23(33(31(13(32(23(32(23(33(32(21(13(32(23(31(x1)))))))))))))))))) | → | 23(32(23(32(22(21(13(32(21(13(33(33(33(33(33(32(23(31(x1)))))))))))))))))) | (340) |
23(33(32(23(33(31(13(32(23(32(23(33(32(21(13(32(23(33(x1)))))))))))))))))) | → | 23(32(23(32(22(21(13(32(21(13(33(33(33(33(33(32(23(33(x1)))))))))))))))))) | (341) |
23(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(00(x1))))))))))))))))))) | → | 22(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(00(x1))))))))))))))))))) | (598) |
23(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(02(x1))))))))))))))))))) | → | 22(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(02(x1))))))))))))))))))) | (599) |
23(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(01(x1))))))))))))))))))) | → | 22(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(01(x1))))))))))))))))))) | (600) |
23(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(03(x1))))))))))))))))))) | → | 22(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(03(x1))))))))))))))))))) | (601) |
03(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(20(x1))))))))))))))))))) | → | 02(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(20(x1))))))))))))))))))) | (658) |
03(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(22(x1))))))))))))))))))) | → | 02(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(22(x1))))))))))))))))))) | (659) |
03(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(21(x1))))))))))))))))))) | → | 02(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(21(x1))))))))))))))))))) | (660) |
03(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(23(x1))))))))))))))))))) | → | 02(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(23(x1))))))))))))))))))) | (661) |
23(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(20(x1))))))))))))))))))) | → | 22(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(20(x1))))))))))))))))))) | (662) |
23(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(22(x1))))))))))))))))))) | → | 22(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(22(x1))))))))))))))))))) | (663) |
23(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(21(x1))))))))))))))))))) | → | 22(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(21(x1))))))))))))))))))) | (664) |
23(31(13(32(22(22(22(23(32(20(03(30(00(03(32(22(22(22(23(x1))))))))))))))))))) | → | 22(22(21(10(03(32(22(22(23(30(00(02(23(33(33(32(22(22(23(x1))))))))))))))))))) | (665) |
[03(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 + 1 |
[01(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
03(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(00(x1))))))))))))))))))) | → | 02(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(00(x1))))))))))))))))))) | (594) |
03(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(02(x1))))))))))))))))))) | → | 02(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(02(x1))))))))))))))))))) | (595) |
03(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(01(x1))))))))))))))))))) | → | 02(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(01(x1))))))))))))))))))) | (596) |
03(31(10(00(02(20(01(11(12(21(13(32(22(22(22(20(00(00(03(x1))))))))))))))))))) | → | 02(23(32(21(10(02(23(31(10(00(01(11(12(22(22(20(00(00(03(x1))))))))))))))))))) | (597) |
There are no rules in the TRS. Hence, it is terminating.