The relative rewrite relation R/S is considered where R is the following TRS
0(0(0(3(1(3(1(0(0(2(0(2(1(3(2(3(3(0(x1)))))))))))))))))) | → | 0(2(3(0(2(0(1(0(3(0(1(0(2(0(1(3(3(3(x1)))))))))))))))))) | (1) |
0(0(0(3(2(1(1(2(0(1(3(2(2(1(3(1(0(1(x1)))))))))))))))))) | → | 0(2(3(1(0(1(2(1(0(0(1(2(2(0(3(3(1(1(x1)))))))))))))))))) | (2) |
0(0(1(0(0(2(2(1(3(1(3(3(2(0(0(2(0(3(x1)))))))))))))))))) | → | 0(1(0(0(3(3(0(3(3(1(2(2(0(0(1(2(2(0(x1)))))))))))))))))) | (3) |
0(0(1(0(1(3(1(1(1(1(2(2(2(3(1(3(1(3(x1)))))))))))))))))) | → | 0(3(1(2(3(3(1(1(1(0(2(2(1(1(1(1(3(0(x1)))))))))))))))))) | (4) |
0(0(3(0(0(2(3(2(1(2(1(3(2(0(0(3(1(2(x1)))))))))))))))))) | → | 0(0(2(1(1(2(2(0(0(3(0(2(0(3(1(2(3(3(x1)))))))))))))))))) | (5) |
0(0(3(1(3(2(3(2(3(1(2(0(3(0(3(2(1(3(x1)))))))))))))))))) | → | 0(3(3(3(2(1(2(0(3(0(2(1(1(0(3(3(3(2(x1)))))))))))))))))) | (6) |
0(1(0(0(2(2(3(1(3(3(3(2(0(0(1(3(3(0(x1)))))))))))))))))) | → | 3(0(3(2(0(2(0(1(0(2(0(3(1(1(0(3(3(3(x1)))))))))))))))))) | (7) |
0(1(1(0(2(1(0(1(3(2(2(0(0(2(0(2(3(3(x1)))))))))))))))))) | → | 0(1(0(3(3(2(1(3(2(0(0(2(1(2(1(2(0(0(x1)))))))))))))))))) | (8) |
0(1(1(3(0(0(0(1(3(1(3(1(3(3(0(0(2(3(x1)))))))))))))))))) | → | 1(0(1(0(1(3(2(3(1(3(0(3(3(0(3(1(0(0(x1)))))))))))))))))) | (9) |
0(1(1(3(0(3(3(2(0(1(3(0(1(3(2(0(0(3(x1)))))))))))))))))) | → | 0(3(2(0(0(1(2(0(0(3(3(0(1(1(3(1(3(3(x1)))))))))))))))))) | (10) |
0(1(3(0(0(0(1(3(3(1(2(3(2(3(3(0(0(0(x1)))))))))))))))))) | → | 0(1(0(0(3(0(0(3(0(2(0(3(3(2(1(3(1(3(x1)))))))))))))))))) | (11) |
0(1(3(1(3(0(2(3(3(3(2(2(3(2(2(0(0(0(x1)))))))))))))))))) | → | 0(3(1(2(2(2(0(3(0(0(1(2(3(0(2(3(3(3(x1)))))))))))))))))) | (12) |
0(1(3(2(0(3(0(2(0(0(3(0(3(3(1(0(1(3(x1)))))))))))))))))) | → | 0(2(3(3(3(0(0(0(1(2(0(0(3(1(1(0(3(3(x1)))))))))))))))))) | (13) |
0(2(0(1(3(0(1(0(0(2(3(1(3(0(1(3(3(2(x1)))))))))))))))))) | → | 2(1(2(3(1(2(1(0(0(1(0(0(3(3(0(3(3(0(x1)))))))))))))))))) | (14) |
0(2(3(2(3(2(0(0(3(3(2(1(3(2(3(0(2(0(x1)))))))))))))))))) | → | 0(0(3(0(2(0(2(3(3(2(2(0(2(3(3(1(2(3(x1)))))))))))))))))) | (15) |
0(3(0(0(1(2(0(3(1(3(0(1(3(1(0(1(3(3(x1)))))))))))))))))) | → | 0(3(1(0(1(3(0(3(3(0(0(1(0(1(2(3(1(3(x1)))))))))))))))))) | (16) |
0(3(0(0(2(0(0(2(3(3(0(2(1(3(0(3(2(2(x1)))))))))))))))))) | → | 0(3(0(3(3(0(3(0(2(2(1(3(2(0(0(0(2(2(x1)))))))))))))))))) | (17) |
0(3(0(2(0(0(3(1(2(0(1(3(3(1(2(1(1(3(x1)))))))))))))))))) | → | 0(2(1(3(3(3(1(0(0(3(3(2(1(1(1(0(2(0(x1)))))))))))))))))) | (18) |
0(3(2(3(3(0(0(1(0(2(3(2(3(3(3(1(1(2(x1)))))))))))))))))) | → | 0(3(3(0(3(0(1(2(2(1(3(2(0(3(3(3(1(2(x1)))))))))))))))))) | (19) |
1(0(0(1(1(3(3(3(2(2(0(2(3(3(1(3(3(3(x1)))))))))))))))))) | → | 2(3(3(2(1(1(0(3(3(1(0(3(2(1(3(3(0(3(x1)))))))))))))))))) | (20) |
1(0(0(3(2(0(2(0(0(1(3(2(1(1(0(0(0(3(x1)))))))))))))))))) | → | 2(0(3(0(2(0(0(1(0(3(0(1(1(1(2(0(0(3(x1)))))))))))))))))) | (21) |
1(0(1(3(2(3(2(2(0(2(0(1(3(0(0(2(2(1(x1)))))))))))))))))) | → | 2(0(2(3(2(1(0(1(2(3(2(0(0(1(0(2(3(1(x1)))))))))))))))))) | (22) |
1(0(2(0(0(0(3(1(3(0(1(2(0(1(3(0(2(0(x1)))))))))))))))))) | → | 2(2(0(1(0(0(2(1(0(3(0(3(1(0(0(3(1(0(x1)))))))))))))))))) | (23) |
1(0(2(3(0(1(3(1(3(3(3(0(1(2(0(0(2(0(x1)))))))))))))))))) | → | 1(2(0(0(3(1(2(1(3(1(2(0(3(3(3(0(0(0(x1)))))))))))))))))) | (24) |
1(0(2(3(1(1(1(1(2(3(1(2(0(1(0(3(2(0(x1)))))))))))))))))) | → | 1(1(2(3(1(2(1(2(1(1(0(3(3(2(0(0(1(0(x1)))))))))))))))))) | (25) |
1(0(2(3(2(2(1(2(3(0(2(2(3(1(3(0(3(0(x1)))))))))))))))))) | → | 2(0(1(2(2(0(3(3(1(1(3(2(3(0(3(2(2(0(x1)))))))))))))))))) | (26) |
1(1(0(2(1(2(3(1(0(2(2(3(2(3(2(0(1(2(x1)))))))))))))))))) | → | 1(2(1(2(1(2(1(0(2(1(0(0(2(2(3(2(3(3(x1)))))))))))))))))) | (27) |
1(1(1(1(0(3(1(2(0(1(0(0(2(3(2(1(3(0(x1)))))))))))))))))) | → | 1(1(1(1(2(1(1(0(0(3(2(0(0(2(1(3(3(0(x1)))))))))))))))))) | (28) |
1(1(1(3(1(1(0(2(2(2(3(2(0(1(3(0(1(2(x1)))))))))))))))))) | → | 1(2(2(1(2(2(0(0(1(1(0(1(1(3(1(2(3(3(x1)))))))))))))))))) | (29) |
1(1(2(0(0(1(1(2(3(0(2(1(2(1(0(2(1(1(x1)))))))))))))))))) | → | 1(2(2(0(0(2(1(0(2(1(0(3(1(2(1(1(1(1(x1)))))))))))))))))) | (30) |
1(1(3(1(3(1(3(3(0(3(2(0(3(1(0(1(2(0(x1)))))))))))))))))) | → | 1(2(3(0(1(3(1(0(3(0(3(3(1(1(2(1(0(3(x1)))))))))))))))))) | (31) |
1(1(3(2(1(3(0(0(2(3(1(1(3(2(2(1(3(2(x1)))))))))))))))))) | → | 1(1(2(2(3(3(3(2(3(1(1(2(3(1(0(2(1(0(x1)))))))))))))))))) | (32) |
1(2(0(0(1(0(1(3(0(3(3(3(1(3(2(3(0(3(x1)))))))))))))))))) | → | 2(1(1(3(3(0(3(0(0(1(2(3(3(1(0(3(3(0(x1)))))))))))))))))) | (33) |
1(2(2(3(0(2(3(3(3(2(0(1(0(0(2(1(2(3(x1)))))))))))))))))) | → | 1(2(2(2(3(3(1(0(3(2(0(3(2(1(0(2(3(0(x1)))))))))))))))))) | (34) |
1(2(3(0(2(0(2(3(2(0(0(1(0(3(0(0(1(3(x1)))))))))))))))))) | → | 1(2(3(0(0(1(0(0(0(3(2(3(2(0(0(1(2(3(x1)))))))))))))))))) | (35) |
1(3(0(0(0(1(1(1(1(2(2(3(3(0(1(2(0(3(x1)))))))))))))))))) | → | 1(1(1(2(1(1(2(0(3(2(0(1(0(0(3(3(3(0(x1)))))))))))))))))) | (36) |
1(3(0(0(3(1(1(1(3(1(1(2(0(2(1(3(3(2(x1)))))))))))))))))) | → | 1(2(1(2(3(0(1(1(1(2(3(0(3(0(3(3(1(1(x1)))))))))))))))))) | (37) |
1(3(0(1(2(0(1(0(3(0(3(1(2(2(1(3(1(3(x1)))))))))))))))))) | → | 1(1(1(3(2(0(1(0(3(2(3(1(0(1(0(3(2(3(x1)))))))))))))))))) | (38) |
1(3(0(3(3(0(3(3(1(2(3(0(2(1(2(0(0(1(x1)))))))))))))))))) | → | 2(1(1(2(0(0(3(1(3(0(3(3(2(0(3(3(0(1(x1)))))))))))))))))) | (39) |
1(3(1(3(0(0(1(0(1(3(0(2(1(2(1(3(1(3(x1)))))))))))))))))) | → | 1(1(1(3(2(2(3(3(0(3(3(1(0(0(1(1(1(0(x1)))))))))))))))))) | (40) |
1(3(1(3(1(2(3(2(3(2(2(3(1(1(0(1(1(0(x1)))))))))))))))))) | → | 2(1(1(2(1(1(0(1(0(1(3(3(3(2(2(3(1(3(x1)))))))))))))))))) | (41) |
1(3(1(3(3(0(0(2(3(2(3(1(2(2(2(2(1(3(x1)))))))))))))))))) | → | 1(3(3(1(0(3(2(2(2(2(1(3(0(3(2(2(1(3(x1)))))))))))))))))) | (42) |
1(3(1(3(3(3(3(0(0(1(3(1(2(3(2(3(3(3(x1)))))))))))))))))) | → | 1(0(2(3(3(3(3(3(2(1(3(3(0(3(1(1(3(3(x1)))))))))))))))))) | (43) |
1(3(2(0(0(0(2(2(2(2(3(2(1(3(1(1(0(3(x1)))))))))))))))))) | → | 1(2(1(2(2(3(3(0(1(3(2(2(2(1(0(3(0(0(x1)))))))))))))))))) | (44) |
1(3(2(0(1(3(2(1(0(0(2(2(2(1(1(1(3(3(x1)))))))))))))))))) | → | 2(1(2(1(0(3(0(1(0(2(1(1(2(3(3(1(2(3(x1)))))))))))))))))) | (45) |
1(3(2(1(2(1(2(3(0(1(0(3(3(1(0(2(0(0(x1)))))))))))))))))) | → | 1(2(1(0(3(2(3(1(0(1(0(3(1(2(2(3(0(0(x1)))))))))))))))))) | (46) |
1(3(2(2(1(0(0(2(1(0(1(3(1(3(0(3(1(3(x1)))))))))))))))))) | → | 1(0(1(0(3(2(0(3(3(1(1(1(1(0(3(3(2(2(x1)))))))))))))))))) | (47) |
1(3(3(1(3(0(3(3(1(3(1(3(3(1(2(3(2(3(x1)))))))))))))))))) | → | 2(3(3(3(3(3(3(1(1(2(3(1(1(0(1(3(3(3(x1)))))))))))))))))) | (48) |
2(0(0(1(3(1(0(1(1(2(1(1(3(2(1(1(3(0(x1)))))))))))))))))) | → | 2(0(3(3(1(1(1(1(1(1(1(1(2(3(2(0(0(0(x1)))))))))))))))))) | (49) |
2(0(1(0(2(0(1(3(1(3(3(0(1(0(2(3(0(3(x1)))))))))))))))))) | → | 2(1(0(3(0(0(3(0(1(2(3(2(1(0(1(3(3(0(x1)))))))))))))))))) | (50) |
2(0(2(3(3(1(1(0(0(1(3(1(3(0(3(0(0(0(x1)))))))))))))))))) | → | 1(0(0(0(3(1(0(3(2(1(3(3(0(0(2(1(0(3(x1)))))))))))))))))) | (51) |
2(1(0(0(3(0(3(1(3(0(3(2(2(0(2(3(3(3(x1)))))))))))))))))) | → | 2(2(1(2(0(3(0(0(2(0(3(3(3(3(3(3(1(0(x1)))))))))))))))))) | (52) |
2(1(0(1(3(2(0(0(0(3(2(3(0(2(0(2(2(2(x1)))))))))))))))))) | → | 2(2(0(2(3(0(0(3(2(0(0(3(0(1(2(1(2(2(x1)))))))))))))))))) | (53) |
2(1(0(2(2(0(2(1(3(1(2(1(1(1(0(2(1(2(x1)))))))))))))))))) | → | 1(2(1(2(1(2(2(0(2(0(2(3(1(0(1(1(1(2(x1)))))))))))))))))) | (54) |
2(1(0(3(1(3(1(0(1(3(3(2(2(3(0(3(2(3(x1)))))))))))))))))) | → | 2(1(3(2(3(0(3(1(1(1(0(3(3(2(2(0(3(3(x1)))))))))))))))))) | (55) |
2(1(2(3(2(3(2(1(1(2(2(1(2(0(1(3(2(2(x1)))))))))))))))))) | → | 2(2(1(2(1(0(1(2(1(2(2(3(3(2(2(1(2(3(x1)))))))))))))))))) | (56) |
2(1(3(2(0(1(1(2(1(0(0(3(0(2(1(3(1(3(x1)))))))))))))))))) | → | 1(1(2(3(0(2(0(3(3(1(2(2(1(0(0(1(1(3(x1)))))))))))))))))) | (57) |
2(3(0(0(0(1(1(0(2(2(2(2(2(0(3(1(3(0(x1)))))))))))))))))) | → | 2(3(2(0(3(2(0(2(2(0(3(1(2(1(1(0(0(0(x1)))))))))))))))))) | (58) |
3(0(0(0(1(3(3(2(1(3(2(3(1(3(0(2(3(1(x1)))))))))))))))))) | → | 1(3(2(2(3(2(0(0(3(0(1(1(3(3(0(3(3(1(x1)))))))))))))))))) | (59) |
3(0(0(2(0(2(0(0(1(3(0(3(3(2(0(2(3(3(x1)))))))))))))))))) | → | 3(0(2(2(3(2(3(0(0(1(0(3(0(3(0(2(0(3(x1)))))))))))))))))) | (60) |
3(0(0(2(0(3(1(0(1(0(0(2(3(2(0(0(3(0(x1)))))))))))))))))) | → | 3(0(0(0(3(2(0(2(0(0(3(3(1(0(2(1(0(0(x1)))))))))))))))))) | (61) |
3(0(0(2(1(3(1(3(1(2(3(0(3(1(0(0(2(0(x1)))))))))))))))))) | → | 3(3(3(1(1(2(1(2(1(0(0(0(0(2(3(0(0(3(x1)))))))))))))))))) | (62) |
3(0(1(0(3(0(2(3(0(0(2(3(0(2(3(3(0(0(x1)))))))))))))))))) | → | 3(0(1(0(0(2(0(2(0(2(0(0(3(3(0(3(3(3(x1)))))))))))))))))) | (63) |
3(0(1(3(0(0(3(3(2(3(1(3(2(0(2(3(3(2(x1)))))))))))))))))) | → | 3(1(0(2(0(1(3(3(3(0(0(3(2(2(3(3(3(2(x1)))))))))))))))))) | (64) |
3(0(2(2(3(3(2(0(3(0(2(2(0(1(3(0(2(2(x1)))))))))))))))))) | → | 3(0(2(2(0(3(3(2(2(1(3(2(0(3(2(0(0(2(x1)))))))))))))))))) | (65) |
3(0(3(1(2(3(2(1(0(1(3(3(0(3(3(2(1(3(x1)))))))))))))))))) | → | 3(1(3(3(3(1(1(0(2(2(3(2(1(0(3(0(3(3(x1)))))))))))))))))) | (66) |
3(0(3(1(3(1(3(2(2(3(2(2(2(0(1(3(1(2(x1)))))))))))))))))) | → | 1(1(2(3(3(0(0(3(3(3(2(1(2(1(2(3(2(2(x1)))))))))))))))))) | (67) |
3(0(3(3(2(3(2(3(0(2(0(0(3(1(3(1(2(0(x1)))))))))))))))))) | → | 3(3(2(0(3(3(3(3(1(2(1(0(0(3(2(0(2(0(x1)))))))))))))))))) | (68) |
3(1(0(3(1(3(3(3(0(0(1(0(3(3(1(3(0(3(x1)))))))))))))))))) | → | 1(0(3(3(3(3(3(0(1(0(3(0(1(1(0(3(3(3(x1)))))))))))))))))) | (69) |
3(1(1(2(2(3(0(0(0(1(1(3(2(3(1(0(2(3(x1)))))))))))))))))) | → | 2(1(0(3(1(1(2(3(1(1(0(2(0(3(2(0(3(3(x1)))))))))))))))))) | (70) |
3(1(1(3(3(1(3(3(1(0(3(0(0(3(0(0(0(1(x1)))))))))))))))))) | → | 3(1(3(1(3(0(3(3(3(1(0(1(0(0(0(3(0(1(x1)))))))))))))))))) | (71) |
3(1(2(0(0(2(3(0(0(2(3(3(2(0(0(2(0(0(x1)))))))))))))))))) | → | 3(0(2(3(0(0(2(2(0(2(3(0(1(0(2(0(3(0(x1)))))))))))))))))) | (72) |
3(1(3(2(0(3(0(2(1(3(2(1(3(1(2(1(2(0(x1)))))))))))))))))) | → | 3(2(1(3(1(2(2(3(1(2(1(2(3(1(0(0(3(0(x1)))))))))))))))))) | (73) |
3(1(3(3(1(3(1(1(2(3(1(3(3(1(3(2(2(3(x1)))))))))))))))))) | → | 3(3(1(3(2(1(3(3(1(1(2(1(3(3(1(2(3(3(x1)))))))))))))))))) | (74) |
3(1(3(3(2(3(2(1(3(0(1(1(3(3(3(0(0(3(x1)))))))))))))))))) | → | 3(3(0(3(2(0(1(3(1(0(3(1(3(3(2(1(3(3(x1)))))))))))))))))) | (75) |
3(2(0(3(1(3(0(1(1(3(0(0(0(3(0(3(1(3(x1)))))))))))))))))) | → | 3(1(0(3(1(3(3(3(0(1(0(0(1(2(0(3(3(0(x1)))))))))))))))))) | (76) |
3(2(3(1(2(0(1(2(3(1(1(3(3(3(3(3(0(0(x1)))))))))))))))))) | → | 2(2(1(0(2(1(0(1(0(3(3(3(1(3(3(3(3(3(x1)))))))))))))))))) | (77) |
3(2(3(3(2(1(0(0(2(2(3(0(0(1(0(3(1(3(x1)))))))))))))))))) | → | 3(2(3(1(0(2(0(2(1(0(2(3(1(0(3(3(3(0(x1)))))))))))))))))) | (78) |
3(2(3(3(2(3(2(1(1(3(0(1(0(2(2(1(3(0(x1)))))))))))))))))) | → | 3(1(3(1(2(1(0(1(2(3(2(3(3(3(2(0(2(0(x1)))))))))))))))))) | (79) |
3(3(1(2(1(1(1(3(2(1(3(3(1(3(2(3(2(1(x1)))))))))))))))))) | → | 3(3(1(2(3(2(1(1(3(3(1(2(1(1(2(3(3(1(x1)))))))))))))))))) | (80) |
and S is the following TRS.
0(1(2(3(x1)))) | → | 0(1(2(3(x1)))) | (81) |
{0(☐), 3(☐), 1(☐), 2(☐)}
We obtain the transformed TRSThere are 143 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRSThere are 572 ruless (increase limit for explicit display).
[00(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 + 9 |
[10(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 + 2 |
[32(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 + 9 |
[33(x1)] | = | 1 · x1 + 3 |
[30(x1)] | = | 1 · x1 + 1 |
[01(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 + 3 |
[12(x1)] | = | 1 · x1 + 1 |
[22(x1)] | = | 1 · x1 |
There are 532 ruless (increase limit for explicit display).
[01(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 + 7 |
[03(x1)] | = | 1 · x1 + 2 |
[30(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 7 |
[23(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 + 5 |
[11(x1)] | = | 1 · x1 + 3 |
[22(x1)] | = | 1 · x1 + 6 |
[21(x1)] | = | 1 · x1 + 4 |
01(13(32(20(03(30(02(20(00(03(30(03(33(31(10(01(13(30(x1)))))))))))))))))) | → | 02(23(33(33(30(00(00(01(12(20(00(03(31(11(10(03(33(30(x1)))))))))))))))))) | (206) |
01(13(32(20(03(30(02(20(00(03(30(03(33(31(10(01(13(33(x1)))))))))))))))))) | → | 02(23(33(33(30(00(00(01(12(20(00(03(31(11(10(03(33(33(x1)))))))))))))))))) | (207) |
01(13(32(20(03(30(02(20(00(03(30(03(33(31(10(01(13(31(x1)))))))))))))))))) | → | 02(23(33(33(30(00(00(01(12(20(00(03(31(11(10(03(33(31(x1)))))))))))))))))) | (208) |
01(13(32(20(03(30(02(20(00(03(30(03(33(31(10(01(13(32(x1)))))))))))))))))) | → | 02(23(33(33(30(00(00(01(12(20(00(03(31(11(10(03(33(32(x1)))))))))))))))))) | (209) |
12(23(30(02(20(02(23(32(20(00(01(10(03(30(00(01(13(30(x1)))))))))))))))))) | → | 12(23(30(00(01(10(00(00(03(32(23(32(20(00(01(12(23(30(x1)))))))))))))))))) | (266) |
12(23(30(02(20(02(23(32(20(00(01(10(03(30(00(01(13(33(x1)))))))))))))))))) | → | 12(23(30(00(01(10(00(00(03(32(23(32(20(00(01(12(23(33(x1)))))))))))))))))) | (267) |
12(23(30(02(20(02(23(32(20(00(01(10(03(30(00(01(13(31(x1)))))))))))))))))) | → | 12(23(30(00(01(10(00(00(03(32(23(32(20(00(01(12(23(31(x1)))))))))))))))))) | (268) |
12(23(30(02(20(02(23(32(20(00(01(10(03(30(00(01(13(32(x1)))))))))))))))))) | → | 12(23(30(00(01(10(00(00(03(32(23(32(20(00(01(12(23(32(x1)))))))))))))))))) | (269) |
[03(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 + 1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 + 1 |
[20(x1)] | = | 1 · x1 + 1 |
[31(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 + 4 |
[10(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 + 3 |
[32(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 + 2 |
[11(x1)] | = | 1 · x1 + 3 |
[02(x1)] | = | 1 · x1 |
03(30(00(01(12(20(03(31(13(30(01(13(31(10(01(13(33(30(x1)))))))))))))))))) | → | 03(31(10(01(13(30(03(33(30(00(01(10(01(12(23(31(13(30(x1)))))))))))))))))) | (214) |
03(30(00(01(12(20(03(31(13(30(01(13(31(10(01(13(33(33(x1)))))))))))))))))) | → | 03(31(10(01(13(30(03(33(30(00(01(10(01(12(23(31(13(33(x1)))))))))))))))))) | (215) |
03(30(00(01(12(20(03(31(13(30(01(13(31(10(01(13(33(31(x1)))))))))))))))))) | → | 03(31(10(01(13(30(03(33(30(00(01(10(01(12(23(31(13(31(x1)))))))))))))))))) | (216) |
03(30(00(01(12(20(03(31(13(30(01(13(31(10(01(13(33(32(x1)))))))))))))))))) | → | 03(31(10(01(13(30(03(33(30(00(01(10(01(12(23(31(13(32(x1)))))))))))))))))) | (217) |
01(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(10(x1))))))))))))))))))) | → | 02(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(10(x1))))))))))))))))))) | (482) |
01(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(13(x1))))))))))))))))))) | → | 02(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(13(x1))))))))))))))))))) | (483) |
01(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(11(x1))))))))))))))))))) | → | 02(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(11(x1))))))))))))))))))) | (484) |
01(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(12(x1))))))))))))))))))) | → | 02(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(12(x1))))))))))))))))))) | (485) |
31(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(10(x1))))))))))))))))))) | → | 32(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(10(x1))))))))))))))))))) | (486) |
31(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(13(x1))))))))))))))))))) | → | 32(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(13(x1))))))))))))))))))) | (487) |
31(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(11(x1))))))))))))))))))) | → | 32(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(11(x1))))))))))))))))))) | (488) |
31(10(01(13(32(23(32(22(20(02(20(01(13(30(00(02(22(21(12(x1))))))))))))))))))) | → | 32(20(02(23(32(21(10(01(12(23(32(20(00(01(10(02(23(31(12(x1))))))))))))))))))) | (489) |
[13(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 + 1 |
[20(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 1 |
[03(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 + 1 |
[21(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
13(30(01(12(20(01(10(03(30(03(31(12(22(21(13(31(13(30(x1)))))))))))))))))) | → | 11(11(13(32(20(01(10(03(32(23(31(10(01(10(03(32(23(30(x1)))))))))))))))))) | (278) |
13(30(01(12(20(01(10(03(30(03(31(12(22(21(13(31(13(33(x1)))))))))))))))))) | → | 11(11(13(32(20(01(10(03(32(23(31(10(01(10(03(32(23(33(x1)))))))))))))))))) | (279) |
13(30(01(12(20(01(10(03(30(03(31(12(22(21(13(31(13(31(x1)))))))))))))))))) | → | 11(11(13(32(20(01(10(03(32(23(31(10(01(10(03(32(23(31(x1)))))))))))))))))) | (280) |
13(30(01(12(20(01(10(03(30(03(31(12(22(21(13(31(13(32(x1)))))))))))))))))) | → | 11(11(13(32(20(01(10(03(32(23(31(10(01(10(03(32(23(32(x1)))))))))))))))))) | (281) |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 + 2 |
[00(x1)] | = | 1 · x1 + 2 |
[10(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 + 1 |
[11(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 + 1 |
01(12(20(00(01(10(01(13(30(03(33(33(31(13(32(23(30(03(31(x1))))))))))))))))))) | → | 02(21(11(13(33(30(03(30(00(01(12(23(33(31(10(03(33(30(01(x1))))))))))))))))))) | (532) |
01(12(20(00(01(10(01(13(30(03(33(33(31(13(32(23(30(03(32(x1))))))))))))))))))) | → | 02(21(11(13(33(30(03(30(00(01(12(23(33(31(10(03(33(30(02(x1))))))))))))))))))) | (533) |
31(12(20(00(01(10(01(13(30(03(33(33(31(13(32(23(30(03(31(x1))))))))))))))))))) | → | 32(21(11(13(33(30(03(30(00(01(12(23(33(31(10(03(33(30(01(x1))))))))))))))))))) | (536) |
31(12(20(00(01(10(01(13(30(03(33(33(31(13(32(23(30(03(32(x1))))))))))))))))))) | → | 32(21(11(13(33(30(03(30(00(01(12(23(33(31(10(03(33(30(02(x1))))))))))))))))))) | (537) |
[12(x1)] | = | 1 · x1 + 1 |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 + 2 |
[22(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 + 2 |
[30(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
12(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(20(x1))))))))))))))))))) | → | 11(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(20(x1))))))))))))))))))) | (634) |
12(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(23(x1))))))))))))))))))) | → | 11(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(23(x1))))))))))))))))))) | (635) |
12(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(21(x1))))))))))))))))))) | → | 11(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(21(x1))))))))))))))))))) | (636) |
12(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(22(x1))))))))))))))))))) | → | 11(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(22(x1))))))))))))))))))) | (637) |
[22(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 1 |
[02(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
22(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(20(x1))))))))))))))))))) | → | 21(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(20(x1))))))))))))))))))) | (638) |
22(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(23(x1))))))))))))))))))) | → | 21(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(23(x1))))))))))))))))))) | (639) |
22(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(21(x1))))))))))))))))))) | → | 21(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(21(x1))))))))))))))))))) | (640) |
22(21(10(02(22(20(02(21(13(31(12(21(11(11(10(02(21(12(22(x1))))))))))))))))))) | → | 21(12(21(12(21(12(22(20(02(20(02(23(31(10(01(11(11(12(22(x1))))))))))))))))))) | (641) |
[03(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 + 1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
03(30(03(31(13(31(13(32(22(23(32(22(22(20(01(13(31(12(20(x1))))))))))))))))))) | → | 01(11(12(23(33(30(00(03(33(33(32(21(12(21(12(23(32(22(20(x1))))))))))))))))))) | (674) |
03(30(03(31(13(31(13(32(22(23(32(22(22(20(01(13(31(12(23(x1))))))))))))))))))) | → | 01(11(12(23(33(30(00(03(33(33(32(21(12(21(12(23(32(22(23(x1))))))))))))))))))) | (675) |
03(30(03(31(13(31(13(32(22(23(32(22(22(20(01(13(31(12(21(x1))))))))))))))))))) | → | 01(11(12(23(33(30(00(03(33(33(32(21(12(21(12(23(32(22(21(x1))))))))))))))))))) | (676) |
03(30(03(31(13(31(13(32(22(23(32(22(22(20(01(13(31(12(22(x1))))))))))))))))))) | → | 01(11(12(23(33(30(00(03(33(33(32(21(12(21(12(23(32(22(22(x1))))))))))))))))))) | (677) |
There are no rules in the TRS. Hence, it is terminating.