The relative rewrite relation R/S is considered where R is the following TRS
0(1(0(1(x1)))) | → | 0(1(1(1(0(0(1(2(2(2(x1)))))))))) | (1) |
0(3(4(4(x1)))) | → | 0(0(0(3(1(1(4(2(2(0(x1)))))))))) | (2) |
1(5(1(5(4(x1))))) | → | 1(0(0(2(2(0(5(2(2(4(x1)))))))))) | (3) |
3(4(5(3(4(x1))))) | → | 3(5(0(2(1(1(1(2(1(4(x1)))))))))) | (4) |
4(3(4(3(4(x1))))) | → | 2(1(1(1(4(1(2(4(2(0(x1)))))))))) | (5) |
5(0(1(0(1(x1))))) | → | 5(0(2(0(1(1(4(2(1(2(x1)))))))))) | (6) |
1(0(1(0(1(4(x1)))))) | → | 1(0(2(4(5(4(2(4(2(4(x1)))))))))) | (7) |
1(1(3(4(1(5(x1)))))) | → | 1(1(0(0(2(2(5(2(0(0(x1)))))))))) | (8) |
1(3(1(1(3(3(x1)))))) | → | 1(2(4(2(0(2(1(0(2(5(x1)))))))))) | (9) |
1(3(1(5(2(3(x1)))))) | → | 1(4(3(2(1(0(0(2(4(3(x1)))))))))) | (10) |
1(5(0(5(5(3(x1)))))) | → | 2(1(1(1(1(2(1(3(5(3(x1)))))))))) | (11) |
2(1(3(1(5(5(x1)))))) | → | 1(1(2(2(0(5(0(0(2(2(x1)))))))))) | (12) |
2(2(4(3(4(5(x1)))))) | → | 2(0(1(4(0(0(2(0(0(0(x1)))))))))) | (13) |
2(3(1(0(3(4(x1)))))) | → | 0(0(1(1(5(2(4(1(1(4(x1)))))))))) | (14) |
2(3(3(4(1(5(x1)))))) | → | 0(0(2(4(4(2(0(4(1(3(x1)))))))))) | (15) |
2(5(0(5(5(1(x1)))))) | → | 3(0(1(4(4(0(0(0(0(1(x1)))))))))) | (16) |
3(0(4(3(3(4(x1)))))) | → | 2(3(0(3(5(1(2(4(2(4(x1)))))))))) | (17) |
3(2(3(3(0(4(x1)))))) | → | 5(4(2(2(0(0(4(2(4(4(x1)))))))))) | (18) |
3(3(5(4(3(4(x1)))))) | → | 0(5(1(1(0(4(0(2(4(4(x1)))))))))) | (19) |
3(5(4(2(1(0(x1)))))) | → | 2(5(0(0(0(0(0(4(4(0(x1)))))))))) | (20) |
4(1(3(4(3(1(x1)))))) | → | 4(2(5(0(1(0(0(0(4(4(x1)))))))))) | (21) |
4(2(1(0(2(5(x1)))))) | → | 4(2(5(4(2(2(2(4(2(5(x1)))))))))) | (22) |
4(3(3(5(1(1(x1)))))) | → | 4(4(2(4(4(2(5(0(1(2(x1)))))))))) | (23) |
5(4(0(1(3(0(x1)))))) | → | 0(2(4(2(2(1(2(0(0(0(x1)))))))))) | (24) |
0(4(1(5(5(3(5(x1))))))) | → | 0(2(2(0(1(2(5(2(5(0(x1)))))))))) | (25) |
0(4(4(3(4(1(3(x1))))))) | → | 0(4(2(4(1(3(2(0(2(2(x1)))))))))) | (26) |
1(3(3(4(5(2(5(x1))))))) | → | 1(1(1(4(5(1(2(5(2(4(x1)))))))))) | (27) |
1(5(2(5(1(5(2(x1))))))) | → | 1(2(3(0(2(3(0(1(0(2(x1)))))))))) | (28) |
1(5(3(2(4(5(4(x1))))))) | → | 1(1(0(3(0(0(0(0(3(4(x1)))))))))) | (29) |
1(5(5(5(3(2(1(x1))))))) | → | 1(4(1(4(2(1(3(0(1(1(x1)))))))))) | (30) |
2(1(2(3(1(3(3(x1))))))) | → | 2(1(4(1(5(1(1(1(1(1(x1)))))))))) | (31) |
3(0(2(1(3(2(1(x1))))))) | → | 1(2(0(0(3(3(4(2(2(1(x1)))))))))) | (32) |
3(0(4(4(3(4(5(x1))))))) | → | 1(2(2(4(3(2(2(2(0(4(x1)))))))))) | (33) |
3(1(3(1(5(4(1(x1))))))) | → | 0(1(2(2(5(5(5(4(2(0(x1)))))))))) | (34) |
3(2(5(2(1(3(4(x1))))))) | → | 0(2(1(3(1(2(1(4(2(2(x1)))))))))) | (35) |
3(3(1(3(1(3(3(x1))))))) | → | 1(2(1(3(0(5(5(1(2(1(x1)))))))))) | (36) |
3(3(1(5(0(3(4(x1))))))) | → | 2(0(0(5(1(2(1(4(1(4(x1)))))))))) | (37) |
3(3(3(5(2(4(5(x1))))))) | → | 3(1(0(0(1(4(2(2(0(5(x1)))))))))) | (38) |
3(4(3(3(4(3(5(x1))))))) | → | 5(1(1(1(1(1(4(2(3(3(x1)))))))))) | (39) |
3(4(3(4(4(3(2(x1))))))) | → | 2(5(4(5(3(4(2(4(4(0(x1)))))))))) | (40) |
4(1(3(4(1(0(2(x1))))))) | → | 4(4(1(5(1(2(1(4(2(2(x1)))))))))) | (41) |
4(5(0(4(1(3(1(x1))))))) | → | 1(1(1(2(0(0(4(4(5(1(x1)))))))))) | (42) |
4(5(0(5(3(2(1(x1))))))) | → | 1(1(4(1(3(0(2(4(2(1(x1)))))))))) | (43) |
4(5(0(5(3(4(5(x1))))))) | → | 1(1(1(0(5(4(0(2(4(5(x1)))))))))) | (44) |
4(5(3(1(4(4(3(x1))))))) | → | 4(5(5(5(4(2(4(4(2(3(x1)))))))))) | (45) |
4(5(3(4(1(4(5(x1))))))) | → | 4(5(4(0(2(0(1(2(1(0(x1)))))))))) | (46) |
4(5(4(3(4(1(0(x1))))))) | → | 1(4(1(1(2(4(0(1(2(0(x1)))))))))) | (47) |
5(3(2(1(5(3(4(x1))))))) | → | 5(1(2(1(3(3(5(1(2(4(x1)))))))))) | (48) |
5(3(4(3(1(3(3(x1))))))) | → | 5(1(1(4(2(4(3(3(4(3(x1)))))))))) | (49) |
5(3(4(4(3(1(2(x1))))))) | → | 5(1(0(5(0(3(5(1(1(1(x1)))))))))) | (50) |
5(4(3(2(3(1(3(x1))))))) | → | 0(0(0(2(3(0(2(5(4(3(x1)))))))))) | (51) |
5(4(3(4(3(1(5(x1))))))) | → | 0(2(0(0(0(0(4(1(5(0(x1)))))))))) | (52) |
5(5(3(3(3(5(4(x1))))))) | → | 0(3(5(2(2(1(0(4(2(2(x1)))))))))) | (53) |
5(5(4(5(3(5(5(x1))))))) | → | 5(2(4(2(2(2(4(1(5(2(x1)))))))))) | (54) |
and S is the following TRS.
0(4(3(4(3(1(x1)))))) | → | 2(5(0(3(0(2(2(4(0(0(x1)))))))))) | (55) |
2(3(2(5(5(3(x1)))))) | → | 0(0(2(3(1(2(2(1(0(4(x1)))))))))) | (56) |
3(3(2(4(5(1(2(x1))))))) | → | 5(1(1(5(1(4(1(2(2(2(x1)))))))))) | (57) |
1(3(1(3(5(4(1(x1))))))) | → | 1(0(4(0(0(5(1(0(5(4(x1)))))))))) | (58) |
5(0(1(5(1(5(x1)))))) | → | 5(0(1(4(0(1(1(0(0(2(x1)))))))))) | (59) |
4(4(5(3(1(1(0(x1))))))) | → | 4(0(5(0(1(2(2(2(0(2(x1)))))))))) | (60) |
1(0(1(0(x1)))) | → | 2(2(2(1(0(0(1(1(1(0(x1)))))))))) | (61) |
4(4(3(0(x1)))) | → | 0(2(2(4(1(1(3(0(0(0(x1)))))))))) | (62) |
4(5(1(5(1(x1))))) | → | 4(2(2(5(0(2(2(0(0(1(x1)))))))))) | (63) |
4(3(5(4(3(x1))))) | → | 4(1(2(1(1(1(2(0(5(3(x1)))))))))) | (64) |
4(3(4(3(4(x1))))) | → | 0(2(4(2(1(4(1(1(1(2(x1)))))))))) | (65) |
1(0(1(0(5(x1))))) | → | 2(1(2(4(1(1(0(2(0(5(x1)))))))))) | (66) |
4(1(0(1(0(1(x1)))))) | → | 4(2(4(2(4(5(4(2(0(1(x1)))))))))) | (67) |
5(1(4(3(1(1(x1)))))) | → | 0(0(2(5(2(2(0(0(1(1(x1)))))))))) | (68) |
3(3(1(1(3(1(x1)))))) | → | 5(2(0(1(2(0(2(4(2(1(x1)))))))))) | (69) |
3(2(5(1(3(1(x1)))))) | → | 3(4(2(0(0(1(2(3(4(1(x1)))))))))) | (70) |
3(5(5(0(5(1(x1)))))) | → | 3(5(3(1(2(1(1(1(1(2(x1)))))))))) | (71) |
5(5(1(3(1(2(x1)))))) | → | 2(2(0(0(5(0(2(2(1(1(x1)))))))))) | (72) |
5(4(3(4(2(2(x1)))))) | → | 0(0(0(2(0(0(4(1(0(2(x1)))))))))) | (73) |
4(3(0(1(3(2(x1)))))) | → | 4(1(1(4(2(5(1(1(0(0(x1)))))))))) | (74) |
5(1(4(3(3(2(x1)))))) | → | 3(1(4(0(2(4(4(2(0(0(x1)))))))))) | (75) |
1(5(5(0(5(2(x1)))))) | → | 1(0(0(0(0(4(4(1(0(3(x1)))))))))) | (76) |
4(3(3(4(0(3(x1)))))) | → | 4(2(4(2(1(5(3(0(3(2(x1)))))))))) | (77) |
4(0(3(3(2(3(x1)))))) | → | 4(4(2(4(0(0(2(2(4(5(x1)))))))))) | (78) |
4(3(4(5(3(3(x1)))))) | → | 4(4(2(0(4(0(1(1(5(0(x1)))))))))) | (79) |
0(1(2(4(5(3(x1)))))) | → | 0(4(4(0(0(0(0(0(5(2(x1)))))))))) | (80) |
1(3(4(3(1(4(x1)))))) | → | 4(4(0(0(0(1(0(5(2(4(x1)))))))))) | (81) |
5(2(0(1(2(4(x1)))))) | → | 5(2(4(2(2(2(4(5(2(4(x1)))))))))) | (82) |
1(1(5(3(3(4(x1)))))) | → | 2(1(0(5(2(4(4(2(4(4(x1)))))))))) | (83) |
0(3(1(0(4(5(x1)))))) | → | 0(0(0(2(1(2(2(4(2(0(x1)))))))))) | (84) |
5(3(5(5(1(4(0(x1))))))) | → | 0(5(2(5(2(1(0(2(2(0(x1)))))))))) | (85) |
3(1(4(3(4(4(0(x1))))))) | → | 2(2(0(2(3(1(4(2(4(0(x1)))))))))) | (86) |
5(2(5(4(3(3(1(x1))))))) | → | 4(2(5(2(1(5(4(1(1(1(x1)))))))))) | (87) |
2(5(1(5(2(5(1(x1))))))) | → | 2(0(1(0(3(2(0(3(2(1(x1)))))))))) | (88) |
4(5(4(2(3(5(1(x1))))))) | → | 4(3(0(0(0(0(3(0(1(1(x1)))))))))) | (89) |
1(2(3(5(5(5(1(x1))))))) | → | 1(1(0(3(1(2(4(1(4(1(x1)))))))))) | (90) |
3(3(1(3(2(1(2(x1))))))) | → | 1(1(1(1(1(5(1(4(1(2(x1)))))))))) | (91) |
1(2(3(1(2(0(3(x1))))))) | → | 1(2(2(4(3(3(0(0(2(1(x1)))))))))) | (92) |
5(4(3(4(4(0(3(x1))))))) | → | 4(0(2(2(2(3(4(2(2(1(x1)))))))))) | (93) |
1(4(5(1(3(1(3(x1))))))) | → | 0(2(4(5(5(5(2(2(1(0(x1)))))))))) | (94) |
4(3(1(2(5(2(3(x1))))))) | → | 2(2(4(1(2(1(3(1(2(0(x1)))))))))) | (95) |
3(3(1(3(1(3(3(x1))))))) | → | 1(2(1(5(5(0(3(1(2(1(x1)))))))))) | (96) |
4(3(0(5(1(3(3(x1))))))) | → | 4(1(4(1(2(1(5(0(0(2(x1)))))))))) | (97) |
5(4(2(5(3(3(3(x1))))))) | → | 5(0(2(2(4(1(0(0(1(3(x1)))))))))) | (98) |
5(3(4(3(3(4(3(x1))))))) | → | 3(3(2(4(1(1(1(1(1(5(x1)))))))))) | (99) |
2(3(4(4(3(4(3(x1))))))) | → | 0(4(4(2(4(3(5(4(5(2(x1)))))))))) | (100) |
2(0(1(4(3(1(4(x1))))))) | → | 2(2(4(1(2(1(5(1(4(4(x1)))))))))) | (101) |
1(3(1(4(0(5(4(x1))))))) | → | 1(5(4(4(0(0(2(1(1(1(x1)))))))))) | (102) |
1(2(3(5(0(5(4(x1))))))) | → | 1(2(4(2(0(3(1(4(1(1(x1)))))))))) | (103) |
5(4(3(5(0(5(4(x1))))))) | → | 5(4(2(0(4(5(0(1(1(1(x1)))))))))) | (104) |
3(4(4(1(3(5(4(x1))))))) | → | 3(2(4(4(2(4(5(5(5(4(x1)))))))))) | (105) |
5(4(1(4(3(5(4(x1))))))) | → | 0(1(2(1(0(2(0(4(5(4(x1)))))))))) | (106) |
0(1(4(3(4(5(4(x1))))))) | → | 0(2(1(0(4(2(1(1(4(1(x1)))))))))) | (107) |
4(3(5(1(2(3(5(x1))))))) | → | 4(2(1(5(3(3(1(2(1(5(x1)))))))))) | (108) |
3(3(1(3(4(3(5(x1))))))) | → | 3(4(3(3(4(2(4(1(1(5(x1)))))))))) | (109) |
2(1(3(4(4(3(5(x1))))))) | → | 1(1(1(5(3(0(5(0(1(5(x1)))))))))) | (110) |
3(1(3(2(3(4(5(x1))))))) | → | 3(4(5(2(0(3(2(0(0(0(x1)))))))))) | (111) |
5(1(3(4(3(4(5(x1))))))) | → | 0(5(1(4(0(0(0(0(2(0(x1)))))))))) | (112) |
4(5(3(3(3(5(5(x1))))))) | → | 2(2(4(0(1(2(2(5(3(0(x1)))))))))) | (113) |
5(5(3(5(4(5(5(x1))))))) | → | 2(5(1(4(2(2(2(4(2(5(x1)))))))))) | (114) |
1(3(4(3(4(0(x1)))))) | → | 0(0(4(2(2(0(3(0(5(2(x1)))))))))) | (115) |
3(5(5(2(3(2(x1)))))) | → | 4(0(1(2(2(1(3(2(0(0(x1)))))))))) | (116) |
2(1(5(4(2(3(3(x1))))))) | → | 2(2(2(1(4(1(5(1(1(5(x1)))))))))) | (117) |
1(4(5(3(1(3(1(x1))))))) | → | 4(5(0(1(5(0(0(4(0(1(x1)))))))))) | (118) |
5(1(5(1(0(5(x1)))))) | → | 2(0(0(1(1(0(4(1(0(5(x1)))))))))) | (119) |
0(1(1(3(5(4(4(x1))))))) | → | 2(0(2(2(2(1(0(5(0(4(x1)))))))))) | (120) |
{1(☐), 0(☐), 2(☐), 4(☐), 3(☐), 5(☐)}
We obtain the transformed TRSThere are 215 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRSThere are 1290 ruless (increase limit for explicit display).
[45(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 + 1 · x1 |
[15(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 + 1 · x1 |
[50(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 + 1 · x1 |
[11(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 + 1 · x1 |
[43(x1)] | = | 1 + 1 · x1 |
[35(x1)] | = | 1 + 1 · x1 |
[54(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 + 1 · x1 |
[31(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 + 1 · x1 |
[24(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 + 1 · x1 |
[55(x1)] | = | 1 + 1 · x1 |
[04(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 + 1 · x1 |
[52(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
There are 1136 ruless (increase limit for explicit display).
[45(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 + 1 · x1 |
[15(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 + 1 · x1 |
[55(x1)] | = | 1 + 1 · x1 |
[05(x1)] | = | 1 + 1 · x1 |
[53(x1)] | = | 1 + 1 · x1 |
[31(x1)] | = | 1 + 1 · x1 |
[21(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 + 1 · x1 |
[30(x1)] | = | 1 + 1 · x1 |
[32(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 + 1 · x1 |
[24(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 + 1 · x1 |
[34(x1)] | = | 1 + 1 · x1 |
[23(x1)] | = | 1 + 1 · x1 |
[33(x1)] | = | 1 + 1 · x1 |
[54(x1)] | = | 1 + 1 · x1 |
[40(x1)] | = | 1 · x1 |
There are 103 ruless (increase limit for explicit display).
[45(x1)] | = | 1 + 1 · x1 |
[54(x1)] | = | 1 + 1 · x1 |
[42(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 + 1 · x1 |
[35(x1)] | = | 1 + 1 · x1 |
[51(x1)] | = | 1 + 1 · x1 |
[14(x1)] | = | 1 + 1 · x1 |
[43(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 + 1 · x1 |
[13(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 + 1 · x1 |
[20(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 + 1 · x1 |
[44(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 + 1 · x1 |
[55(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 + 1 · x1 |
[53(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
45(54(42(23(35(51(14(x1))))))) | → | 43(30(00(00(00(03(30(01(11(14(x1)))))))))) | (391) |
45(54(42(23(35(51(15(x1))))))) | → | 43(30(00(00(00(03(30(01(11(15(x1)))))))))) | (392) |
45(54(42(23(35(51(11(x1))))))) | → | 43(30(00(00(00(03(30(01(11(11(x1)))))))))) | (393) |
45(54(42(23(35(51(12(x1))))))) | → | 43(30(00(00(00(03(30(01(11(12(x1)))))))))) | (394) |
45(54(42(23(35(51(10(x1))))))) | → | 43(30(00(00(00(03(30(01(11(10(x1)))))))))) | (395) |
45(54(42(23(35(51(13(x1))))))) | → | 43(30(00(00(00(03(30(01(11(13(x1)))))))))) | (396) |
12(23(31(12(20(03(32(x1))))))) | → | 12(22(24(43(33(30(00(02(21(12(x1)))))))))) | (406) |
34(44(41(13(35(54(44(x1))))))) | → | 32(24(44(42(24(45(55(55(54(44(x1)))))))))) | (445) |
34(44(41(13(35(54(45(x1))))))) | → | 32(24(44(42(24(45(55(55(54(45(x1)))))))))) | (446) |
34(44(41(13(35(54(41(x1))))))) | → | 32(24(44(42(24(45(55(55(54(41(x1)))))))))) | (447) |
34(44(41(13(35(54(42(x1))))))) | → | 32(24(44(42(24(45(55(55(54(42(x1)))))))))) | (448) |
34(44(41(13(35(54(40(x1))))))) | → | 32(24(44(42(24(45(55(55(54(40(x1)))))))))) | (449) |
34(44(41(13(35(54(43(x1))))))) | → | 32(24(44(42(24(45(55(55(54(43(x1)))))))))) | (450) |
41(10(01(10(04(x1))))) | → | 42(22(22(21(10(00(01(11(11(10(04(x1))))))))))) | (493) |
41(10(01(10(05(x1))))) | → | 42(22(22(21(10(00(01(11(11(10(05(x1))))))))))) | (494) |
41(10(01(10(01(x1))))) | → | 42(22(22(21(10(00(01(11(11(10(01(x1))))))))))) | (495) |
41(10(01(10(02(x1))))) | → | 42(22(22(21(10(00(01(11(11(10(02(x1))))))))))) | (496) |
41(10(01(10(00(x1))))) | → | 42(22(22(21(10(00(01(11(11(10(00(x1))))))))))) | (497) |
41(10(01(10(03(x1))))) | → | 42(22(22(21(10(00(01(11(11(10(03(x1))))))))))) | (498) |
11(14(45(51(13(31(13(31(x1)))))))) | → | 10(02(24(45(55(55(52(22(21(10(01(x1))))))))))) | (1053) |
21(14(45(51(13(31(13(31(x1)))))))) | → | 20(02(24(45(55(55(52(22(21(10(01(x1))))))))))) | (1065) |
41(14(45(51(13(31(13(31(x1)))))))) | → | 40(02(24(45(55(55(52(22(21(10(01(x1))))))))))) | (1071) |
31(14(45(51(13(31(13(31(x1)))))))) | → | 30(02(24(45(55(55(52(22(21(10(01(x1))))))))))) | (1077) |
02(21(13(34(44(43(35(54(x1)))))))) | → | 01(11(11(15(53(30(05(50(01(15(54(x1))))))))))) | (1273) |
02(21(13(34(44(43(35(55(x1)))))))) | → | 01(11(11(15(53(30(05(50(01(15(55(x1))))))))))) | (1274) |
02(21(13(34(44(43(35(51(x1)))))))) | → | 01(11(11(15(53(30(05(50(01(15(51(x1))))))))))) | (1275) |
02(21(13(34(44(43(35(52(x1)))))))) | → | 01(11(11(15(53(30(05(50(01(15(52(x1))))))))))) | (1276) |
02(21(13(34(44(43(35(50(x1)))))))) | → | 01(11(11(15(53(30(05(50(01(15(50(x1))))))))))) | (1277) |
02(21(13(34(44(43(35(53(x1)))))))) | → | 01(11(11(15(53(30(05(50(01(15(53(x1))))))))))) | (1278) |
52(21(13(34(44(43(35(54(x1)))))))) | → | 51(11(11(15(53(30(05(50(01(15(54(x1))))))))))) | (1297) |
52(21(13(34(44(43(35(55(x1)))))))) | → | 51(11(11(15(53(30(05(50(01(15(55(x1))))))))))) | (1298) |
52(21(13(34(44(43(35(51(x1)))))))) | → | 51(11(11(15(53(30(05(50(01(15(51(x1))))))))))) | (1299) |
52(21(13(34(44(43(35(52(x1)))))))) | → | 51(11(11(15(53(30(05(50(01(15(52(x1))))))))))) | (1300) |
52(21(13(34(44(43(35(50(x1)))))))) | → | 51(11(11(15(53(30(05(50(01(15(50(x1))))))))))) | (1301) |
52(21(13(34(44(43(35(53(x1)))))))) | → | 51(11(11(15(53(30(05(50(01(15(53(x1))))))))))) | (1302) |
21(13(34(43(34(40(05(x1))))))) | → | 20(00(04(42(22(20(03(30(05(52(25(x1))))))))))) | (1430) |
41(13(34(43(34(40(05(x1))))))) | → | 40(00(04(42(22(20(03(30(05(52(25(x1))))))))))) | (1436) |
31(13(34(43(34(40(05(x1))))))) | → | 30(00(04(42(22(20(03(30(05(52(25(x1))))))))))) | (1442) |
[11(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 + 1 · x1 |
[01(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 + 1 · x1 |
[12(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 + 1 · x1 |
[13(x1)] | = | 1 + 1 · x1 |
[34(x1)] | = | 1 + 1 · x1 |
[43(x1)] | = | 1 + 1 · x1 |
[40(x1)] | = | 1 + 1 · x1 |
[42(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 + 1 · x1 |
[25(x1)] | = | 1 · x1 |
11(13(34(43(34(40(05(x1))))))) | → | 10(00(04(42(22(20(03(30(05(52(25(x1))))))))))) | (1418) |
04(10(01(10(11(x1))))) | → | 04(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1597) |
05(10(01(10(11(x1))))) | → | 05(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1598) |
01(10(01(10(11(x1))))) | → | 01(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1599) |
02(10(01(10(11(x1))))) | → | 02(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1600) |
00(10(01(10(11(x1))))) | → | 00(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1601) |
03(10(01(10(11(x1))))) | → | 03(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1602) |
04(10(01(10(21(x1))))) | → | 04(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1603) |
05(10(01(10(21(x1))))) | → | 05(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1604) |
01(10(01(10(21(x1))))) | → | 01(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1605) |
02(10(01(10(21(x1))))) | → | 02(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1606) |
00(10(01(10(21(x1))))) | → | 00(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1607) |
03(10(01(10(21(x1))))) | → | 03(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1608) |
The TRS is overlay and locally confluent:
10Hence, it suffices to show innermost termination in the following.
04#(10(01(10(11(x1))))) | → | 04#(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1609) |
04#(10(01(10(11(x1))))) | → | 01#(00(10(21(22(22(12(x1))))))) | (1610) |
04#(10(01(10(11(x1))))) | → | 00#(10(21(22(22(12(x1)))))) | (1611) |
05#(10(01(10(11(x1))))) | → | 05#(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1612) |
05#(10(01(10(11(x1))))) | → | 01#(00(10(21(22(22(12(x1))))))) | (1613) |
05#(10(01(10(11(x1))))) | → | 00#(10(21(22(22(12(x1)))))) | (1614) |
01#(10(01(10(11(x1))))) | → | 01#(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1615) |
01#(10(01(10(11(x1))))) | → | 01#(00(10(21(22(22(12(x1))))))) | (1616) |
01#(10(01(10(11(x1))))) | → | 00#(10(21(22(22(12(x1)))))) | (1617) |
02#(10(01(10(11(x1))))) | → | 02#(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1618) |
02#(10(01(10(11(x1))))) | → | 01#(00(10(21(22(22(12(x1))))))) | (1619) |
02#(10(01(10(11(x1))))) | → | 00#(10(21(22(22(12(x1)))))) | (1620) |
00#(10(01(10(11(x1))))) | → | 00#(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1621) |
00#(10(01(10(11(x1))))) | → | 01#(00(10(21(22(22(12(x1))))))) | (1622) |
00#(10(01(10(11(x1))))) | → | 00#(10(21(22(22(12(x1)))))) | (1623) |
03#(10(01(10(11(x1))))) | → | 03#(10(11(11(01(00(10(21(22(22(12(x1))))))))))) | (1624) |
03#(10(01(10(11(x1))))) | → | 01#(00(10(21(22(22(12(x1))))))) | (1625) |
03#(10(01(10(11(x1))))) | → | 00#(10(21(22(22(12(x1)))))) | (1626) |
04#(10(01(10(21(x1))))) | → | 04#(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1627) |
04#(10(01(10(21(x1))))) | → | 01#(00(10(21(22(22(22(x1))))))) | (1628) |
04#(10(01(10(21(x1))))) | → | 00#(10(21(22(22(22(x1)))))) | (1629) |
05#(10(01(10(21(x1))))) | → | 05#(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1630) |
05#(10(01(10(21(x1))))) | → | 01#(00(10(21(22(22(22(x1))))))) | (1631) |
05#(10(01(10(21(x1))))) | → | 00#(10(21(22(22(22(x1)))))) | (1632) |
01#(10(01(10(21(x1))))) | → | 01#(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1633) |
01#(10(01(10(21(x1))))) | → | 01#(00(10(21(22(22(22(x1))))))) | (1634) |
01#(10(01(10(21(x1))))) | → | 00#(10(21(22(22(22(x1)))))) | (1635) |
02#(10(01(10(21(x1))))) | → | 02#(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1636) |
02#(10(01(10(21(x1))))) | → | 01#(00(10(21(22(22(22(x1))))))) | (1637) |
02#(10(01(10(21(x1))))) | → | 00#(10(21(22(22(22(x1)))))) | (1638) |
00#(10(01(10(21(x1))))) | → | 00#(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1639) |
00#(10(01(10(21(x1))))) | → | 01#(00(10(21(22(22(22(x1))))))) | (1640) |
00#(10(01(10(21(x1))))) | → | 00#(10(21(22(22(22(x1)))))) | (1641) |
03#(10(01(10(21(x1))))) | → | 03#(10(11(11(01(00(10(21(22(22(22(x1))))))))))) | (1642) |
03#(10(01(10(21(x1))))) | → | 01#(00(10(21(22(22(22(x1))))))) | (1643) |
03#(10(01(10(21(x1))))) | → | 00#(10(21(22(22(22(x1)))))) | (1644) |
The dependency pairs are split into 0 components.