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.