The relative rewrite relation R/S is considered where R is the following TRS
0(1(1(2(x1)))) | → | 0(2(3(0(2(0(0(0(2(0(x1)))))))))) | (1) |
1(1(3(3(1(x1))))) | → | 5(3(3(2(3(0(2(2(2(0(x1)))))))))) | (2) |
1(3(3(4(4(x1))))) | → | 0(3(5(5(3(0(2(0(0(1(x1)))))))))) | (3) |
3(1(3(5(2(x1))))) | → | 5(3(1(5(3(0(0(2(2(2(x1)))))))))) | (4) |
4(2(3(3(3(x1))))) | → | 5(0(3(0(2(0(0(2(0(0(x1)))))))))) | (5) |
0(1(2(1(1(4(x1)))))) | → | 0(0(4(2(3(0(2(2(0(4(x1)))))))))) | (6) |
2(4(4(3(4(2(x1)))))) | → | 2(4(5(0(3(0(0(2(2(0(x1)))))))))) | (7) |
3(3(0(3(3(3(x1)))))) | → | 5(1(4(5(4(0(3(0(2(0(x1)))))))))) | (8) |
3(5(2(5(4(1(x1)))))) | → | 3(0(2(0(0(4(2(3(0(0(x1)))))))))) | (9) |
0(1(3(1(3(1(0(x1))))))) | → | 2(3(0(2(0(1(4(3(1(0(x1)))))))))) | (10) |
0(1(3(3(3(5(3(x1))))))) | → | 0(0(0(4(0(2(4(2(3(0(x1)))))))))) | (11) |
0(1(3(3(4(3(4(x1))))))) | → | 0(3(0(2(0(4(2(0(2(4(x1)))))))))) | (12) |
0(2(3(3(5(1(3(x1))))))) | → | 2(3(2(0(2(0(0(0(5(3(x1)))))))))) | (13) |
1(1(1(3(1(2(1(x1))))))) | → | 1(2(5(3(0(2(2(2(5(1(x1)))))))))) | (14) |
1(1(3(1(2(3(3(x1))))))) | → | 3(0(2(1(5(3(2(5(3(0(x1)))))))))) | (15) |
1(1(3(3(4(0(1(x1))))))) | → | 3(2(1(0(5(1(2(3(2(2(x1)))))))))) | (16) |
1(2(4(3(4(3(3(x1))))))) | → | 3(0(2(1(0(1(1(5(5(3(x1)))))))))) | (17) |
1(3(0(5(4(1(3(x1))))))) | → | 1(3(2(4(0(0(2(2(5(3(x1)))))))))) | (18) |
1(3(3(0(3(2(4(x1))))))) | → | 1(5(2(3(2(4(0(0(0(2(x1)))))))))) | (19) |
1(3(3(3(3(1(3(x1))))))) | → | 1(3(0(2(4(1(4(2(2(3(x1)))))))))) | (20) |
1(3(3(3(3(4(4(x1))))))) | → | 1(0(0(4(5(5(5(1(1(4(x1)))))))))) | (21) |
1(3(3(4(1(1(2(x1))))))) | → | 3(1(5(2(4(3(0(2(2(0(x1)))))))))) | (22) |
1(3(3(5(1(1(1(x1))))))) | → | 1(0(0(3(1(0(0(2(2(2(x1)))))))))) | (23) |
1(3(4(4(1(3(5(x1))))))) | → | 1(3(3(3(0(2(0(2(1(5(x1)))))))))) | (24) |
1(3(5(0(2(3(4(x1))))))) | → | 3(3(4(5(5(5(0(3(5(4(x1)))))))))) | (25) |
1(3(5(1(1(5(1(x1))))))) | → | 1(0(0(4(4(0(0(4(0(0(x1)))))))))) | (26) |
1(3(5(1(3(4(3(x1))))))) | → | 2(5(0(0(5(5(5(1(1(3(x1)))))))))) | (27) |
2(1(3(3(3(3(1(x1))))))) | → | 2(3(0(2(0(4(0(0(3(1(x1)))))))))) | (28) |
2(3(1(1(1(1(0(x1))))))) | → | 2(1(5(0(3(5(5(4(0(0(x1)))))))))) | (29) |
2(3(1(3(3(1(1(x1))))))) | → | 2(2(2(2(2(0(5(5(5(1(x1)))))))))) | (30) |
2(3(3(5(1(3(3(x1))))))) | → | 2(4(4(5(5(3(4(3(2(3(x1)))))))))) | (31) |
2(4(3(3(4(2(5(x1))))))) | → | 0(4(2(4(0(2(5(1(0(5(x1)))))))))) | (32) |
2(5(2(0(3(5(1(x1))))))) | → | 2(5(2(0(4(0(2(0(0(2(x1)))))))))) | (33) |
3(1(3(1(1(1(4(x1))))))) | → | 5(3(5(3(0(0(4(0(1(4(x1)))))))))) | (34) |
3(1(3(1(4(4(0(x1))))))) | → | 3(2(1(4(0(2(0(0(4(2(x1)))))))))) | (35) |
3(2(5(4(4(2(4(x1))))))) | → | 5(3(1(0(2(2(2(0(0(4(x1)))))))))) | (36) |
3(3(3(3(4(5(2(x1))))))) | → | 5(5(1(1(2(4(0(0(2(1(x1)))))))))) | (37) |
3(3(5(1(5(1(1(x1))))))) | → | 5(3(0(2(4(5(5(4(3(1(x1)))))))))) | (38) |
3(3(5(2(5(0(4(x1))))))) | → | 5(5(1(0(1(5(5(3(0(2(x1)))))))))) | (39) |
3(3(5(3(0(1(1(x1))))))) | → | 5(1(4(5(5(3(5(4(5(1(x1)))))))))) | (40) |
3(4(1(1(3(1(1(x1))))))) | → | 1(2(2(4(5(3(5(5(5(1(x1)))))))))) | (41) |
3(4(2(0(4(1(1(x1))))))) | → | 5(3(3(0(2(0(2(5(5(1(x1)))))))))) | (42) |
3(4(2(5(0(2(3(x1))))))) | → | 5(5(1(0(0(5(3(5(5(3(x1)))))))))) | (43) |
4(1(1(1(4(5(1(x1))))))) | → | 5(3(0(4(3(0(2(4(0(2(x1)))))))))) | (44) |
4(2(1(3(3(3(4(x1))))))) | → | 5(4(2(0(0(0(5(1(4(5(x1)))))))))) | (45) |
4(3(3(5(1(4(1(x1))))))) | → | 5(3(5(0(0(5(3(2(0(4(x1)))))))))) | (46) |
4(4(0(4(3(3(3(x1))))))) | → | 4(5(3(0(2(2(3(2(1(3(x1)))))))))) | (47) |
4(4(3(3(3(4(1(x1))))))) | → | 4(0(1(0(2(1(0(2(0(2(x1)))))))))) | (48) |
4(5(1(5(2(4(3(x1))))))) | → | 4(3(3(0(2(0(0(0(0(3(x1)))))))))) | (49) |
4(5(2(0(3(2(5(x1))))))) | → | 5(0(3(4(5(4(0(0(0(5(x1)))))))))) | (50) |
4(5(2(5(4(1(3(x1))))))) | → | 5(0(3(2(1(4(3(0(2(4(x1)))))))))) | (51) |
5(0(1(3(2(5(4(x1))))))) | → | 4(2(3(0(0(0(0(2(5(1(x1)))))))))) | (52) |
5(1(1(1(1(5(0(x1))))))) | → | 3(4(5(5(4(2(0(0(5(0(x1)))))))))) | (53) |
5(1(1(2(1(1(1(x1))))))) | → | 0(5(0(0(5(1(2(0(2(1(x1)))))))))) | (54) |
5(2(1(3(5(2(2(x1))))))) | → | 4(2(1(2(3(0(0(0(0(0(x1)))))))))) | (55) |
and S is the following TRS.
2(3(1(1(x1)))) | → | 1(4(5(5(3(0(0(2(0(0(x1)))))))))) | (56) |
0(1(1(1(3(3(3(x1))))))) | → | 3(5(4(5(3(2(1(5(2(3(x1)))))))))) | (57) |
1(1(4(5(2(1(5(x1))))))) | → | 5(1(2(1(4(0(2(0(1(5(x1)))))))))) | (58) |
3(2(1(1(3(x1))))) | → | 3(0(2(0(2(0(1(0(4(0(x1)))))))))) | (59) |
0(3(5(1(1(2(4(x1))))))) | → | 0(5(4(0(0(5(2(0(0(4(x1)))))))))) | (60) |
2(1(1(0(x1)))) | → | 0(2(0(0(0(2(0(3(2(0(x1)))))))))) | (61) |
1(3(3(1(1(x1))))) | → | 0(2(2(2(0(3(2(3(3(5(x1)))))))))) | (62) |
4(4(3(3(1(x1))))) | → | 1(0(0(2(0(3(5(5(3(0(x1)))))))))) | (63) |
2(5(3(1(3(x1))))) | → | 2(2(2(0(0(3(5(1(3(5(x1)))))))))) | (64) |
3(3(3(2(4(x1))))) | → | 0(0(2(0(0(2(0(3(0(5(x1)))))))))) | (65) |
4(1(1(2(1(0(x1)))))) | → | 4(0(2(2(0(3(2(4(0(0(x1)))))))))) | (66) |
2(4(3(4(4(2(x1)))))) | → | 0(2(2(0(0(3(0(5(4(2(x1)))))))))) | (67) |
3(3(3(0(3(3(x1)))))) | → | 0(2(0(3(0(4(5(4(1(5(x1)))))))))) | (68) |
1(4(5(2(5(3(x1)))))) | → | 0(0(3(2(4(0(0(2(0(3(x1)))))))))) | (69) |
0(1(3(1(3(1(0(x1))))))) | → | 0(1(3(4(1(0(2(0(3(2(x1)))))))))) | (70) |
3(5(3(3(3(1(0(x1))))))) | → | 0(3(2(4(2(0(4(0(0(0(x1)))))))))) | (71) |
4(3(4(3(3(1(0(x1))))))) | → | 4(2(0(2(4(0(2(0(3(0(x1)))))))))) | (72) |
3(1(5(3(3(2(0(x1))))))) | → | 3(5(0(0(0(2(0(2(3(2(x1)))))))))) | (73) |
1(2(1(3(1(1(1(x1))))))) | → | 1(5(2(2(2(0(3(5(2(1(x1)))))))))) | (74) |
3(3(2(1(3(1(1(x1))))))) | → | 0(3(5(2(3(5(1(2(0(3(x1)))))))))) | (75) |
1(0(4(3(3(1(1(x1))))))) | → | 2(2(3(2(1(5(0(1(2(3(x1)))))))))) | (76) |
3(3(4(3(4(2(1(x1))))))) | → | 3(5(5(1(1(0(1(2(0(3(x1)))))))))) | (77) |
3(1(4(5(0(3(1(x1))))))) | → | 3(5(2(2(0(0(4(2(3(1(x1)))))))))) | (78) |
4(2(3(0(3(3(1(x1))))))) | → | 2(0(0(0(4(2(3(2(5(1(x1)))))))))) | (79) |
3(1(3(3(3(3(1(x1))))))) | → | 3(2(2(4(1(4(2(0(3(1(x1)))))))))) | (80) |
4(4(3(3(3(3(1(x1))))))) | → | 4(1(1(5(5(5(4(0(0(1(x1)))))))))) | (81) |
2(1(1(4(3(3(1(x1))))))) | → | 0(2(2(0(3(4(2(5(1(3(x1)))))))))) | (82) |
1(1(1(5(3(3(1(x1))))))) | → | 2(2(2(0(0(1(3(0(0(1(x1)))))))))) | (83) |
5(3(1(4(4(3(1(x1))))))) | → | 5(1(2(0(2(0(3(3(3(1(x1)))))))))) | (84) |
4(3(2(0(5(3(1(x1))))))) | → | 4(5(3(0(5(5(5(4(3(3(x1)))))))))) | (85) |
1(5(1(1(5(3(1(x1))))))) | → | 0(0(4(0(0(4(4(0(0(1(x1)))))))))) | (86) |
3(4(3(1(5(3(1(x1))))))) | → | 3(1(1(5(5(5(0(0(5(2(x1)))))))))) | (87) |
1(3(3(3(3(1(2(x1))))))) | → | 1(3(0(0(4(0(2(0(3(2(x1)))))))))) | (88) |
0(1(1(1(1(3(2(x1))))))) | → | 0(0(4(5(5(3(0(5(1(2(x1)))))))))) | (89) |
1(1(3(3(1(3(2(x1))))))) | → | 1(5(5(5(0(2(2(2(2(2(x1)))))))))) | (90) |
3(3(1(5(3(3(2(x1))))))) | → | 3(2(3(4(3(5(5(4(4(2(x1)))))))))) | (91) |
5(2(4(3(3(4(2(x1))))))) | → | 5(0(1(5(2(0(4(2(4(0(x1)))))))))) | (92) |
1(5(3(0(2(5(2(x1))))))) | → | 2(0(0(2(0(4(0(2(5(2(x1)))))))))) | (93) |
4(1(1(1(3(1(3(x1))))))) | → | 4(1(0(4(0(0(3(5(3(5(x1)))))))))) | (94) |
0(4(4(1(3(1(3(x1))))))) | → | 2(4(0(0(2(0(4(1(2(3(x1)))))))))) | (95) |
4(2(4(4(5(2(3(x1))))))) | → | 4(0(0(2(2(2(0(1(3(5(x1)))))))))) | (96) |
2(5(4(3(3(3(3(x1))))))) | → | 1(2(0(0(4(2(1(1(5(5(x1)))))))))) | (97) |
1(1(5(1(5(3(3(x1))))))) | → | 1(3(4(5(5(4(2(0(3(5(x1)))))))))) | (98) |
4(0(5(2(5(3(3(x1))))))) | → | 2(0(3(5(5(1(0(1(5(5(x1)))))))))) | (99) |
1(1(0(3(5(3(3(x1))))))) | → | 1(5(4(5(3(5(5(4(1(5(x1)))))))))) | (100) |
1(1(3(1(1(4(3(x1))))))) | → | 1(5(5(5(3(5(4(2(2(1(x1)))))))))) | (101) |
1(1(4(0(2(4(3(x1))))))) | → | 1(5(5(2(0(2(0(3(3(5(x1)))))))))) | (102) |
3(2(0(5(2(4(3(x1))))))) | → | 3(5(5(3(5(0(0(1(5(5(x1)))))))))) | (103) |
1(5(4(1(1(1(4(x1))))))) | → | 2(0(4(2(0(3(4(0(3(5(x1)))))))))) | (104) |
4(3(3(3(1(2(4(x1))))))) | → | 5(4(1(5(0(0(0(2(4(5(x1)))))))))) | (105) |
1(4(1(5(3(3(4(x1))))))) | → | 4(0(2(3(5(0(0(5(3(5(x1)))))))))) | (106) |
3(3(3(4(0(4(4(x1))))))) | → | 3(1(2(3(2(2(0(3(5(4(x1)))))))))) | (107) |
1(4(3(3(3(4(4(x1))))))) | → | 2(0(2(0(1(2(0(1(0(4(x1)))))))))) | (108) |
3(4(2(5(1(5(4(x1))))))) | → | 3(0(0(0(0(2(0(3(3(4(x1)))))))))) | (109) |
5(2(3(0(2(5(4(x1))))))) | → | 5(0(0(0(4(5(4(3(0(5(x1)))))))))) | (110) |
3(1(4(5(2(5(4(x1))))))) | → | 4(2(0(3(4(1(2(3(0(5(x1)))))))))) | (111) |
4(5(2(3(1(0(5(x1))))))) | → | 1(5(2(0(0(0(0(3(2(4(x1)))))))))) | (112) |
0(5(1(1(1(1(5(x1))))))) | → | 0(5(0(0(2(4(5(5(4(3(x1)))))))))) | (113) |
1(1(1(2(1(1(5(x1))))))) | → | 1(2(0(2(1(5(0(0(5(0(x1)))))))))) | (114) |
2(2(5(3(1(2(5(x1))))))) | → | 0(0(0(0(0(3(2(1(2(4(x1)))))))))) | (115) |
1(1(3(2(x1)))) | → | 0(0(2(0(0(3(5(5(4(1(x1)))))))))) | (116) |
3(3(3(1(1(1(0(x1))))))) | → | 3(2(5(1(2(3(5(4(5(3(x1)))))))))) | (117) |
5(1(2(5(4(1(1(x1))))))) | → | 5(1(0(2(0(4(1(2(1(5(x1)))))))))) | (118) |
3(1(1(2(3(x1))))) | → | 0(4(0(1(0(2(0(2(0(3(x1)))))))))) | (119) |
4(2(1(1(5(3(0(x1))))))) | → | 4(0(0(2(5(0(0(4(5(0(x1)))))))))) | (120) |
{2(☐), 1(☐), 0(☐), 3(☐), 5(☐), 4(☐)}
We obtain the transformed TRSThere are 195 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRSThere are 1170 ruless (increase limit for explicit display).
[25(x1)] | = | 1 + 1 · x1 |
[53(x1)] | = | 1 + 1 · x1 |
[31(x1)] | = | 1 + 1 · x1 |
[13(x1)] | = | 1 + 1 · x1 |
[32(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[55(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 + 1 · x1 |
[30(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 + 1 · x1 |
[12(x1)] | = | 1 + 1 · x1 |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 + 1 · x1 |
[02(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 + 1 · x1 |
[42(x1)] | = | 1 + 1 · x1 |
[15(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
There are 1084 ruless (increase limit for explicit display).
[33(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 + 1 |
[42(x1)] | = | 1 · x1 + 7 |
[21(x1)] | = | 1 · x1 + 25 |
[15(x1)] | = | 1 · x1 + 17 |
[35(x1)] | = | 1 · x1 |
[55(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 + 10 |
[11(x1)] | = | 1 · x1 + 10 |
[10(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 + 6 |
[20(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 + 1 |
[13(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 + 15 |
[14(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 + 9 |
[50(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 + 18 |
[22(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 + 1 |
[02(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 + 8 |
[30(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 + 9 |
[40(x1)] | = | 1 · x1 + 21 |
[41(x1)] | = | 1 · x1 + 11 |
[25(x1)] | = | 1 · x1 |
33(34(43(34(42(21(15(x1))))))) | → | 35(55(51(11(10(01(12(20(03(35(x1)))))))))) | (320) |
33(34(43(34(42(21(13(x1))))))) | → | 35(55(51(11(10(01(12(20(03(33(x1)))))))))) | (321) |
33(34(43(34(42(21(11(x1))))))) | → | 35(55(51(11(10(01(12(20(03(31(x1)))))))))) | (322) |
33(34(43(34(42(21(14(x1))))))) | → | 35(55(51(11(10(01(12(20(03(34(x1)))))))))) | (324) |
43(32(20(05(53(31(15(x1))))))) | → | 45(53(30(05(55(55(54(43(33(35(x1)))))))))) | (350) |
43(32(20(05(53(31(13(x1))))))) | → | 45(53(30(05(55(55(54(43(33(33(x1)))))))))) | (351) |
43(32(20(05(53(31(11(x1))))))) | → | 45(53(30(05(55(55(54(43(33(31(x1)))))))))) | (352) |
43(32(20(05(53(31(14(x1))))))) | → | 45(53(30(05(55(55(54(43(33(34(x1)))))))))) | (354) |
42(24(44(45(52(23(32(x1))))))) | → | 40(00(02(22(22(20(01(13(35(52(x1)))))))))) | (397) |
42(24(44(45(52(23(35(x1))))))) | → | 40(00(02(22(22(20(01(13(35(55(x1)))))))))) | (398) |
42(24(44(45(52(23(33(x1))))))) | → | 40(00(02(22(22(20(01(13(35(53(x1)))))))))) | (399) |
42(24(44(45(52(23(30(x1))))))) | → | 40(00(02(22(22(20(01(13(35(50(x1)))))))))) | (401) |
42(24(44(45(52(23(34(x1))))))) | → | 40(00(02(22(22(20(01(13(35(54(x1)))))))))) | (402) |
32(20(05(52(24(43(32(x1))))))) | → | 35(55(53(35(50(00(01(15(55(52(x1)))))))))) | (427) |
32(20(05(52(24(43(35(x1))))))) | → | 35(55(53(35(50(00(01(15(55(55(x1)))))))))) | (428) |
32(20(05(52(24(43(33(x1))))))) | → | 35(55(53(35(50(00(01(15(55(53(x1)))))))))) | (429) |
32(20(05(52(24(43(30(x1))))))) | → | 35(55(53(35(50(00(01(15(55(50(x1)))))))))) | (431) |
32(20(05(52(24(43(34(x1))))))) | → | 35(55(53(35(50(00(01(15(55(54(x1)))))))))) | (432) |
52(23(30(02(25(54(45(x1))))))) | → | 50(00(00(04(45(54(43(30(05(55(x1)))))))))) | (446) |
52(23(30(02(25(54(43(x1))))))) | → | 50(00(00(04(45(54(43(30(05(53(x1)))))))))) | (447) |
52(23(30(02(25(54(41(x1))))))) | → | 50(00(00(04(45(54(43(30(05(51(x1)))))))))) | (448) |
52(23(30(02(25(54(40(x1))))))) | → | 50(00(00(04(45(54(43(30(05(50(x1)))))))))) | (449) |
52(23(30(02(25(54(44(x1))))))) | → | 50(00(00(04(45(54(43(30(05(54(x1)))))))))) | (450) |
14(44(43(33(31(15(x1)))))) | → | 11(10(00(02(20(03(35(55(53(30(05(x1))))))))))) | (542) |
14(44(43(33(31(14(x1)))))) | → | 11(10(00(02(20(03(35(55(53(30(04(x1))))))))))) | (546) |
34(44(43(33(31(15(x1)))))) | → | 31(10(00(02(20(03(35(55(53(30(05(x1))))))))))) | (554) |
34(44(43(33(31(14(x1)))))) | → | 31(10(00(02(20(03(35(55(53(30(04(x1))))))))))) | (558) |
41(15(54(41(11(11(14(45(x1)))))))) | → | 42(20(04(42(20(03(34(40(03(35(55(x1))))))))))) | (1142) |
41(15(54(41(11(11(14(43(x1)))))))) | → | 42(20(04(42(20(03(34(40(03(35(53(x1))))))))))) | (1143) |
41(15(54(41(11(11(14(41(x1)))))))) | → | 42(20(04(42(20(03(34(40(03(35(51(x1))))))))))) | (1144) |
41(15(54(41(11(11(14(40(x1)))))))) | → | 42(20(04(42(20(03(34(40(03(35(50(x1))))))))))) | (1145) |
41(15(54(41(11(11(14(44(x1)))))))) | → | 42(20(04(42(20(03(34(40(03(35(54(x1))))))))))) | (1146) |
23(31(14(45(52(25(54(45(x1)))))))) | → | 24(42(20(03(34(41(12(23(30(05(55(x1))))))))))) | (1256) |
23(31(14(45(52(25(54(43(x1)))))))) | → | 24(42(20(03(34(41(12(23(30(05(53(x1))))))))))) | (1257) |
23(31(14(45(52(25(54(41(x1)))))))) | → | 24(42(20(03(34(41(12(23(30(05(51(x1))))))))))) | (1258) |
23(31(14(45(52(25(54(40(x1)))))))) | → | 24(42(20(03(34(41(12(23(30(05(50(x1))))))))))) | (1259) |
23(31(14(45(52(25(54(44(x1)))))))) | → | 24(42(20(03(34(41(12(23(30(05(54(x1))))))))))) | (1260) |
03(31(14(45(52(25(54(45(x1)))))))) | → | 04(42(20(03(34(41(12(23(30(05(55(x1))))))))))) | (1268) |
03(31(14(45(52(25(54(43(x1)))))))) | → | 04(42(20(03(34(41(12(23(30(05(53(x1))))))))))) | (1269) |
03(31(14(45(52(25(54(41(x1)))))))) | → | 04(42(20(03(34(41(12(23(30(05(51(x1))))))))))) | (1270) |
03(31(14(45(52(25(54(40(x1)))))))) | → | 04(42(20(03(34(41(12(23(30(05(50(x1))))))))))) | (1271) |
03(31(14(45(52(25(54(44(x1)))))))) | → | 04(42(20(03(34(41(12(23(30(05(54(x1))))))))))) | (1272) |
14(45(52(23(31(10(05(52(x1)))))))) | → | 11(15(52(20(00(00(00(03(32(24(42(x1))))))))))) | (1297) |
34(45(52(23(31(10(05(52(x1)))))))) | → | 31(15(52(20(00(00(00(03(32(24(42(x1))))))))))) | (1309) |
[31(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 + 1 |
[03(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
31(14(45(50(03(31(12(x1))))))) | → | 35(52(22(20(00(04(42(23(31(12(x1)))))))))) | (325) |
31(14(45(50(03(31(15(x1))))))) | → | 35(52(22(20(00(04(42(23(31(15(x1)))))))))) | (326) |
31(14(45(50(03(31(13(x1))))))) | → | 35(52(22(20(00(04(42(23(31(13(x1)))))))))) | (327) |
31(14(45(50(03(31(11(x1))))))) | → | 35(52(22(20(00(04(42(23(31(11(x1)))))))))) | (328) |
31(14(45(50(03(31(10(x1))))))) | → | 35(52(22(20(00(04(42(23(31(10(x1)))))))))) | (329) |
31(14(45(50(03(31(14(x1))))))) | → | 35(52(22(20(00(04(42(23(31(14(x1)))))))))) | (330) |
[53(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 + 1 |
[12(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 1 |
[34(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
53(31(14(44(43(31(12(x1))))))) | → | 51(12(20(02(20(03(33(33(31(12(x1)))))))))) | (343) |
53(31(14(44(43(31(15(x1))))))) | → | 51(12(20(02(20(03(33(33(31(15(x1)))))))))) | (344) |
53(31(14(44(43(31(13(x1))))))) | → | 51(12(20(02(20(03(33(33(31(13(x1)))))))))) | (345) |
53(31(14(44(43(31(11(x1))))))) | → | 51(12(20(02(20(03(33(33(31(11(x1)))))))))) | (346) |
53(31(14(44(43(31(10(x1))))))) | → | 51(12(20(02(20(03(33(33(31(10(x1)))))))))) | (347) |
53(31(14(44(43(31(14(x1))))))) | → | 51(12(20(02(20(03(33(33(31(14(x1)))))))))) | (348) |
[33(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 + 1 |
[04(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 + 1 |
[13(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
33(33(34(40(04(44(42(x1))))))) | → | 31(12(23(32(22(20(03(35(54(42(x1)))))))))) | (433) |
33(33(34(40(04(44(45(x1))))))) | → | 31(12(23(32(22(20(03(35(54(45(x1)))))))))) | (434) |
33(33(34(40(04(44(43(x1))))))) | → | 31(12(23(32(22(20(03(35(54(43(x1)))))))))) | (435) |
33(33(34(40(04(44(41(x1))))))) | → | 31(12(23(32(22(20(03(35(54(41(x1)))))))))) | (436) |
33(33(34(40(04(44(40(x1))))))) | → | 31(12(23(32(22(20(03(35(54(40(x1)))))))))) | (437) |
33(33(34(40(04(44(44(x1))))))) | → | 31(12(23(32(22(20(03(35(54(44(x1)))))))))) | (438) |
[14(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 + 1 |
[23(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 + 1 |
[33(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 + 1 |
[13(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 + 1 |
[01(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
14(42(23(30(03(33(31(12(x1)))))))) | → | 12(20(00(00(04(42(23(32(25(51(12(x1))))))))))) | (829) |
14(42(23(30(03(33(31(15(x1)))))))) | → | 12(20(00(00(04(42(23(32(25(51(15(x1))))))))))) | (830) |
14(42(23(30(03(33(31(13(x1)))))))) | → | 12(20(00(00(04(42(23(32(25(51(13(x1))))))))))) | (831) |
14(42(23(30(03(33(31(11(x1)))))))) | → | 12(20(00(00(04(42(23(32(25(51(11(x1))))))))))) | (832) |
14(42(23(30(03(33(31(10(x1)))))))) | → | 12(20(00(00(04(42(23(32(25(51(10(x1))))))))))) | (833) |
14(42(23(30(03(33(31(14(x1)))))))) | → | 12(20(00(00(04(42(23(32(25(51(14(x1))))))))))) | (834) |
[44(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 + 1 |
[33(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
44(42(23(30(03(33(31(12(x1)))))))) | → | 42(20(00(00(04(42(23(32(25(51(12(x1))))))))))) | (853) |
44(42(23(30(03(33(31(15(x1)))))))) | → | 42(20(00(00(04(42(23(32(25(51(15(x1))))))))))) | (854) |
44(42(23(30(03(33(31(13(x1)))))))) | → | 42(20(00(00(04(42(23(32(25(51(13(x1))))))))))) | (855) |
44(42(23(30(03(33(31(11(x1)))))))) | → | 42(20(00(00(04(42(23(32(25(51(11(x1))))))))))) | (856) |
44(42(23(30(03(33(31(10(x1)))))))) | → | 42(20(00(00(04(42(23(32(25(51(10(x1))))))))))) | (857) |
44(42(23(30(03(33(31(14(x1)))))))) | → | 42(20(00(00(04(42(23(32(25(51(14(x1))))))))))) | (858) |
[41(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 + 1 |
[30(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
41(15(53(30(02(25(52(22(x1)))))))) | → | 42(20(00(02(20(04(40(02(25(52(22(x1))))))))))) | (997) |
41(15(53(30(02(25(52(25(x1)))))))) | → | 42(20(00(02(20(04(40(02(25(52(25(x1))))))))))) | (998) |
41(15(53(30(02(25(52(23(x1)))))))) | → | 42(20(00(02(20(04(40(02(25(52(23(x1))))))))))) | (999) |
41(15(53(30(02(25(52(21(x1)))))))) | → | 42(20(00(02(20(04(40(02(25(52(21(x1))))))))))) | (1000) |
41(15(53(30(02(25(52(20(x1)))))))) | → | 42(20(00(02(20(04(40(02(25(52(20(x1))))))))))) | (1001) |
41(15(53(30(02(25(52(24(x1)))))))) | → | 42(20(00(02(20(04(40(02(25(52(24(x1))))))))))) | (1002) |
[41(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 + 1 |
[42(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
41(14(43(33(33(34(44(42(x1)))))))) | → | 42(20(02(20(01(12(20(01(10(04(42(x1))))))))))) | (1249) |
41(14(43(33(33(34(44(45(x1)))))))) | → | 42(20(02(20(01(12(20(01(10(04(45(x1))))))))))) | (1250) |
41(14(43(33(33(34(44(43(x1)))))))) | → | 42(20(02(20(01(12(20(01(10(04(43(x1))))))))))) | (1251) |
41(14(43(33(33(34(44(41(x1)))))))) | → | 42(20(02(20(01(12(20(01(10(04(41(x1))))))))))) | (1252) |
41(14(43(33(33(34(44(40(x1)))))))) | → | 42(20(02(20(01(12(20(01(10(04(40(x1))))))))))) | (1253) |
41(14(43(33(33(34(44(44(x1)))))))) | → | 42(20(02(20(01(12(20(01(10(04(44(x1))))))))))) | (1254) |
There are no rules in the TRS. Hence, it is terminating.