The relative rewrite relation R/S is considered where R is the following TRS
0(1(1(x1))) | → | 0(2(0(2(2(3(0(2(3(1(x1)))))))))) | (1) |
0(4(2(1(5(x1))))) | → | 3(0(4(5(3(3(2(3(3(3(x1)))))))))) | (2) |
1(1(4(1(0(x1))))) | → | 3(5(3(3(2(0(2(3(3(3(x1)))))))))) | (3) |
0(0(5(2(2(1(x1)))))) | → | 1(3(5(3(1(2(0(2(2(3(x1)))))))))) | (4) |
0(4(1(4(0(0(x1)))))) | → | 3(3(2(3(0(4(5(0(3(0(x1)))))))))) | (5) |
0(4(3(4(2(1(x1)))))) | → | 0(5(3(3(3(0(0(2(0(2(x1)))))))))) | (6) |
1(1(2(0(5(4(x1)))))) | → | 1(3(2(0(2(3(1(5(1(4(x1)))))))))) | (7) |
1(1(3(1(4(2(x1)))))) | → | 0(2(0(2(2(2(3(0(5(2(x1)))))))))) | (8) |
1(3(4(0(4(1(x1)))))) | → | 1(3(3(0(2(5(4(5(3(0(x1)))))))))) | (9) |
1(4(0(4(1(4(x1)))))) | → | 5(2(5(0(5(5(4(5(0(2(x1)))))))))) | (10) |
1(4(1(5(4(3(x1)))))) | → | 3(2(4(2(5(5(4(3(3(2(x1)))))))))) | (11) |
1(4(2(3(4(4(x1)))))) | → | 3(0(3(3(2(5(3(2(1(2(x1)))))))))) | (12) |
1(4(3(1(5(1(x1)))))) | → | 3(3(2(4(3(3(0(2(0(2(x1)))))))))) | (13) |
1(5(4(0(5(3(x1)))))) | → | 3(1(3(2(0(3(3(1(3(2(x1)))))))))) | (14) |
1(5(5(0(1(0(x1)))))) | → | 1(3(2(3(5(5(4(0(2(5(x1)))))))))) | (15) |
5(1(1(5(5(4(x1)))))) | → | 5(1(3(3(3(0(2(0(3(2(x1)))))))))) | (16) |
0(0(0(0(5(5(1(x1))))))) | → | 0(0(2(2(3(3(2(2(5(0(x1)))))))))) | (17) |
0(0(1(5(1(2(1(x1))))))) | → | 1(0(2(2(0(4(5(0(2(1(x1)))))))))) | (18) |
0(0(3(4(0(5(4(x1))))))) | → | 0(2(2(1(0(2(1(4(3(2(x1)))))))))) | (19) |
0(0(5(2(2(0(5(x1))))))) | → | 0(2(3(3(4(2(4(0(2(1(x1)))))))))) | (20) |
0(1(1(1(0(0(5(x1))))))) | → | 0(2(2(0(2(5(2(5(5(3(x1)))))))))) | (21) |
0(4(1(1(0(0(5(x1))))))) | → | 1(3(2(3(4(3(0(2(5(3(x1)))))))))) | (22) |
0(4(3(4(0(1(0(x1))))))) | → | 3(2(4(0(5(0(1(5(2(0(x1)))))))))) | (23) |
0(5(1(1(4(2(3(x1))))))) | → | 0(2(4(2(4(4(1(5(3(2(x1)))))))))) | (24) |
0(5(1(4(4(0(4(x1))))))) | → | 0(5(1(2(5(3(3(2(0(4(x1)))))))))) | (25) |
1(0(0(3(4(3(5(x1))))))) | → | 3(2(4(3(3(1(3(2(1(1(x1)))))))))) | (26) |
1(0(1(0(0(4(2(x1))))))) | → | 1(3(2(3(2(1(2(5(0(5(x1)))))))))) | (27) |
1(0(3(4(1(1(5(x1))))))) | → | 1(0(3(5(2(4(3(1(3(2(x1)))))))))) | (28) |
1(0(4(1(1(4(1(x1))))))) | → | 0(0(5(0(2(4(2(0(2(3(x1)))))))))) | (29) |
1(1(0(3(0(1(5(x1))))))) | → | 0(2(0(2(0(2(0(4(5(1(x1)))))))))) | (30) |
1(1(1(3(1(1(4(x1))))))) | → | 3(1(2(3(3(0(2(0(5(2(x1)))))))))) | (31) |
1(1(1(4(0(5(0(x1))))))) | → | 3(5(5(2(2(4(0(2(0(0(x1)))))))))) | (32) |
1(1(1(5(4(0(5(x1))))))) | → | 3(4(3(5(3(3(2(5(3(3(x1)))))))))) | (33) |
1(1(4(0(5(1(4(x1))))))) | → | 4(2(2(3(0(3(2(5(0(2(x1)))))))))) | (34) |
1(1(4(2(0(4(3(x1))))))) | → | 3(1(3(4(4(3(0(2(3(3(x1)))))))))) | (35) |
1(3(4(0(5(1(5(x1))))))) | → | 1(3(3(5(0(2(0(3(3(1(x1)))))))))) | (36) |
1(3(5(0(0(0(0(x1))))))) | → | 3(3(3(3(5(5(3(2(0(1(x1)))))))))) | (37) |
1(4(0(0(0(1(5(x1))))))) | → | 3(3(0(4(4(0(3(1(1(3(x1)))))))))) | (38) |
1(4(0(0(5(4(4(x1))))))) | → | 2(2(4(0(4(2(5(3(3(2(x1)))))))))) | (39) |
1(4(1(1(1(1(1(x1))))))) | → | 4(1(0(2(2(1(2(5(1(3(x1)))))))))) | (40) |
1(4(2(1(1(1(1(x1))))))) | → | 1(5(2(4(0(2(4(5(0(1(x1)))))))))) | (41) |
1(4(2(1(3(4(3(x1))))))) | → | 3(1(3(2(3(3(5(2(5(1(x1)))))))))) | (42) |
1(4(3(0(0(4(1(x1))))))) | → | 5(5(2(4(2(5(2(2(4(3(x1)))))))))) | (43) |
2(0(0(1(1(1(1(x1))))))) | → | 2(1(5(4(5(5(0(2(2(1(x1)))))))))) | (44) |
2(0(4(0(0(0(0(x1))))))) | → | 2(5(2(2(2(5(4(2(0(0(x1)))))))))) | (45) |
2(1(1(3(5(1(4(x1))))))) | → | 2(1(1(3(2(2(3(5(0(2(x1)))))))))) | (46) |
2(1(4(0(1(4(5(x1))))))) | → | 2(4(5(3(3(2(3(3(3(5(x1)))))))))) | (47) |
3(0(0(1(1(4(3(x1))))))) | → | 0(5(3(1(3(2(0(2(4(3(x1)))))))))) | (48) |
3(0(0(5(4(4(4(x1))))))) | → | 3(3(1(3(2(3(0(3(3(1(x1)))))))))) | (49) |
3(0(4(1(4(0(0(x1))))))) | → | 0(4(0(2(2(2(0(5(5(0(x1)))))))))) | (50) |
3(4(3(4(3(4(0(x1))))))) | → | 3(5(5(1(0(2(4(3(2(0(x1)))))))))) | (51) |
3(5(1(4(0(1(4(x1))))))) | → | 0(3(2(5(0(2(2(2(0(2(x1)))))))))) | (52) |
4(0(1(1(0(5(1(x1))))))) | → | 4(3(2(5(2(1(1(3(3(2(x1)))))))))) | (53) |
4(1(1(2(0(4(1(x1))))))) | → | 4(0(2(4(0(0(2(0(2(3(x1)))))))))) | (54) |
4(1(5(0(1(0(1(x1))))))) | → | 4(3(0(3(5(5(2(4(0(2(x1)))))))))) | (55) |
5(1(2(3(4(4(5(x1))))))) | → | 5(4(0(2(0(2(1(2(4(5(x1)))))))))) | (56) |
5(3(1(4(4(1(1(x1))))))) | → | 5(0(2(5(2(5(0(2(4(1(x1)))))))))) | (57) |
and S is the following TRS.
3(3(4(0(4(x1))))) | → | 0(2(1(2(0(2(2(2(2(1(x1)))))))))) | (58) |
1(0(1(1(5(x1))))) | → | 1(3(2(3(2(2(2(4(0(3(x1)))))))))) | (59) |
4(2(0(4(5(x1))))) | → | 5(4(0(2(3(5(3(3(3(3(x1)))))))))) | (60) |
1(1(0(x1))) | → | 1(3(2(0(3(2(2(0(2(0(x1)))))))))) | (61) |
5(1(2(4(0(x1))))) | → | 3(3(3(2(3(3(5(4(0(3(x1)))))))))) | (62) |
0(1(4(1(1(x1))))) | → | 3(3(3(2(0(2(3(3(5(3(x1)))))))))) | (63) |
1(2(2(5(0(0(x1)))))) | → | 3(2(2(0(2(1(3(5(3(1(x1)))))))))) | (64) |
0(0(4(1(4(0(x1)))))) | → | 0(3(0(5(4(0(3(2(3(3(x1)))))))))) | (65) |
1(2(4(3(4(0(x1)))))) | → | 2(0(2(0(0(3(3(3(5(0(x1)))))))))) | (66) |
4(5(0(2(1(1(x1)))))) | → | 4(1(5(1(3(2(0(2(3(1(x1)))))))))) | (67) |
2(4(1(3(1(1(x1)))))) | → | 2(5(0(3(2(2(2(0(2(0(x1)))))))))) | (68) |
1(4(0(4(3(1(x1)))))) | → | 0(3(5(4(5(2(0(3(3(1(x1)))))))))) | (69) |
4(1(4(0(4(1(x1)))))) | → | 2(0(5(4(5(5(0(5(2(5(x1)))))))))) | (70) |
3(4(5(1(4(1(x1)))))) | → | 2(3(3(4(5(5(2(4(2(3(x1)))))))))) | (71) |
4(4(3(2(4(1(x1)))))) | → | 2(1(2(3(5(2(3(3(0(3(x1)))))))))) | (72) |
1(5(1(3(4(1(x1)))))) | → | 2(0(2(0(3(3(4(2(3(3(x1)))))))))) | (73) |
3(5(0(4(5(1(x1)))))) | → | 2(3(1(3(3(0(2(3(1(3(x1)))))))))) | (74) |
0(1(0(5(5(1(x1)))))) | → | 5(2(0(4(5(5(3(2(3(1(x1)))))))))) | (75) |
4(5(5(1(1(5(x1)))))) | → | 2(3(0(2(0(3(3(3(1(5(x1)))))))))) | (76) |
1(5(5(0(0(0(0(x1))))))) | → | 0(5(2(2(3(3(2(2(0(0(x1)))))))))) | (77) |
1(2(1(5(1(0(0(x1))))))) | → | 1(2(0(5(4(0(2(2(0(1(x1)))))))))) | (78) |
4(5(0(4(3(0(0(x1))))))) | → | 2(3(4(1(2(0(1(2(2(0(x1)))))))))) | (79) |
5(0(2(2(5(0(0(x1))))))) | → | 1(2(0(4(2(4(3(3(2(0(x1)))))))))) | (80) |
5(0(0(1(1(1(0(x1))))))) | → | 3(5(5(2(5(2(0(2(2(0(x1)))))))))) | (81) |
5(0(0(1(1(4(0(x1))))))) | → | 3(5(2(0(3(4(3(2(3(1(x1)))))))))) | (82) |
0(1(0(4(3(4(0(x1))))))) | → | 0(2(5(1(0(5(0(4(2(3(x1)))))))))) | (83) |
3(2(4(1(1(5(0(x1))))))) | → | 2(3(5(1(4(4(2(4(2(0(x1)))))))))) | (84) |
4(0(4(4(1(5(0(x1))))))) | → | 4(0(2(3(3(5(2(1(5(0(x1)))))))))) | (85) |
5(3(4(3(0(0(1(x1))))))) | → | 1(1(2(3(1(3(3(4(2(3(x1)))))))))) | (86) |
2(4(0(0(1(0(1(x1))))))) | → | 5(0(5(2(1(2(3(2(3(1(x1)))))))))) | (87) |
5(1(1(4(3(0(1(x1))))))) | → | 2(3(1(3(4(2(5(3(0(1(x1)))))))))) | (88) |
1(4(1(1(4(0(1(x1))))))) | → | 3(2(0(2(4(2(0(5(0(0(x1)))))))))) | (89) |
5(1(0(3(0(1(1(x1))))))) | → | 1(5(4(0(2(0(2(0(2(0(x1)))))))))) | (90) |
4(1(1(3(1(1(1(x1))))))) | → | 2(5(0(2(0(3(3(2(1(3(x1)))))))))) | (91) |
0(5(0(4(1(1(1(x1))))))) | → | 0(0(2(0(4(2(2(5(5(3(x1)))))))))) | (92) |
5(0(4(5(1(1(1(x1))))))) | → | 3(3(5(2(3(3(5(3(4(3(x1)))))))))) | (93) |
4(1(5(0(4(1(1(x1))))))) | → | 2(0(5(2(3(0(3(2(2(4(x1)))))))))) | (94) |
3(4(0(2(4(1(1(x1))))))) | → | 3(3(2(0(3(4(4(3(1(3(x1)))))))))) | (95) |
5(1(5(0(4(3(1(x1))))))) | → | 1(3(3(0(2(0(5(3(3(1(x1)))))))))) | (96) |
0(0(0(0(5(3(1(x1))))))) | → | 1(0(2(3(5(5(3(3(3(3(x1)))))))))) | (97) |
5(1(0(0(0(4(1(x1))))))) | → | 3(1(1(3(0(4(4(0(3(3(x1)))))))))) | (98) |
4(4(5(0(0(4(1(x1))))))) | → | 2(3(3(5(2(4(0(4(2(2(x1)))))))))) | (99) |
1(1(1(1(1(4(1(x1))))))) | → | 3(1(5(2(1(2(2(0(1(4(x1)))))))))) | (100) |
1(1(1(1(2(4(1(x1))))))) | → | 1(0(5(4(2(0(4(2(5(1(x1)))))))))) | (101) |
3(4(3(1(2(4(1(x1))))))) | → | 1(5(2(5(3(3(2(3(1(3(x1)))))))))) | (102) |
1(4(0(0(3(4(1(x1))))))) | → | 3(4(2(2(5(2(4(2(5(5(x1)))))))))) | (103) |
1(1(1(1(0(0(2(x1))))))) | → | 1(2(2(0(5(5(4(5(1(2(x1)))))))))) | (104) |
0(0(0(0(4(0(2(x1))))))) | → | 0(0(2(4(5(2(2(2(5(2(x1)))))))))) | (105) |
4(1(5(3(1(1(2(x1))))))) | → | 2(0(5(3(2(2(3(1(1(2(x1)))))))))) | (106) |
5(4(1(0(4(1(2(x1))))))) | → | 5(3(3(3(2(3(3(5(4(2(x1)))))))))) | (107) |
3(4(1(1(0(0(3(x1))))))) | → | 3(4(2(0(2(3(1(3(5(0(x1)))))))))) | (108) |
4(4(4(5(0(0(3(x1))))))) | → | 1(3(3(0(3(2(3(1(3(3(x1)))))))))) | (109) |
0(0(4(1(4(0(3(x1))))))) | → | 0(5(5(0(2(2(2(0(4(0(x1)))))))))) | (110) |
0(4(3(4(3(4(3(x1))))))) | → | 0(2(3(4(2(0(1(5(5(3(x1)))))))))) | (111) |
4(1(0(4(1(5(3(x1))))))) | → | 2(0(2(2(2(0(5(2(3(0(x1)))))))))) | (112) |
1(5(0(1(1(0(4(x1))))))) | → | 2(3(3(1(1(2(5(2(3(4(x1)))))))))) | (113) |
1(4(0(2(1(1(4(x1))))))) | → | 3(2(0(2(0(0(4(2(0(4(x1)))))))))) | (114) |
1(0(1(0(5(1(4(x1))))))) | → | 2(0(4(2(5(5(3(0(3(4(x1)))))))))) | (115) |
5(4(4(3(2(1(5(x1))))))) | → | 5(4(2(1(2(0(2(0(4(5(x1)))))))))) | (116) |
1(1(4(4(1(3(5(x1))))))) | → | 1(4(2(0(5(2(5(2(0(5(x1)))))))))) | (117) |
4(0(4(3(3(x1))))) | → | 1(2(2(2(2(0(2(1(2(0(x1)))))))))) | (118) |
5(1(1(0(1(x1))))) | → | 3(0(4(2(2(2(3(2(3(1(x1)))))))))) | (119) |
5(4(0(2(4(x1))))) | → | 3(3(3(3(5(3(2(0(4(5(x1)))))))))) | (120) |
{1(☐), 0(☐), 3(☐), 2(☐), 5(☐), 4(☐)}
We obtain the transformed TRSThere are 270 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRSThere are 1620 ruless (increase limit for explicit display).
[11(x1)] | = | 1 + 1 · x1 |
[10(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 + 1 · x1 |
[13(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 + 1 · x1 |
[04(x1)] | = | 1 + 1 · x1 |
[05(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 + 1 · x1 |
[14(x1)] | = | 1 + 1 · x1 |
[40(x1)] | = | 1 + 1 · x1 |
[30(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 + 1 · x1 |
[35(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 + 1 · x1 |
[21(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 + 1 · x1 |
[12(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 + 1 · x1 |
[25(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 + 1 · x1 |
[52(x1)] | = | 1 · x1 |
[55(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
There are 1511 ruless (increase limit for explicit display).
[45(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 + 1 · x1 |
[02(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 + 1 · x1 |
[20(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 + 1 · x1 |
[52(x1)] | = | 1 · x1 |
[55(x1)] | = | 1 + 1 · x1 |
[30(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 + 1 · x1 |
[33(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 + 1 · x1 |
54(44(43(32(21(15(51(x1))))))) | → | 54(42(21(12(20(02(20(04(45(51(x1)))))))))) | (469) |
54(44(43(32(21(15(50(x1))))))) | → | 54(42(21(12(20(02(20(04(45(50(x1)))))))))) | (470) |
54(44(43(32(21(15(53(x1))))))) | → | 54(42(21(12(20(02(20(04(45(53(x1)))))))))) | (471) |
54(44(43(32(21(15(52(x1))))))) | → | 54(42(21(12(20(02(20(04(45(52(x1)))))))))) | (472) |
54(44(43(32(21(15(54(x1))))))) | → | 54(42(21(12(20(02(20(04(45(54(x1)))))))))) | (473) |
54(44(43(32(21(15(55(x1))))))) | → | 54(42(21(12(20(02(20(04(45(55(x1)))))))))) | (474) |
54(45(50(04(43(30(00(01(x1)))))))) | → | 52(23(34(41(12(20(01(12(22(20(01(x1))))))))))) | (973) |
54(45(50(04(43(30(00(00(x1)))))))) | → | 52(23(34(41(12(20(01(12(22(20(00(x1))))))))))) | (974) |
54(45(50(04(43(30(00(03(x1)))))))) | → | 52(23(34(41(12(20(01(12(22(20(03(x1))))))))))) | (975) |
54(45(50(04(43(30(00(02(x1)))))))) | → | 52(23(34(41(12(20(01(12(22(20(02(x1))))))))))) | (976) |
54(45(50(04(43(30(00(04(x1)))))))) | → | 52(23(34(41(12(20(01(12(22(20(04(x1))))))))))) | (977) |
54(45(50(04(43(30(00(05(x1)))))))) | → | 52(23(34(41(12(20(01(12(22(20(05(x1))))))))))) | (978) |
55(50(02(22(25(50(00(01(x1)))))))) | → | 51(12(20(04(42(24(43(33(32(20(01(x1))))))))))) | (1009) |
55(50(02(22(25(50(00(00(x1)))))))) | → | 51(12(20(04(42(24(43(33(32(20(00(x1))))))))))) | (1010) |
55(50(02(22(25(50(00(03(x1)))))))) | → | 51(12(20(04(42(24(43(33(32(20(03(x1))))))))))) | (1011) |
55(50(02(22(25(50(00(02(x1)))))))) | → | 51(12(20(04(42(24(43(33(32(20(02(x1))))))))))) | (1012) |
55(50(02(22(25(50(00(04(x1)))))))) | → | 51(12(20(04(42(24(43(33(32(20(04(x1))))))))))) | (1013) |
55(50(02(22(25(50(00(05(x1)))))))) | → | 51(12(20(04(42(24(43(33(32(20(05(x1))))))))))) | (1014) |
13(32(24(41(11(15(50(01(x1)))))))) | → | 12(23(35(51(14(44(42(24(42(20(01(x1))))))))))) | (1093) |
13(32(24(41(11(15(50(00(x1)))))))) | → | 12(23(35(51(14(44(42(24(42(20(00(x1))))))))))) | (1094) |
13(32(24(41(11(15(50(03(x1)))))))) | → | 12(23(35(51(14(44(42(24(42(20(03(x1))))))))))) | (1095) |
13(32(24(41(11(15(50(02(x1)))))))) | → | 12(23(35(51(14(44(42(24(42(20(02(x1))))))))))) | (1096) |
13(32(24(41(11(15(50(04(x1)))))))) | → | 12(23(35(51(14(44(42(24(42(20(04(x1))))))))))) | (1097) |
13(32(24(41(11(15(50(05(x1)))))))) | → | 12(23(35(51(14(44(42(24(42(20(05(x1))))))))))) | (1098) |
03(32(24(41(11(15(50(01(x1)))))))) | → | 02(23(35(51(14(44(42(24(42(20(01(x1))))))))))) | (1099) |
03(32(24(41(11(15(50(00(x1)))))))) | → | 02(23(35(51(14(44(42(24(42(20(00(x1))))))))))) | (1100) |
03(32(24(41(11(15(50(03(x1)))))))) | → | 02(23(35(51(14(44(42(24(42(20(03(x1))))))))))) | (1101) |
03(32(24(41(11(15(50(02(x1)))))))) | → | 02(23(35(51(14(44(42(24(42(20(02(x1))))))))))) | (1102) |
03(32(24(41(11(15(50(04(x1)))))))) | → | 02(23(35(51(14(44(42(24(42(20(04(x1))))))))))) | (1103) |
03(32(24(41(11(15(50(05(x1)))))))) | → | 02(23(35(51(14(44(42(24(42(20(05(x1))))))))))) | (1104) |
23(32(24(41(11(15(50(01(x1)))))))) | → | 22(23(35(51(14(44(42(24(42(20(01(x1))))))))))) | (1111) |
23(32(24(41(11(15(50(00(x1)))))))) | → | 22(23(35(51(14(44(42(24(42(20(00(x1))))))))))) | (1112) |
23(32(24(41(11(15(50(03(x1)))))))) | → | 22(23(35(51(14(44(42(24(42(20(03(x1))))))))))) | (1113) |
23(32(24(41(11(15(50(02(x1)))))))) | → | 22(23(35(51(14(44(42(24(42(20(02(x1))))))))))) | (1114) |
23(32(24(41(11(15(50(04(x1)))))))) | → | 22(23(35(51(14(44(42(24(42(20(04(x1))))))))))) | (1115) |
23(32(24(41(11(15(50(05(x1)))))))) | → | 22(23(35(51(14(44(42(24(42(20(05(x1))))))))))) | (1116) |
53(32(24(41(11(15(50(01(x1)))))))) | → | 52(23(35(51(14(44(42(24(42(20(01(x1))))))))))) | (1117) |
53(32(24(41(11(15(50(00(x1)))))))) | → | 52(23(35(51(14(44(42(24(42(20(00(x1))))))))))) | (1118) |
53(32(24(41(11(15(50(03(x1)))))))) | → | 52(23(35(51(14(44(42(24(42(20(03(x1))))))))))) | (1119) |
53(32(24(41(11(15(50(02(x1)))))))) | → | 52(23(35(51(14(44(42(24(42(20(02(x1))))))))))) | (1120) |
53(32(24(41(11(15(50(04(x1)))))))) | → | 52(23(35(51(14(44(42(24(42(20(04(x1))))))))))) | (1121) |
53(32(24(41(11(15(50(05(x1)))))))) | → | 52(23(35(51(14(44(42(24(42(20(05(x1))))))))))) | (1122) |
43(32(24(41(11(15(50(01(x1)))))))) | → | 42(23(35(51(14(44(42(24(42(20(01(x1))))))))))) | (1123) |
43(32(24(41(11(15(50(00(x1)))))))) | → | 42(23(35(51(14(44(42(24(42(20(00(x1))))))))))) | (1124) |
43(32(24(41(11(15(50(03(x1)))))))) | → | 42(23(35(51(14(44(42(24(42(20(03(x1))))))))))) | (1125) |
43(32(24(41(11(15(50(02(x1)))))))) | → | 42(23(35(51(14(44(42(24(42(20(02(x1))))))))))) | (1126) |
43(32(24(41(11(15(50(04(x1)))))))) | → | 42(23(35(51(14(44(42(24(42(20(04(x1))))))))))) | (1127) |
43(32(24(41(11(15(50(05(x1)))))))) | → | 42(23(35(51(14(44(42(24(42(20(05(x1))))))))))) | (1128) |
15(53(34(43(30(00(01(10(x1)))))))) | → | 11(11(12(23(31(13(33(34(42(23(30(x1))))))))))) | (1130) |
15(53(34(43(30(00(01(13(x1)))))))) | → | 11(11(12(23(31(13(33(34(42(23(33(x1))))))))))) | (1131) |
15(53(34(43(30(00(01(14(x1)))))))) | → | 11(11(12(23(31(13(33(34(42(23(34(x1))))))))))) | (1133) |
05(53(34(43(30(00(01(10(x1)))))))) | → | 01(11(12(23(31(13(33(34(42(23(30(x1))))))))))) | (1136) |
05(53(34(43(30(00(01(13(x1)))))))) | → | 01(11(12(23(31(13(33(34(42(23(33(x1))))))))))) | (1137) |
05(53(34(43(30(00(01(14(x1)))))))) | → | 01(11(12(23(31(13(33(34(42(23(34(x1))))))))))) | (1139) |
55(53(34(43(30(00(01(10(x1)))))))) | → | 51(11(12(23(31(13(33(34(42(23(30(x1))))))))))) | (1154) |
55(53(34(43(30(00(01(13(x1)))))))) | → | 51(11(12(23(31(13(33(34(42(23(33(x1))))))))))) | (1155) |
55(53(34(43(30(00(01(12(x1)))))))) | → | 51(11(12(23(31(13(33(34(42(23(32(x1))))))))))) | (1156) |
55(53(34(43(30(00(01(14(x1)))))))) | → | 51(11(12(23(31(13(33(34(42(23(34(x1))))))))))) | (1157) |
55(53(34(43(30(00(01(15(x1)))))))) | → | 51(11(12(23(31(13(33(34(42(23(35(x1))))))))))) | (1158) |
45(53(34(43(30(00(01(10(x1)))))))) | → | 41(11(12(23(31(13(33(34(42(23(30(x1))))))))))) | (1160) |
45(53(34(43(30(00(01(13(x1)))))))) | → | 41(11(12(23(31(13(33(34(42(23(33(x1))))))))))) | (1161) |
45(53(34(43(30(00(01(14(x1)))))))) | → | 41(11(12(23(31(13(33(34(42(23(34(x1))))))))))) | (1163) |
55(51(10(03(30(01(11(10(x1)))))))) | → | 51(15(54(40(02(20(02(20(02(20(00(x1))))))))))) | (1298) |
[45(x1)] | = | 1 + 1 · x1 |
[50(x1)] | = | 1 + 1 · x1 |
[02(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 + 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 + 1 · x1 |
[51(x1)] | = | 1 + 1 · x1 |
[13(x1)] | = | 1 + 1 · x1 |
[32(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 + 1 · x1 |
[12(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 + 1 · x1 |
[01(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 + 1 · x1 |
[54(x1)] | = | 1 + 1 · x1 |
[40(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 + 1 · x1 |
[04(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 + 1 · x1 |
[42(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 + 1 · x1 |
[43(x1)] | = | 1 + 1 · x1 |
[33(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 + 1 · x1 |
12(21(15(51(10(00(01(x1))))))) | → | 12(20(05(54(40(02(22(20(01(11(x1)))))))))) | (397) |
12(21(15(51(10(00(03(x1))))))) | → | 12(20(05(54(40(02(22(20(01(13(x1)))))))))) | (399) |
12(21(15(51(10(00(02(x1))))))) | → | 12(20(05(54(40(02(22(20(01(12(x1)))))))))) | (400) |
12(21(15(51(10(00(04(x1))))))) | → | 12(20(05(54(40(02(22(20(01(14(x1)))))))))) | (401) |
12(21(15(51(10(00(05(x1))))))) | → | 12(20(05(54(40(02(22(20(01(15(x1)))))))))) | (402) |
15(50(02(22(25(50(00(01(x1)))))))) | → | 11(12(20(04(42(24(43(33(32(20(01(x1))))))))))) | (985) |
15(50(02(22(25(50(00(00(x1)))))))) | → | 11(12(20(04(42(24(43(33(32(20(00(x1))))))))))) | (986) |
15(50(02(22(25(50(00(03(x1)))))))) | → | 11(12(20(04(42(24(43(33(32(20(03(x1))))))))))) | (987) |
15(50(02(22(25(50(00(02(x1)))))))) | → | 11(12(20(04(42(24(43(33(32(20(02(x1))))))))))) | (988) |
15(50(02(22(25(50(00(04(x1)))))))) | → | 11(12(20(04(42(24(43(33(32(20(04(x1))))))))))) | (989) |
15(50(02(22(25(50(00(05(x1)))))))) | → | 11(12(20(04(42(24(43(33(32(20(05(x1))))))))))) | (990) |
05(50(02(22(25(50(00(01(x1)))))))) | → | 01(12(20(04(42(24(43(33(32(20(01(x1))))))))))) | (991) |
05(50(02(22(25(50(00(00(x1)))))))) | → | 01(12(20(04(42(24(43(33(32(20(00(x1))))))))))) | (992) |
05(50(02(22(25(50(00(03(x1)))))))) | → | 01(12(20(04(42(24(43(33(32(20(03(x1))))))))))) | (993) |
05(50(02(22(25(50(00(02(x1)))))))) | → | 01(12(20(04(42(24(43(33(32(20(02(x1))))))))))) | (994) |
05(50(02(22(25(50(00(04(x1)))))))) | → | 01(12(20(04(42(24(43(33(32(20(04(x1))))))))))) | (995) |
05(50(02(22(25(50(00(05(x1)))))))) | → | 01(12(20(04(42(24(43(33(32(20(05(x1))))))))))) | (996) |
45(50(02(22(25(50(00(01(x1)))))))) | → | 41(12(20(04(42(24(43(33(32(20(01(x1))))))))))) | (1015) |
45(50(02(22(25(50(00(00(x1)))))))) | → | 41(12(20(04(42(24(43(33(32(20(00(x1))))))))))) | (1016) |
45(50(02(22(25(50(00(03(x1)))))))) | → | 41(12(20(04(42(24(43(33(32(20(03(x1))))))))))) | (1017) |
45(50(02(22(25(50(00(02(x1)))))))) | → | 41(12(20(04(42(24(43(33(32(20(02(x1))))))))))) | (1018) |
45(50(02(22(25(50(00(04(x1)))))))) | → | 41(12(20(04(42(24(43(33(32(20(04(x1))))))))))) | (1019) |
45(50(02(22(25(50(00(05(x1)))))))) | → | 41(12(20(04(42(24(43(33(32(20(05(x1))))))))))) | (1020) |
33(32(24(41(11(15(50(01(x1)))))))) | → | 32(23(35(51(14(44(42(24(42(20(01(x1))))))))))) | (1105) |
33(32(24(41(11(15(50(00(x1)))))))) | → | 32(23(35(51(14(44(42(24(42(20(00(x1))))))))))) | (1106) |
33(32(24(41(11(15(50(03(x1)))))))) | → | 32(23(35(51(14(44(42(24(42(20(03(x1))))))))))) | (1107) |
33(32(24(41(11(15(50(02(x1)))))))) | → | 32(23(35(51(14(44(42(24(42(20(02(x1))))))))))) | (1108) |
33(32(24(41(11(15(50(04(x1)))))))) | → | 32(23(35(51(14(44(42(24(42(20(04(x1))))))))))) | (1109) |
33(32(24(41(11(15(50(05(x1)))))))) | → | 32(23(35(51(14(44(42(24(42(20(05(x1))))))))))) | (1110) |
15(53(34(43(30(00(01(12(x1)))))))) | → | 11(11(12(23(31(13(33(34(42(23(32(x1))))))))))) | (1132) |
15(53(34(43(30(00(01(15(x1)))))))) | → | 11(11(12(23(31(13(33(34(42(23(35(x1))))))))))) | (1134) |
05(53(34(43(30(00(01(12(x1)))))))) | → | 01(11(12(23(31(13(33(34(42(23(32(x1))))))))))) | (1138) |
05(53(34(43(30(00(01(15(x1)))))))) | → | 01(11(12(23(31(13(33(34(42(23(35(x1))))))))))) | (1140) |
45(53(34(43(30(00(01(12(x1)))))))) | → | 41(11(12(23(31(13(33(34(42(23(32(x1))))))))))) | (1162) |
45(53(34(43(30(00(01(15(x1)))))))) | → | 41(11(12(23(31(13(33(34(42(23(35(x1))))))))))) | (1164) |
15(51(10(03(30(01(11(10(x1)))))))) | → | 11(15(54(40(02(20(02(20(02(20(00(x1))))))))))) | (1274) |
05(51(10(03(30(01(11(10(x1)))))))) | → | 01(15(54(40(02(20(02(20(02(20(00(x1))))))))))) | (1280) |
45(51(10(03(30(01(11(10(x1)))))))) | → | 41(15(54(40(02(20(02(20(02(20(00(x1))))))))))) | (1304) |
[45(x1)] | = | 1 + 1 · x1 |
[50(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 + 1 · x1 |
[21(x1)] | = | 1 + 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 + 1 · x1 |
[10(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 + 1 · x1 |
[40(x1)] | = | 1 + 1 · x1 |
[04(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 + 1 · x1 |
[33(x1)] | = | 1 + 1 · x1 |
[22(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 + 1 · x1 |
[00(x1)] | = | 1 · x1 |
45(50(02(21(11(11(x1)))))) | → | 41(15(51(13(32(20(02(23(31(11(x1)))))))))) | (385) |
45(50(02(21(11(10(x1)))))) | → | 41(15(51(13(32(20(02(23(31(10(x1)))))))))) | (386) |
45(50(02(21(11(13(x1)))))) | → | 41(15(51(13(32(20(02(23(31(13(x1)))))))))) | (387) |
45(50(02(21(11(12(x1)))))) | → | 41(15(51(13(32(20(02(23(31(12(x1)))))))))) | (388) |
45(50(02(21(11(14(x1)))))) | → | 41(15(51(13(32(20(02(23(31(14(x1)))))))))) | (389) |
45(50(02(21(11(15(x1)))))) | → | 41(15(51(13(32(20(02(23(31(15(x1)))))))))) | (390) |
54(40(04(43(33(31(x1)))))) | → | 51(12(22(22(22(20(02(21(12(20(01(x1))))))))))) | (1909) |
54(40(04(43(33(30(x1)))))) | → | 51(12(22(22(22(20(02(21(12(20(00(x1))))))))))) | (1910) |
There are no rules in the TRS. Hence, it is terminating.