The rewrite relation of the following TRS is considered.
| 1(3(3(x1))) | → | 3(5(3(2(5(0(2(4(5(4(x1)))))))))) | (1) |
| 0(3(3(3(x1)))) | → | 5(4(3(5(3(0(5(4(4(0(x1)))))))))) | (2) |
| 0(3(3(3(1(x1))))) | → | 5(4(4(0(3(1(0(5(1(0(x1)))))))))) | (3) |
| 1(2(3(3(3(x1))))) | → | 4(1(1(2(3(5(0(4(0(5(x1)))))))))) | (4) |
| 1(4(4(2(2(x1))))) | → | 1(1(2(0(1(1(1(0(2(2(x1)))))))))) | (5) |
| 0(3(3(1(4(3(x1)))))) | → | 4(4(3(0(2(3(0(3(0(0(x1)))))))))) | (6) |
| 3(3(3(3(4(0(x1)))))) | → | 3(0(0(2(1(0(5(3(5(4(x1)))))))))) | (7) |
| 4(0(1(3(4(0(x1)))))) | → | 2(2(3(0(0(0(5(0(0(0(x1)))))))))) | (8) |
| 4(1(4(4(4(1(x1)))))) | → | 4(1(0(3(3(5(5(5(4(1(x1)))))))))) | (9) |
| 0(1(3(5(2(2(3(x1))))))) | → | 0(3(0(0(5(0(0(4(4(3(x1)))))))))) | (10) |
| 0(2(3(1(3(2(5(x1))))))) | → | 0(4(3(1(2(3(2(3(2(0(x1)))))))))) | (11) |
| 1(1(3(3(5(3(1(x1))))))) | → | 3(5(0(5(3(2(5(0(0(1(x1)))))))))) | (12) |
| 3(5(2(0(1(3(3(x1))))))) | → | 3(4(3(2(3(2(4(4(5(5(x1)))))))))) | (13) |
| 4(1(4(2(4(0(1(x1))))))) | → | 5(2(2(1(0(5(5(4(5(1(x1)))))))))) | (14) |
| 4(5(1(2(4(4(4(x1))))))) | → | 4(1(1(4(5(3(0(1(0(4(x1)))))))))) | (15) |
| 5(1(4(5(3(3(3(x1))))))) | → | 5(1(4(5(3(4(4(2(3(2(x1)))))))))) | (16) |
| 3(3(1(x1))) | → | 4(5(4(2(0(5(2(3(5(3(x1)))))))))) | (17) |
| 3(3(3(0(x1)))) | → | 0(4(4(5(0(3(5(3(4(5(x1)))))))))) | (18) |
| 1(3(3(3(0(x1))))) | → | 0(1(5(0(1(3(0(4(4(5(x1)))))))))) | (19) |
| 3(3(3(2(1(x1))))) | → | 5(0(4(0(5(3(2(1(1(4(x1)))))))))) | (20) |
| 2(2(4(4(1(x1))))) | → | 2(2(0(1(1(1(0(2(1(1(x1)))))))))) | (21) |
| 3(4(1(3(3(0(x1)))))) | → | 0(0(3(0(3(2(0(3(4(4(x1)))))))))) | (22) |
| 0(4(3(3(3(3(x1)))))) | → | 4(5(3(5(0(1(2(0(0(3(x1)))))))))) | (23) |
| 0(4(3(1(0(4(x1)))))) | → | 0(0(0(5(0(0(0(3(2(2(x1)))))))))) | (24) |
| 1(4(4(4(1(4(x1)))))) | → | 1(4(5(5(5(3(3(0(1(4(x1)))))))))) | (25) |
| 3(2(2(5(3(1(0(x1))))))) | → | 3(4(4(0(0(5(0(0(3(0(x1)))))))))) | (26) |
| 5(2(3(1(3(2(0(x1))))))) | → | 0(2(3(2(3(2(1(3(4(0(x1)))))))))) | (27) |
| 1(3(5(3(3(1(1(x1))))))) | → | 1(0(0(5(2(3(5(0(5(3(x1)))))))))) | (28) |
| 3(3(1(0(2(5(3(x1))))))) | → | 5(5(4(4(2(3(2(3(4(3(x1)))))))))) | (29) |
| 1(0(4(2(4(1(4(x1))))))) | → | 1(5(4(5(5(0(1(2(2(5(x1)))))))))) | (30) |
| 4(4(4(2(1(5(4(x1))))))) | → | 4(0(1(0(3(5(4(1(1(4(x1)))))))))) | (31) |
| 3(3(3(5(4(1(5(x1))))))) | → | 2(3(2(4(4(3(5(4(1(5(x1)))))))))) | (32) |
{3(☐), 1(☐), 4(☐), 5(☐), 2(☐), 0(☐)}
We obtain the transformed TRS| 2(2(4(4(1(x1))))) | → | 2(2(0(1(1(1(0(2(1(1(x1)))))))))) | (21) |
| 0(4(3(1(0(4(x1)))))) | → | 0(0(0(5(0(0(0(3(2(2(x1)))))))))) | (24) |
| 1(4(4(4(1(4(x1)))))) | → | 1(4(5(5(5(3(3(0(1(4(x1)))))))))) | (25) |
| 3(2(2(5(3(1(0(x1))))))) | → | 3(4(4(0(0(5(0(0(3(0(x1)))))))))) | (26) |
| 1(3(5(3(3(1(1(x1))))))) | → | 1(0(0(5(2(3(5(0(5(3(x1)))))))))) | (28) |
| 1(0(4(2(4(1(4(x1))))))) | → | 1(5(4(5(5(0(1(2(2(5(x1)))))))))) | (30) |
| 4(4(4(2(1(5(4(x1))))))) | → | 4(0(1(0(3(5(4(1(1(4(x1)))))))))) | (31) |
| 3(3(3(1(x1)))) | → | 3(4(5(4(2(0(5(2(3(5(3(x1))))))))))) | (33) |
| 1(3(3(1(x1)))) | → | 1(4(5(4(2(0(5(2(3(5(3(x1))))))))))) | (34) |
| 4(3(3(1(x1)))) | → | 4(4(5(4(2(0(5(2(3(5(3(x1))))))))))) | (35) |
| 5(3(3(1(x1)))) | → | 5(4(5(4(2(0(5(2(3(5(3(x1))))))))))) | (36) |
| 2(3(3(1(x1)))) | → | 2(4(5(4(2(0(5(2(3(5(3(x1))))))))))) | (37) |
| 0(3(3(1(x1)))) | → | 0(4(5(4(2(0(5(2(3(5(3(x1))))))))))) | (38) |
| 3(3(3(3(0(x1))))) | → | 3(0(4(4(5(0(3(5(3(4(5(x1))))))))))) | (39) |
| 1(3(3(3(0(x1))))) | → | 1(0(4(4(5(0(3(5(3(4(5(x1))))))))))) | (40) |
| 4(3(3(3(0(x1))))) | → | 4(0(4(4(5(0(3(5(3(4(5(x1))))))))))) | (41) |
| 5(3(3(3(0(x1))))) | → | 5(0(4(4(5(0(3(5(3(4(5(x1))))))))))) | (42) |
| 2(3(3(3(0(x1))))) | → | 2(0(4(4(5(0(3(5(3(4(5(x1))))))))))) | (43) |
| 0(3(3(3(0(x1))))) | → | 0(0(4(4(5(0(3(5(3(4(5(x1))))))))))) | (44) |
| 3(1(3(3(3(0(x1)))))) | → | 3(0(1(5(0(1(3(0(4(4(5(x1))))))))))) | (45) |
| 1(1(3(3(3(0(x1)))))) | → | 1(0(1(5(0(1(3(0(4(4(5(x1))))))))))) | (46) |
| 4(1(3(3(3(0(x1)))))) | → | 4(0(1(5(0(1(3(0(4(4(5(x1))))))))))) | (47) |
| 5(1(3(3(3(0(x1)))))) | → | 5(0(1(5(0(1(3(0(4(4(5(x1))))))))))) | (48) |
| 2(1(3(3(3(0(x1)))))) | → | 2(0(1(5(0(1(3(0(4(4(5(x1))))))))))) | (49) |
| 0(1(3(3(3(0(x1)))))) | → | 0(0(1(5(0(1(3(0(4(4(5(x1))))))))))) | (50) |
| 3(3(3(3(2(1(x1)))))) | → | 3(5(0(4(0(5(3(2(1(1(4(x1))))))))))) | (51) |
| 1(3(3(3(2(1(x1)))))) | → | 1(5(0(4(0(5(3(2(1(1(4(x1))))))))))) | (52) |
| 4(3(3(3(2(1(x1)))))) | → | 4(5(0(4(0(5(3(2(1(1(4(x1))))))))))) | (53) |
| 5(3(3(3(2(1(x1)))))) | → | 5(5(0(4(0(5(3(2(1(1(4(x1))))))))))) | (54) |
| 2(3(3(3(2(1(x1)))))) | → | 2(5(0(4(0(5(3(2(1(1(4(x1))))))))))) | (55) |
| 0(3(3(3(2(1(x1)))))) | → | 0(5(0(4(0(5(3(2(1(1(4(x1))))))))))) | (56) |
| 3(3(4(1(3(3(0(x1))))))) | → | 3(0(0(3(0(3(2(0(3(4(4(x1))))))))))) | (57) |
| 1(3(4(1(3(3(0(x1))))))) | → | 1(0(0(3(0(3(2(0(3(4(4(x1))))))))))) | (58) |
| 4(3(4(1(3(3(0(x1))))))) | → | 4(0(0(3(0(3(2(0(3(4(4(x1))))))))))) | (59) |
| 5(3(4(1(3(3(0(x1))))))) | → | 5(0(0(3(0(3(2(0(3(4(4(x1))))))))))) | (60) |
| 2(3(4(1(3(3(0(x1))))))) | → | 2(0(0(3(0(3(2(0(3(4(4(x1))))))))))) | (61) |
| 0(3(4(1(3(3(0(x1))))))) | → | 0(0(0(3(0(3(2(0(3(4(4(x1))))))))))) | (62) |
| 3(0(4(3(3(3(3(x1))))))) | → | 3(4(5(3(5(0(1(2(0(0(3(x1))))))))))) | (63) |
| 1(0(4(3(3(3(3(x1))))))) | → | 1(4(5(3(5(0(1(2(0(0(3(x1))))))))))) | (64) |
| 4(0(4(3(3(3(3(x1))))))) | → | 4(4(5(3(5(0(1(2(0(0(3(x1))))))))))) | (65) |
| 5(0(4(3(3(3(3(x1))))))) | → | 5(4(5(3(5(0(1(2(0(0(3(x1))))))))))) | (66) |
| 2(0(4(3(3(3(3(x1))))))) | → | 2(4(5(3(5(0(1(2(0(0(3(x1))))))))))) | (67) |
| 0(0(4(3(3(3(3(x1))))))) | → | 0(4(5(3(5(0(1(2(0(0(3(x1))))))))))) | (68) |
| 3(5(2(3(1(3(2(0(x1)))))))) | → | 3(0(2(3(2(3(2(1(3(4(0(x1))))))))))) | (69) |
| 1(5(2(3(1(3(2(0(x1)))))))) | → | 1(0(2(3(2(3(2(1(3(4(0(x1))))))))))) | (70) |
| 4(5(2(3(1(3(2(0(x1)))))))) | → | 4(0(2(3(2(3(2(1(3(4(0(x1))))))))))) | (71) |
| 5(5(2(3(1(3(2(0(x1)))))))) | → | 5(0(2(3(2(3(2(1(3(4(0(x1))))))))))) | (72) |
| 2(5(2(3(1(3(2(0(x1)))))))) | → | 2(0(2(3(2(3(2(1(3(4(0(x1))))))))))) | (73) |
| 0(5(2(3(1(3(2(0(x1)))))))) | → | 0(0(2(3(2(3(2(1(3(4(0(x1))))))))))) | (74) |
| 3(3(3(1(0(2(5(3(x1)))))))) | → | 3(5(5(4(4(2(3(2(3(4(3(x1))))))))))) | (75) |
| 1(3(3(1(0(2(5(3(x1)))))))) | → | 1(5(5(4(4(2(3(2(3(4(3(x1))))))))))) | (76) |
| 4(3(3(1(0(2(5(3(x1)))))))) | → | 4(5(5(4(4(2(3(2(3(4(3(x1))))))))))) | (77) |
| 5(3(3(1(0(2(5(3(x1)))))))) | → | 5(5(5(4(4(2(3(2(3(4(3(x1))))))))))) | (78) |
| 2(3(3(1(0(2(5(3(x1)))))))) | → | 2(5(5(4(4(2(3(2(3(4(3(x1))))))))))) | (79) |
| 0(3(3(1(0(2(5(3(x1)))))))) | → | 0(5(5(4(4(2(3(2(3(4(3(x1))))))))))) | (80) |
| 3(3(3(3(5(4(1(5(x1)))))))) | → | 3(2(3(2(4(4(3(5(4(1(5(x1))))))))))) | (81) |
| 1(3(3(3(5(4(1(5(x1)))))))) | → | 1(2(3(2(4(4(3(5(4(1(5(x1))))))))))) | (82) |
| 4(3(3(3(5(4(1(5(x1)))))))) | → | 4(2(3(2(4(4(3(5(4(1(5(x1))))))))))) | (83) |
| 5(3(3(3(5(4(1(5(x1)))))))) | → | 5(2(3(2(4(4(3(5(4(1(5(x1))))))))))) | (84) |
| 2(3(3(3(5(4(1(5(x1)))))))) | → | 2(2(3(2(4(4(3(5(4(1(5(x1))))))))))) | (85) |
| 0(3(3(3(5(4(1(5(x1)))))))) | → | 0(2(3(2(4(4(3(5(4(1(5(x1))))))))))) | (86) |
Root-labeling is applied.
We obtain the labeled TRSThere are 366 ruless (increase limit for explicit display).
| [22(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 + 1 |
| [44(x1)] | = | 1 · x1 + 56 |
| [41(x1)] | = | 1 · x1 + 34 |
| [12(x1)] | = | 1 · x1 + 82 |
| [20(x1)] | = | 1 · x1 |
| [01(x1)] | = | 1 · x1 + 6 |
| [11(x1)] | = | 1 · x1 + 5 |
| [10(x1)] | = | 1 · x1 + 6 |
| [02(x1)] | = | 1 · x1 |
| [21(x1)] | = | 1 · x1 |
| [14(x1)] | = | 1 · x1 + 99 |
| [13(x1)] | = | 1 · x1 + 82 |
| [15(x1)] | = | 1 · x1 + 82 |
| [04(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 + 39 |
| [31(x1)] | = | 1 · x1 + 147 |
| [42(x1)] | = | 1 · x1 + 39 |
| [00(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 + 96 |
| [40(x1)] | = | 1 · x1 + 35 |
| [23(x1)] | = | 1 · x1 |
| [45(x1)] | = | 1 · x1 + 39 |
| [25(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 + 1 |
| [53(x1)] | = | 1 · x1 + 1 |
| [33(x1)] | = | 1 · x1 + 96 |
| [30(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 + 17 |
| [35(x1)] | = | 1 · x1 + 1 |
| [52(x1)] | = | 1 · x1 + 1 |
| [54(x1)] | = | 1 · x1 + 2 |
| [51(x1)] | = | 1 · x1 |
There are 286 ruless (increase limit for explicit display).
| [11(x1)] | = | 1 · x1 + 1 |
| [13(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [04(x1)] | = | 1 · x1 |
| [10(x1)] | = | 1 · x1 |
| [01(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [45(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 + 1 |
| [40(x1)] | = | 1 · x1 |
| [25(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [20(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| [21(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [00(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| 11(13(33(33(30(04(x1)))))) | → | 10(01(15(50(01(13(30(04(44(45(54(x1))))))))))) | (208) |
| 41(13(33(33(30(04(x1)))))) | → | 40(01(15(50(01(13(30(04(44(45(54(x1))))))))))) | (214) |
| [25(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 + 1 |
| [13(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [20(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| [21(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [40(x1)] | = | 1 · x1 |
| [04(x1)] | = | 1 · x1 |
| [01(x1)] | = | 1 · x1 |
| [00(x1)] | = | 1 · x1 + 1 |
| [03(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 |
| [10(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 + 1 |
| [44(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [45(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| 25(52(23(31(13(32(20(02(x1)))))))) | → | 20(02(23(32(23(32(21(13(34(40(02(x1))))))))))) | (369) |
| 25(52(23(31(13(32(20(04(x1)))))))) | → | 20(02(23(32(23(32(21(13(34(40(04(x1))))))))))) | (370) |
| 25(52(23(31(13(32(20(01(x1)))))))) | → | 20(02(23(32(23(32(21(13(34(40(01(x1))))))))))) | (371) |
| 25(52(23(31(13(32(20(00(x1)))))))) | → | 20(02(23(32(23(32(21(13(34(40(00(x1))))))))))) | (372) |
| 25(52(23(31(13(32(20(03(x1)))))))) | → | 20(02(23(32(23(32(21(13(34(40(03(x1))))))))))) | (373) |
| 25(52(23(31(13(32(20(05(x1)))))))) | → | 20(02(23(32(23(32(21(13(34(40(05(x1))))))))))) | (374) |
| [05(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 |
| [13(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [20(x1)] | = | 1 · x1 + 1 |
| [02(x1)] | = | 1 · x1 |
| [00(x1)] | = | 1 · x1 |
| [21(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [40(x1)] | = | 1 · x1 |
| [04(x1)] | = | 1 · x1 |
| [01(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 |
| [10(x1)] | = | 1 · x1 |
| [25(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [45(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| 05(52(23(31(13(32(20(02(x1)))))))) | → | 00(02(23(32(23(32(21(13(34(40(02(x1))))))))))) | (375) |
| 05(52(23(31(13(32(20(04(x1)))))))) | → | 00(02(23(32(23(32(21(13(34(40(04(x1))))))))))) | (376) |
| 05(52(23(31(13(32(20(01(x1)))))))) | → | 00(02(23(32(23(32(21(13(34(40(01(x1))))))))))) | (377) |
| 05(52(23(31(13(32(20(00(x1)))))))) | → | 00(02(23(32(23(32(21(13(34(40(00(x1))))))))))) | (378) |
| 05(52(23(31(13(32(20(03(x1)))))))) | → | 00(02(23(32(23(32(21(13(34(40(03(x1))))))))))) | (379) |
| 05(52(23(31(13(32(20(05(x1)))))))) | → | 00(02(23(32(23(32(21(13(34(40(05(x1))))))))))) | (380) |
| [13(x1)] | = | 1 · x1 + 1 |
| [33(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 |
| [10(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| [25(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [45(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 + 1 |
| [22(x1)] | = | 1 · x1 |
| 13(33(31(10(02(25(53(32(x1)))))))) | → | 15(55(54(44(42(23(32(23(34(43(32(x1))))))))))) | (387) |
| 13(33(31(10(02(25(53(34(x1)))))))) | → | 15(55(54(44(42(23(32(23(34(43(34(x1))))))))))) | (388) |
| 13(33(31(10(02(25(53(31(x1)))))))) | → | 15(55(54(44(42(23(32(23(34(43(31(x1))))))))))) | (389) |
| 13(33(31(10(02(25(53(30(x1)))))))) | → | 15(55(54(44(42(23(32(23(34(43(30(x1))))))))))) | (390) |
| 13(33(31(10(02(25(53(33(x1)))))))) | → | 15(55(54(44(42(23(32(23(34(43(33(x1))))))))))) | (391) |
| 13(33(31(10(02(25(53(35(x1)))))))) | → | 15(55(54(44(42(23(32(23(34(43(35(x1))))))))))) | (392) |
| [43(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 + 1 |
| [10(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| [25(x1)] | = | 1 · x1 + 1 |
| [53(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [45(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 + 1 |
| [54(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 + 1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [13(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| 43(33(31(10(02(25(53(32(x1)))))))) | → | 45(55(54(44(42(23(32(23(34(43(32(x1))))))))))) | (393) |
| 43(33(31(10(02(25(53(34(x1)))))))) | → | 45(55(54(44(42(23(32(23(34(43(34(x1))))))))))) | (394) |
| 43(33(31(10(02(25(53(31(x1)))))))) | → | 45(55(54(44(42(23(32(23(34(43(31(x1))))))))))) | (395) |
| 43(33(31(10(02(25(53(30(x1)))))))) | → | 45(55(54(44(42(23(32(23(34(43(30(x1))))))))))) | (396) |
| 43(33(31(10(02(25(53(33(x1)))))))) | → | 45(55(54(44(42(23(32(23(34(43(33(x1))))))))))) | (397) |
| 43(33(31(10(02(25(53(35(x1)))))))) | → | 45(55(54(44(42(23(32(23(34(43(35(x1))))))))))) | (398) |
| [53(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 |
| [10(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| [25(x1)] | = | 1 · x1 + 1 |
| [32(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 + 1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [13(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| 53(33(31(10(02(25(53(32(x1)))))))) | → | 55(55(54(44(42(23(32(23(34(43(32(x1))))))))))) | (399) |
| 53(33(31(10(02(25(53(34(x1)))))))) | → | 55(55(54(44(42(23(32(23(34(43(34(x1))))))))))) | (400) |
| 53(33(31(10(02(25(53(31(x1)))))))) | → | 55(55(54(44(42(23(32(23(34(43(31(x1))))))))))) | (401) |
| 53(33(31(10(02(25(53(30(x1)))))))) | → | 55(55(54(44(42(23(32(23(34(43(30(x1))))))))))) | (402) |
| 53(33(31(10(02(25(53(33(x1)))))))) | → | 55(55(54(44(42(23(32(23(34(43(33(x1))))))))))) | (403) |
| 53(33(31(10(02(25(53(35(x1)))))))) | → | 55(55(54(44(42(23(32(23(34(43(35(x1))))))))))) | (404) |
| [23(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 |
| [10(x1)] | = | 1 · x1 + 1 |
| [02(x1)] | = | 1 · x1 |
| [25(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 + 1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [13(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| 23(33(31(10(02(25(53(32(x1)))))))) | → | 25(55(54(44(42(23(32(23(34(43(32(x1))))))))))) | (405) |
| 23(33(31(10(02(25(53(34(x1)))))))) | → | 25(55(54(44(42(23(32(23(34(43(34(x1))))))))))) | (406) |
| 23(33(31(10(02(25(53(31(x1)))))))) | → | 25(55(54(44(42(23(32(23(34(43(31(x1))))))))))) | (407) |
| 23(33(31(10(02(25(53(30(x1)))))))) | → | 25(55(54(44(42(23(32(23(34(43(30(x1))))))))))) | (408) |
| 23(33(31(10(02(25(53(33(x1)))))))) | → | 25(55(54(44(42(23(32(23(34(43(33(x1))))))))))) | (409) |
| 23(33(31(10(02(25(53(35(x1)))))))) | → | 25(55(54(44(42(23(32(23(34(43(35(x1))))))))))) | (410) |
| [03(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 |
| [31(x1)] | = | 1 · x1 |
| [10(x1)] | = | 1 · x1 + 1 |
| [02(x1)] | = | 1 · x1 |
| [25(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [05(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [34(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [30(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [13(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| 03(33(31(10(02(25(53(32(x1)))))))) | → | 05(55(54(44(42(23(32(23(34(43(32(x1))))))))))) | (411) |
| 03(33(31(10(02(25(53(34(x1)))))))) | → | 05(55(54(44(42(23(32(23(34(43(34(x1))))))))))) | (412) |
| 03(33(31(10(02(25(53(31(x1)))))))) | → | 05(55(54(44(42(23(32(23(34(43(31(x1))))))))))) | (413) |
| 03(33(31(10(02(25(53(30(x1)))))))) | → | 05(55(54(44(42(23(32(23(34(43(30(x1))))))))))) | (414) |
| 03(33(31(10(02(25(53(33(x1)))))))) | → | 05(55(54(44(42(23(32(23(34(43(33(x1))))))))))) | (415) |
| 03(33(31(10(02(25(53(35(x1)))))))) | → | 05(55(54(44(42(23(32(23(34(43(35(x1))))))))))) | (416) |
| [33(x1)] | = | 1 · x1 + 1 |
| [35(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 + 2 |
| [44(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [13(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| 33(33(33(35(54(41(15(52(x1)))))))) | → | 32(23(32(24(44(43(35(54(41(15(52(x1))))))))))) | (417) |
| 33(33(33(35(54(41(15(54(x1)))))))) | → | 32(23(32(24(44(43(35(54(41(15(54(x1))))))))))) | (418) |
| 33(33(33(35(54(41(15(51(x1)))))))) | → | 32(23(32(24(44(43(35(54(41(15(51(x1))))))))))) | (419) |
| 33(33(33(35(54(41(15(50(x1)))))))) | → | 32(23(32(24(44(43(35(54(41(15(50(x1))))))))))) | (420) |
| 33(33(33(35(54(41(15(53(x1)))))))) | → | 32(23(32(24(44(43(35(54(41(15(53(x1))))))))))) | (421) |
| 33(33(33(35(54(41(15(55(x1)))))))) | → | 32(23(32(24(44(43(35(54(41(15(55(x1))))))))))) | (422) |
| [13(x1)] | = | 1 · x1 + 1 |
| [33(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [12(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [42(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| 13(33(33(35(54(41(15(52(x1)))))))) | → | 12(23(32(24(44(43(35(54(41(15(52(x1))))))))))) | (423) |
| 13(33(33(35(54(41(15(54(x1)))))))) | → | 12(23(32(24(44(43(35(54(41(15(54(x1))))))))))) | (424) |
| 13(33(33(35(54(41(15(51(x1)))))))) | → | 12(23(32(24(44(43(35(54(41(15(51(x1))))))))))) | (425) |
| 13(33(33(35(54(41(15(50(x1)))))))) | → | 12(23(32(24(44(43(35(54(41(15(50(x1))))))))))) | (426) |
| 13(33(33(35(54(41(15(53(x1)))))))) | → | 12(23(32(24(44(43(35(54(41(15(53(x1))))))))))) | (427) |
| 13(33(33(35(54(41(15(55(x1)))))))) | → | 12(23(32(24(44(43(35(54(41(15(55(x1))))))))))) | (428) |
| [43(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 + 1 |
| [35(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 + 1 |
| [42(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 + 1 |
| [24(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 + 1 |
| [03(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 + 1 |
| 43(33(33(35(54(41(15(52(x1)))))))) | → | 42(23(32(24(44(43(35(54(41(15(52(x1))))))))))) | (429) |
| 43(33(33(35(54(41(15(54(x1)))))))) | → | 42(23(32(24(44(43(35(54(41(15(54(x1))))))))))) | (430) |
| 43(33(33(35(54(41(15(51(x1)))))))) | → | 42(23(32(24(44(43(35(54(41(15(51(x1))))))))))) | (431) |
| 43(33(33(35(54(41(15(50(x1)))))))) | → | 42(23(32(24(44(43(35(54(41(15(50(x1))))))))))) | (432) |
| 43(33(33(35(54(41(15(53(x1)))))))) | → | 42(23(32(24(44(43(35(54(41(15(53(x1))))))))))) | (433) |
| 43(33(33(35(54(41(15(55(x1)))))))) | → | 42(23(32(24(44(43(35(54(41(15(55(x1))))))))))) | (434) |
| [53(x1)] | = | 1 · x1 + 1 |
| [33(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| 53(33(33(35(54(41(15(52(x1)))))))) | → | 52(23(32(24(44(43(35(54(41(15(52(x1))))))))))) | (435) |
| 53(33(33(35(54(41(15(54(x1)))))))) | → | 52(23(32(24(44(43(35(54(41(15(54(x1))))))))))) | (436) |
| 53(33(33(35(54(41(15(51(x1)))))))) | → | 52(23(32(24(44(43(35(54(41(15(51(x1))))))))))) | (437) |
| 53(33(33(35(54(41(15(50(x1)))))))) | → | 52(23(32(24(44(43(35(54(41(15(50(x1))))))))))) | (438) |
| 53(33(33(35(54(41(15(53(x1)))))))) | → | 52(23(32(24(44(43(35(54(41(15(53(x1))))))))))) | (439) |
| 53(33(33(35(54(41(15(55(x1)))))))) | → | 52(23(32(24(44(43(35(54(41(15(55(x1))))))))))) | (440) |
| [23(x1)] | = | 1 · x1 |
| [33(x1)] | = | 1 · x1 + 1 |
| [35(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [22(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 + 1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| [03(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 + 1 |
| 23(33(33(35(54(41(15(52(x1)))))))) | → | 22(23(32(24(44(43(35(54(41(15(52(x1))))))))))) | (441) |
| 23(33(33(35(54(41(15(54(x1)))))))) | → | 22(23(32(24(44(43(35(54(41(15(54(x1))))))))))) | (442) |
| 23(33(33(35(54(41(15(51(x1)))))))) | → | 22(23(32(24(44(43(35(54(41(15(51(x1))))))))))) | (443) |
| 23(33(33(35(54(41(15(50(x1)))))))) | → | 22(23(32(24(44(43(35(54(41(15(50(x1))))))))))) | (444) |
| 23(33(33(35(54(41(15(53(x1)))))))) | → | 22(23(32(24(44(43(35(54(41(15(53(x1))))))))))) | (445) |
| 23(33(33(35(54(41(15(55(x1)))))))) | → | 22(23(32(24(44(43(35(54(41(15(55(x1))))))))))) | (446) |
| [03(x1)] | = | 1 · x1 + 1 |
| [33(x1)] | = | 1 · x1 |
| [35(x1)] | = | 1 · x1 |
| [54(x1)] | = | 1 · x1 |
| [41(x1)] | = | 1 · x1 |
| [15(x1)] | = | 1 · x1 |
| [52(x1)] | = | 1 · x1 |
| [02(x1)] | = | 1 · x1 |
| [23(x1)] | = | 1 · x1 |
| [32(x1)] | = | 1 · x1 |
| [24(x1)] | = | 1 · x1 |
| [44(x1)] | = | 1 · x1 |
| [43(x1)] | = | 1 · x1 |
| [51(x1)] | = | 1 · x1 |
| [50(x1)] | = | 1 · x1 |
| [53(x1)] | = | 1 · x1 |
| [55(x1)] | = | 1 · x1 |
| 03(33(33(35(54(41(15(52(x1)))))))) | → | 02(23(32(24(44(43(35(54(41(15(52(x1))))))))))) | (447) |
| 03(33(33(35(54(41(15(54(x1)))))))) | → | 02(23(32(24(44(43(35(54(41(15(54(x1))))))))))) | (448) |
| 03(33(33(35(54(41(15(51(x1)))))))) | → | 02(23(32(24(44(43(35(54(41(15(51(x1))))))))))) | (449) |
| 03(33(33(35(54(41(15(50(x1)))))))) | → | 02(23(32(24(44(43(35(54(41(15(50(x1))))))))))) | (450) |
| 03(33(33(35(54(41(15(53(x1)))))))) | → | 02(23(32(24(44(43(35(54(41(15(53(x1))))))))))) | (451) |
| 03(33(33(35(54(41(15(55(x1)))))))) | → | 02(23(32(24(44(43(35(54(41(15(55(x1))))))))))) | (452) |
There are no rules in the TRS. Hence, it is terminating.