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 TRS2(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.