The rewrite relation of the following TRS is considered.
0(1(0(2(2(0(3(x1))))))) | → | 0(1(3(2(0(2(0(x1))))))) | (1) |
0(4(5(4(3(3(5(x1))))))) | → | 0(4(3(4(5(3(5(x1))))))) | (2) |
2(1(0(4(5(2(4(x1))))))) | → | 2(1(4(2(5(0(4(x1))))))) | (3) |
4(5(2(4(2(1(5(x1))))))) | → | 4(5(2(2(4(1(5(x1))))))) | (4) |
3(3(3(0(0(2(4(4(x1)))))))) | → | 3(3(2(3(0(0(4(4(x1)))))))) | (5) |
4(0(0(5(4(3(3(0(x1)))))))) | → | 4(0(3(5(3(4(0(0(x1)))))))) | (6) |
1(1(3(4(3(1(4(3(5(x1))))))))) | → | 1(1(3(4(1(3(4(3(5(x1))))))))) | (7) |
4(1(2(3(0(0(0(4(0(x1))))))))) | → | 4(1(3(2(0(0(0(4(0(x1))))))))) | (8) |
1(2(3(3(4(3(2(1(5(2(x1)))))))))) | → | 0(5(0(2(5(2(0(2(1(3(x1)))))))))) | (9) |
5(2(3(0(1(1(2(3(3(3(x1)))))))))) | → | 5(3(4(5(0(5(4(2(2(3(x1)))))))))) | (10) |
0(0(2(0(0(3(2(5(1(1(4(x1))))))))))) | → | 3(3(0(4(3(3(1(5(1(3(x1)))))))))) | (11) |
0(0(4(0(5(3(4(0(3(1(1(x1))))))))))) | → | 2(4(0(4(1(0(0(3(4(5(x1)))))))))) | (12) |
0(1(2(5(4(2(1(0(0(1(4(x1))))))))))) | → | 5(4(5(4(1(4(4(4(5(4(x1)))))))))) | (13) |
0(1(3(5(5(2(0(2(3(1(2(x1))))))))))) | → | 3(4(5(1(4(5(1(0(5(5(x1)))))))))) | (14) |
0(4(2(1(2(0(3(3(5(4(3(x1))))))))))) | → | 1(5(0(4(4(4(4(3(3(4(x1)))))))))) | (15) |
0(4(5(4(0(5(0(3(1(5(4(x1))))))))))) | → | 2(3(3(2(5(1(2(4(3(4(x1)))))))))) | (16) |
0(5(1(4(0(3(2(3(3(3(4(x1))))))))))) | → | 3(5(4(2(5(0(1(3(4(3(x1)))))))))) | (17) |
1(0(1(3(5(0(1(0(4(4(4(x1))))))))))) | → | 4(5(4(4(0(4(0(0(5(5(x1)))))))))) | (18) |
1(0(2(5(4(5(1(4(4(2(0(x1))))))))))) | → | 1(2(1(2(3(4(4(3(3(3(x1)))))))))) | (19) |
1(0(5(3(3(3(5(5(1(5(0(x1))))))))))) | → | 5(1(2(4(2(4(2(2(1(3(x1)))))))))) | (20) |
1(1(4(3(5(5(4(0(1(5(0(x1))))))))))) | → | 5(0(3(4(2(5(4(5(3(2(x1)))))))))) | (21) |
1(2(4(0(3(4(2(2(3(5(4(x1))))))))))) | → | 4(5(5(3(1(1(5(0(0(3(x1)))))))))) | (22) |
1(3(0(1(1(4(1(5(5(0(4(x1))))))))))) | → | 4(2(0(5(0(4(5(3(1(5(x1)))))))))) | (23) |
1(5(0(3(3(1(3(5(0(1(0(x1))))))))))) | → | 3(0(2(1(0(4(2(2(0(5(x1)))))))))) | (24) |
1(5(4(5(2(0(0(1(1(1(0(x1))))))))))) | → | 5(4(4(4(2(3(1(2(5(1(x1)))))))))) | (25) |
2(0(3(3(0(1(0(5(2(3(5(x1))))))))))) | → | 5(3(5(4(1(2(2(3(1(1(x1)))))))))) | (26) |
2(1(3(1(4(0(1(4(2(2(2(x1))))))))))) | → | 1(2(3(5(4(5(0(5(3(0(x1)))))))))) | (27) |
2(2(2(5(3(2(5(0(0(0(1(x1))))))))))) | → | 2(5(0(5(2(2(2(3(2(0(x1)))))))))) | (28) |
2(2(3(1(1(5(4(4(0(0(1(x1))))))))))) | → | 2(0(0(1(1(2(0(5(4(2(x1)))))))))) | (29) |
2(3(3(3(2(2(5(5(0(1(0(x1))))))))))) | → | 2(2(2(2(3(4(0(5(2(5(x1)))))))))) | (30) |
2(4(2(4(5(4(3(5(4(1(5(x1))))))))))) | → | 5(1(0(4(4(5(1(1(5(1(x1)))))))))) | (31) |
2(4(4(5(5(4(3(4(2(2(0(x1))))))))))) | → | 3(0(3(2(0(4(5(3(0(4(x1)))))))))) | (32) |
3(0(2(4(0(3(3(1(2(1(5(x1))))))))))) | → | 0(2(4(3(5(5(5(4(1(0(x1)))))))))) | (33) |
3(0(3(5(2(3(1(1(0(4(2(x1))))))))))) | → | 2(5(4(5(3(4(1(5(2(4(x1)))))))))) | (34) |
3(1(1(1(3(4(1(3(1(2(0(x1))))))))))) | → | 0(5(0(3(3(4(0(1(3(1(x1)))))))))) | (35) |
3(1(1(3(4(0(2(3(3(1(5(x1))))))))))) | → | 4(2(5(3(2(0(2(2(3(4(x1)))))))))) | (36) |
3(2(5(2(1(3(1(3(0(1(1(x1))))))))))) | → | 5(0(5(4(0(3(1(4(2(0(x1)))))))))) | (37) |
3(3(0(2(4(5(4(4(0(0(3(x1))))))))))) | → | 3(2(0(3(2(0(1(2(2(1(x1)))))))))) | (38) |
3(3(0(5(4(2(3(3(5(4(1(x1))))))))))) | → | 4(3(0(5(2(2(2(4(4(2(x1)))))))))) | (39) |
3(4(1(2(0(3(4(1(5(2(3(x1))))))))))) | → | 2(1(4(2(3(0(2(2(5(4(x1)))))))))) | (40) |
3(5(0(1(5(2(3(3(5(0(0(x1))))))))))) | → | 2(5(2(1(5(4(1(1(4(0(x1)))))))))) | (41) |
3(5(1(3(4(4(0(2(5(5(3(x1))))))))))) | → | 2(2(5(0(3(0(4(4(2(5(x1)))))))))) | (42) |
3(5(2(5(4(1(0(1(0(5(0(x1))))))))))) | → | 2(0(3(5(1(3(3(5(2(4(x1)))))))))) | (43) |
4(0(5(1(5(0(5(5(1(2(5(x1))))))))))) | → | 1(1(3(1(1(1(0(4(3(3(x1)))))))))) | (44) |
4(1(2(1(2(4(0(0(3(2(1(x1))))))))))) | → | 5(4(5(4(4(0(3(4(2(5(x1)))))))))) | (45) |
4(1(3(1(5(1(5(4(2(4(5(x1))))))))))) | → | 0(4(3(2(5(4(3(3(3(3(x1)))))))))) | (46) |
4(1(4(1(3(4(3(2(5(0(4(x1))))))))))) | → | 3(5(5(2(3(5(3(2(0(0(x1)))))))))) | (47) |
4(2(3(2(1(5(4(1(1(3(3(x1))))))))))) | → | 4(1(0(3(0(1(0(2(3(4(x1)))))))))) | (48) |
4(2(5(2(1(5(2(0(2(5(3(x1))))))))))) | → | 5(2(0(5(0(0(3(2(1(4(x1)))))))))) | (49) |
4(3(2(0(1(3(3(3(5(0(3(x1))))))))))) | → | 4(2(1(0(0(5(4(1(4(1(x1)))))))))) | (50) |
4(3(3(2(4(2(0(2(3(0(3(x1))))))))))) | → | 4(5(4(3(4(1(2(0(1(4(x1)))))))))) | (51) |
4(3(4(0(5(1(3(0(1(0(1(x1))))))))))) | → | 4(5(2(3(1(3(0(4(1(5(x1)))))))))) | (52) |
4(3(4(1(4(1(1(2(0(4(0(x1))))))))))) | → | 5(5(1(0(5(1(5(3(3(5(x1)))))))))) | (53) |
4(4(3(0(4(1(1(0(5(3(3(x1))))))))))) | → | 2(4(3(2(3(0(0(2(4(5(x1)))))))))) | (54) |
5(1(2(5(3(5(1(1(3(3(3(x1))))))))))) | → | 2(3(0(4(1(5(1(4(4(5(x1)))))))))) | (55) |
5(3(2(2(2(5(1(3(4(3(0(x1))))))))))) | → | 0(0(3(3(5(1(3(2(4(2(x1)))))))))) | (56) |
5(4(1(0(2(1(4(1(0(4(2(x1))))))))))) | → | 1(5(3(2(0(4(0(5(1(1(x1)))))))))) | (57) |
5(5(4(5(3(3(3(0(2(4(5(x1))))))))))) | → | 1(2(1(5(5(3(2(1(0(3(x1)))))))))) | (58) |
0(5(5(4(3(3(5(1(3(4(4(2(x1)))))))))))) | → | 0(5(4(5(3(3(5(1(3(4(4(2(x1)))))))))))) | (59) |
3(1(2(2(1(0(2(0(4(3(2(0(x1)))))))))))) | → | 3(1(2(2(1(0(0(2(4(3(2(0(x1)))))))))))) | (60) |
1(2(2(2(0(1(4(2(3(1(3(5(1(x1))))))))))))) | → | 1(2(2(2(0(1(4(3(2(1(3(5(1(x1))))))))))))) | (61) |
2(0(2(3(1(0(1(4(4(2(2(2(3(x1))))))))))))) | → | 2(0(2(3(1(4(0(1(4(2(2(2(3(x1))))))))))))) | (62) |
4(2(3(1(3(4(4(1(5(5(0(1(4(x1))))))))))))) | → | 4(2(3(5(4(0(4(1(1(3(5(1(4(x1))))))))))))) | (63) |
5(0(4(5(1(4(2(2(4(3(0(0(2(x1))))))))))))) | → | 5(0(4(5(1(4(2(2(3(4(0(0(2(x1))))))))))))) | (64) |
4(2(0(1(2(4(2(1(0(1(0(2(1(1(x1)))))))))))))) | → | 4(2(0(1(2(2(4(1(0(1(0(2(1(1(x1)))))))))))))) | (65) |
0(1(4(0(1(1(2(3(2(2(5(5(3(5(1(x1))))))))))))))) | → | 0(1(0(1(4(2(1(2(2(5(3(3(5(5(1(x1))))))))))))))) | (66) |
2(0(1(4(0(2(0(0(4(3(3(0(2(4(2(x1))))))))))))))) | → | 2(0(1(4(0(2(0(0(4(3(0(3(2(4(2(x1))))))))))))))) | (67) |
3(0(1(5(1(1(3(1(0(3(1(5(0(0(5(x1))))))))))))))) | → | 3(0(1(5(1(1(3(1(0(1(3(5(0(0(5(x1))))))))))))))) | (68) |
3(5(5(5(2(4(0(3(0(3(4(4(2(2(0(x1))))))))))))))) | → | 3(5(2(5(4(5(3(4(0(2(2(4(0(0(3(x1))))))))))))))) | (69) |
3(1(1(2(4(2(5(0(4(4(5(4(1(3(4(1(x1)))))))))))))))) | → | 3(1(1(2(4(2(5(0(4(5(4(4(1(3(4(1(x1)))))))))))))))) | (70) |
3(5(1(4(5(5(5(2(3(1(2(5(0(0(1(4(x1)))))))))))))))) | → | 3(5(5(1(3(5(5(0(5(1(2(4(0(2(1(4(x1)))))))))))))))) | (71) |
1(4(1(1(2(4(3(3(1(4(4(3(4(5(5(4(3(x1))))))))))))))))) | → | 1(4(1(1(2(3(4(3(1(4(4(3(4(5(5(4(3(x1))))))))))))))))) | (72) |
5(4(3(4(1(0(3(1(0(4(2(0(1(4(0(4(0(x1))))))))))))))))) | → | 5(4(3(4(1(0(3(0(1(4(2(0(1(4(0(4(0(x1))))))))))))))))) | (73) |
0(5(3(4(2(5(4(1(0(4(0(3(1(0(2(1(4(1(x1)))))))))))))))))) | → | 0(5(3(4(2(5(4(0(1(4(0(3(1(0(2(1(4(1(x1)))))))))))))))))) | (74) |
3(4(5(5(0(3(4(3(2(5(1(0(4(0(4(1(1(0(x1)))))))))))))))))) | → | 3(4(5(0(5(3(4(3(2(5(1(0(4(0(4(1(1(0(x1)))))))))))))))))) | (75) |
4(3(3(2(5(4(2(0(5(2(1(2(0(1(5(2(2(5(x1)))))))))))))))))) | → | 4(3(3(2(5(4(2(5(0(2(1(2(0(1(5(2(2(5(x1)))))))))))))))))) | (76) |
5(1(1(3(3(1(0(2(5(0(3(0(0(1(5(4(3(0(x1)))))))))))))))))) | → | 5(1(1(3(3(1(0(2(5(0(3(0(0(5(4(1(3(0(x1)))))))))))))))))) | (77) |
3(4(1(5(3(3(0(5(4(1(5(5(5(0(3(3(3(4(5(x1))))))))))))))))))) | → | 3(4(1(5(3(3(0(5(4(5(1(5(5(0(3(3(3(4(5(x1))))))))))))))))))) | (78) |
3(5(5(4(0(4(4(3(4(3(0(1(1(2(5(4(2(2(2(3(x1)))))))))))))))))))) | → | 3(5(5(4(0(4(4(3(3(4(0(1(1(2(5(4(2(2(2(3(x1)))))))))))))))))))) | (79) |
0(2(1(0(1(2(2(5(4(3(3(2(4(0(1(5(2(5(2(0(4(x1))))))))))))))))))))) | → | 0(2(0(1(1(2(4(4(1(2(2(3(3(2(5(0(5(5(2(0(4(x1))))))))))))))))))))) | (80) |
5(2(3(0(1(4(0(4(5(3(4(5(3(5(2(1(1(4(4(5(4(x1))))))))))))))))))))) | → | 5(2(3(0(1(4(0(4(5(3(4(5(3(2(5(1(1(4(4(5(4(x1))))))))))))))))))))) | (81) |
0(3(5(2(0(1(5(2(2(2(0(3(4(3(4(4(3(3(1(0(1(3(x1)))))))))))))))))))))) | → | 0(3(5(2(0(1(5(2(2(2(0(3(4(3(4(4(3(3(0(1(1(3(x1)))))))))))))))))))))) | (82) |
0(5(4(0(3(0(5(1(4(0(4(4(1(2(1(0(5(4(0(4(2(5(x1)))))))))))))))))))))) | → | 0(5(4(3(0(0(5(4(1(4(4(0(1(2(1(0(5(4(0(4(2(5(x1)))))))))))))))))))))) | (83) |
4(3(2(0(4(2(4(0(4(2(5(5(0(2(5(0(1(1(4(5(0(3(5(x1))))))))))))))))))))))) | → | 4(3(2(4(4(0(0(4(2(2(0(5(0(5(5(2(4(1(1(0(5(3(5(x1))))))))))))))))))))))) | (84) |
4(5(3(5(0(3(1(4(5(0(4(4(2(0(4(2(3(3(5(3(5(0(2(x1))))))))))))))))))))))) | → | 4(5(3(5(3(0(1(4(5(0(4(4(2(0(4(2(3(3(5(3(5(0(2(x1))))))))))))))))))))))) | (85) |
4(5(4(4(5(2(0(0(4(4(0(4(0(1(5(2(5(2(3(1(1(3(5(x1))))))))))))))))))))))) | → | 4(5(4(4(5(2(0(0(4(4(0(4(0(1(5(2(2(5(3(1(1(3(5(x1))))))))))))))))))))))) | (86) |
0(1(3(1(5(1(2(3(0(3(2(1(2(0(2(2(1(0(3(5(1(3(4(4(0(x1))))))))))))))))))))))))) | → | 0(1(3(1(5(2(1(3(0(3(2(1(2(0(2(2(1(0(3(5(1(3(4(4(0(x1))))))))))))))))))))))))) | (87) |
2(2(5(4(4(4(5(2(2(4(1(0(5(1(1(5(4(3(4(2(2(2(0(2(0(x1))))))))))))))))))))))))) | → | 2(2(5(4(4(4(5(2(2(4(0(1(5(1(1(5(4(3(4(2(2(2(0(2(0(x1))))))))))))))))))))))))) | (88) |
0(0(2(2(4(4(2(5(4(5(0(3(4(3(5(2(1(2(4(3(1(1(2(5(5(5(4(x1))))))))))))))))))))))))))) | → | 0(0(2(2(4(4(2(5(4(5(0(3(4(3(5(2(2(1(4(3(1(1(2(5(5(5(4(x1))))))))))))))))))))))))))) | (89) |
0(5(4(3(1(5(5(1(5(0(2(2(3(5(5(2(4(2(1(1(2(4(4(5(3(3(5(x1))))))))))))))))))))))))))) | → | 0(5(4(3(1(5(5(1(5(0(2(2(3(5(5(2(4(2(1(1(4(2(4(5(3(3(5(x1))))))))))))))))))))))))))) | (90) |
1(1(5(3(1(2(2(5(3(1(5(4(5(0(5(5(1(1(4(2(0(4(1(4(4(2(0(x1))))))))))))))))))))))))))) | → | 1(1(1(5(3(2(2(5(3(1(5(4(5(0(5(5(1(1(4(2(0(4(1(4(4(2(0(x1))))))))))))))))))))))))))) | (91) |
4(3(3(3(0(4(2(2(4(2(5(2(4(3(3(5(2(2(0(0(2(0(5(2(0(2(2(x1))))))))))))))))))))))))))) | → | 4(3(3(3(0(4(2(2(4(2(5(4(2(3(3(5(2(2(0(0(2(0(5(2(0(2(2(x1))))))))))))))))))))))))))) | (92) |
4(4(5(2(3(4(1(2(5(5(3(5(3(4(4(5(4(1(5(2(5(4(4(1(0(4(5(x1))))))))))))))))))))))))))) | → | 4(4(5(2(3(4(1(2(5(5(3(5(3(4(4(5(4(1(5(2(5(4(4(0(1(4(5(x1))))))))))))))))))))))))))) | (93) |
0(2(0(4(3(3(4(5(0(0(4(4(1(5(2(4(0(5(2(2(0(3(2(1(3(5(4(1(x1)))))))))))))))))))))))))))) | → | 0(2(0(4(3(3(4(5(0(4(0(4(1(5(2(4(0(5(2(2(0(3(2(1(3(5(4(1(x1)))))))))))))))))))))))))))) | (94) |
1(4(5(0(1(5(4(4(2(1(0(4(1(2(1(5(4(5(5(0(4(0(1(0(2(4(5(5(2(4(x1)))))))))))))))))))))))))))))) | → | 1(4(5(0(1(5(4(4(2(1(4(0(1(2(1(5(4(5(5(0(4(0(1(0(2(4(5(5(2(4(x1)))))))))))))))))))))))))))))) | (95) |
2(0(0(0(5(1(1(3(3(3(4(1(2(1(1(2(5(0(3(5(1(4(1(3(1(3(3(3(4(3(x1)))))))))))))))))))))))))))))) | → | 2(0(0(0(5(1(1(3(3(3(4(1(2(1(1(2(5(0(3(5(4(1(1(3(1(3(3(3(4(3(x1)))))))))))))))))))))))))))))) | (96) |
2(3(0(1(2(0(5(2(0(2(1(0(2(5(1(4(5(4(0(4(4(5(0(5(2(3(2(0(1(3(x1)))))))))))))))))))))))))))))) | → | 2(3(0(1(2(0(5(2(0(2(0(1(2(5(1(4(5(4(0(4(4(5(0(5(2(3(2(0(1(3(x1)))))))))))))))))))))))))))))) | (97) |
3(4(1(3(2(0(2(4(4(1(3(3(5(2(3(3(1(1(5(5(5(2(5(1(2(3(2(5(0(4(x1)))))))))))))))))))))))))))))) | → | 3(4(1(3(2(0(2(4(4(1(3(3(5(2(3(3(1(5(1(5(5(2(5(1(2(3(2(5(0(4(x1)))))))))))))))))))))))))))))) | (98) |
[5(x1)] | = |
x1 +
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[4(x1)] | = |
x1 +
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[3(x1)] | = |
x1 +
|
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[2(x1)] | = |
x1 +
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[1(x1)] | = |
x1 +
|
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[0(x1)] | = |
x1 +
|
1(2(3(3(4(3(2(1(5(2(x1)))))))))) | → | 0(5(0(2(5(2(0(2(1(3(x1)))))))))) | (9) |
5(2(3(0(1(1(2(3(3(3(x1)))))))))) | → | 5(3(4(5(0(5(4(2(2(3(x1)))))))))) | (10) |
0(0(2(0(0(3(2(5(1(1(4(x1))))))))))) | → | 3(3(0(4(3(3(1(5(1(3(x1)))))))))) | (11) |
0(0(4(0(5(3(4(0(3(1(1(x1))))))))))) | → | 2(4(0(4(1(0(0(3(4(5(x1)))))))))) | (12) |
0(1(2(5(4(2(1(0(0(1(4(x1))))))))))) | → | 5(4(5(4(1(4(4(4(5(4(x1)))))))))) | (13) |
0(1(3(5(5(2(0(2(3(1(2(x1))))))))))) | → | 3(4(5(1(4(5(1(0(5(5(x1)))))))))) | (14) |
0(4(2(1(2(0(3(3(5(4(3(x1))))))))))) | → | 1(5(0(4(4(4(4(3(3(4(x1)))))))))) | (15) |
0(4(5(4(0(5(0(3(1(5(4(x1))))))))))) | → | 2(3(3(2(5(1(2(4(3(4(x1)))))))))) | (16) |
0(5(1(4(0(3(2(3(3(3(4(x1))))))))))) | → | 3(5(4(2(5(0(1(3(4(3(x1)))))))))) | (17) |
1(0(1(3(5(0(1(0(4(4(4(x1))))))))))) | → | 4(5(4(4(0(4(0(0(5(5(x1)))))))))) | (18) |
1(0(2(5(4(5(1(4(4(2(0(x1))))))))))) | → | 1(2(1(2(3(4(4(3(3(3(x1)))))))))) | (19) |
1(0(5(3(3(3(5(5(1(5(0(x1))))))))))) | → | 5(1(2(4(2(4(2(2(1(3(x1)))))))))) | (20) |
1(1(4(3(5(5(4(0(1(5(0(x1))))))))))) | → | 5(0(3(4(2(5(4(5(3(2(x1)))))))))) | (21) |
1(2(4(0(3(4(2(2(3(5(4(x1))))))))))) | → | 4(5(5(3(1(1(5(0(0(3(x1)))))))))) | (22) |
1(3(0(1(1(4(1(5(5(0(4(x1))))))))))) | → | 4(2(0(5(0(4(5(3(1(5(x1)))))))))) | (23) |
1(5(0(3(3(1(3(5(0(1(0(x1))))))))))) | → | 3(0(2(1(0(4(2(2(0(5(x1)))))))))) | (24) |
1(5(4(5(2(0(0(1(1(1(0(x1))))))))))) | → | 5(4(4(4(2(3(1(2(5(1(x1)))))))))) | (25) |
2(0(3(3(0(1(0(5(2(3(5(x1))))))))))) | → | 5(3(5(4(1(2(2(3(1(1(x1)))))))))) | (26) |
2(1(3(1(4(0(1(4(2(2(2(x1))))))))))) | → | 1(2(3(5(4(5(0(5(3(0(x1)))))))))) | (27) |
2(2(2(5(3(2(5(0(0(0(1(x1))))))))))) | → | 2(5(0(5(2(2(2(3(2(0(x1)))))))))) | (28) |
2(2(3(1(1(5(4(4(0(0(1(x1))))))))))) | → | 2(0(0(1(1(2(0(5(4(2(x1)))))))))) | (29) |
2(3(3(3(2(2(5(5(0(1(0(x1))))))))))) | → | 2(2(2(2(3(4(0(5(2(5(x1)))))))))) | (30) |
2(4(2(4(5(4(3(5(4(1(5(x1))))))))))) | → | 5(1(0(4(4(5(1(1(5(1(x1)))))))))) | (31) |
2(4(4(5(5(4(3(4(2(2(0(x1))))))))))) | → | 3(0(3(2(0(4(5(3(0(4(x1)))))))))) | (32) |
3(0(2(4(0(3(3(1(2(1(5(x1))))))))))) | → | 0(2(4(3(5(5(5(4(1(0(x1)))))))))) | (33) |
3(0(3(5(2(3(1(1(0(4(2(x1))))))))))) | → | 2(5(4(5(3(4(1(5(2(4(x1)))))))))) | (34) |
3(1(1(1(3(4(1(3(1(2(0(x1))))))))))) | → | 0(5(0(3(3(4(0(1(3(1(x1)))))))))) | (35) |
3(1(1(3(4(0(2(3(3(1(5(x1))))))))))) | → | 4(2(5(3(2(0(2(2(3(4(x1)))))))))) | (36) |
3(2(5(2(1(3(1(3(0(1(1(x1))))))))))) | → | 5(0(5(4(0(3(1(4(2(0(x1)))))))))) | (37) |
3(3(0(2(4(5(4(4(0(0(3(x1))))))))))) | → | 3(2(0(3(2(0(1(2(2(1(x1)))))))))) | (38) |
3(3(0(5(4(2(3(3(5(4(1(x1))))))))))) | → | 4(3(0(5(2(2(2(4(4(2(x1)))))))))) | (39) |
3(4(1(2(0(3(4(1(5(2(3(x1))))))))))) | → | 2(1(4(2(3(0(2(2(5(4(x1)))))))))) | (40) |
3(5(0(1(5(2(3(3(5(0(0(x1))))))))))) | → | 2(5(2(1(5(4(1(1(4(0(x1)))))))))) | (41) |
3(5(1(3(4(4(0(2(5(5(3(x1))))))))))) | → | 2(2(5(0(3(0(4(4(2(5(x1)))))))))) | (42) |
3(5(2(5(4(1(0(1(0(5(0(x1))))))))))) | → | 2(0(3(5(1(3(3(5(2(4(x1)))))))))) | (43) |
4(0(5(1(5(0(5(5(1(2(5(x1))))))))))) | → | 1(1(3(1(1(1(0(4(3(3(x1)))))))))) | (44) |
4(1(2(1(2(4(0(0(3(2(1(x1))))))))))) | → | 5(4(5(4(4(0(3(4(2(5(x1)))))))))) | (45) |
4(1(3(1(5(1(5(4(2(4(5(x1))))))))))) | → | 0(4(3(2(5(4(3(3(3(3(x1)))))))))) | (46) |
4(1(4(1(3(4(3(2(5(0(4(x1))))))))))) | → | 3(5(5(2(3(5(3(2(0(0(x1)))))))))) | (47) |
4(2(3(2(1(5(4(1(1(3(3(x1))))))))))) | → | 4(1(0(3(0(1(0(2(3(4(x1)))))))))) | (48) |
4(2(5(2(1(5(2(0(2(5(3(x1))))))))))) | → | 5(2(0(5(0(0(3(2(1(4(x1)))))))))) | (49) |
4(3(2(0(1(3(3(3(5(0(3(x1))))))))))) | → | 4(2(1(0(0(5(4(1(4(1(x1)))))))))) | (50) |
4(3(3(2(4(2(0(2(3(0(3(x1))))))))))) | → | 4(5(4(3(4(1(2(0(1(4(x1)))))))))) | (51) |
4(3(4(0(5(1(3(0(1(0(1(x1))))))))))) | → | 4(5(2(3(1(3(0(4(1(5(x1)))))))))) | (52) |
4(3(4(1(4(1(1(2(0(4(0(x1))))))))))) | → | 5(5(1(0(5(1(5(3(3(5(x1)))))))))) | (53) |
4(4(3(0(4(1(1(0(5(3(3(x1))))))))))) | → | 2(4(3(2(3(0(0(2(4(5(x1)))))))))) | (54) |
5(1(2(5(3(5(1(1(3(3(3(x1))))))))))) | → | 2(3(0(4(1(5(1(4(4(5(x1)))))))))) | (55) |
5(3(2(2(2(5(1(3(4(3(0(x1))))))))))) | → | 0(0(3(3(5(1(3(2(4(2(x1)))))))))) | (56) |
5(4(1(0(2(1(4(1(0(4(2(x1))))))))))) | → | 1(5(3(2(0(4(0(5(1(1(x1)))))))))) | (57) |
5(5(4(5(3(3(3(0(2(4(5(x1))))))))))) | → | 1(2(1(5(5(3(2(1(0(3(x1)))))))))) | (58) |
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 288 ruless (increase limit for explicit display).
As carrier we take the set {0,...,5}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 6):
[5(x1)] | = | 6x1 + 0 |
[4(x1)] | = | 6x1 + 1 |
[3(x1)] | = | 6x1 + 2 |
[2(x1)] | = | 6x1 + 3 |
[1(x1)] | = | 6x1 + 4 |
[0(x1)] | = | 6x1 + 5 |
There are 1728 ruless (increase limit for explicit display).
[50(x1)] | = |
x1 +
|
||||
[51(x1)] | = |
x1 +
|
||||
[52(x1)] | = |
x1 +
|
||||
[53(x1)] | = |
x1 +
|
||||
[54(x1)] | = |
x1 +
|
||||
[55(x1)] | = |
x1 +
|
||||
[40(x1)] | = |
x1 +
|
||||
[41(x1)] | = |
x1 +
|
||||
[42(x1)] | = |
x1 +
|
||||
[43(x1)] | = |
x1 +
|
||||
[44(x1)] | = |
x1 +
|
||||
[45(x1)] | = |
x1 +
|
||||
[30(x1)] | = |
x1 +
|
||||
[31(x1)] | = |
x1 +
|
||||
[32(x1)] | = |
x1 +
|
||||
[33(x1)] | = |
x1 +
|
||||
[34(x1)] | = |
x1 +
|
||||
[35(x1)] | = |
x1 +
|
||||
[20(x1)] | = |
x1 +
|
||||
[21(x1)] | = |
x1 +
|
||||
[22(x1)] | = |
x1 +
|
||||
[23(x1)] | = |
x1 +
|
||||
[24(x1)] | = |
x1 +
|
||||
[25(x1)] | = |
x1 +
|
||||
[10(x1)] | = |
x1 +
|
||||
[11(x1)] | = |
x1 +
|
||||
[12(x1)] | = |
x1 +
|
||||
[13(x1)] | = |
x1 +
|
||||
[14(x1)] | = |
x1 +
|
||||
[15(x1)] | = |
x1 +
|
||||
[00(x1)] | = |
x1 +
|
||||
[01(x1)] | = |
x1 +
|
||||
[02(x1)] | = |
x1 +
|
||||
[03(x1)] | = |
x1 +
|
||||
[04(x1)] | = |
x1 +
|
||||
[05(x1)] | = |
x1 +
|
There are 1692 ruless (increase limit for explicit display).
52#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(10(x1))))))))))))))))) | → | 52#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(10(x1))))))))))))))))) | (2115) |
52#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(11(x1))))))))))))))))) | → | 52#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(11(x1))))))))))))))))) | (2116) |
52#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(12(x1))))))))))))))))) | → | 52#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(12(x1))))))))))))))))) | (2117) |
52#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(13(x1))))))))))))))))) | → | 52#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(13(x1))))))))))))))))) | (2118) |
52#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(14(x1))))))))))))))))) | → | 52#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(14(x1))))))))))))))))) | (2119) |
52#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(15(x1))))))))))))))))) | → | 52#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(15(x1))))))))))))))))) | (2120) |
42#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(10(x1))))))))))))))))) | → | 42#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(10(x1))))))))))))))))) | (2121) |
42#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(11(x1))))))))))))))))) | → | 42#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(11(x1))))))))))))))))) | (2122) |
42#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(12(x1))))))))))))))))) | → | 42#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(12(x1))))))))))))))))) | (2123) |
42#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(13(x1))))))))))))))))) | → | 42#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(13(x1))))))))))))))))) | (2124) |
42#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(14(x1))))))))))))))))) | → | 42#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(14(x1))))))))))))))))) | (2125) |
42#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(15(x1))))))))))))))))) | → | 42#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(15(x1))))))))))))))))) | (2126) |
32#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(10(x1))))))))))))))))) | → | 32#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(10(x1))))))))))))))))) | (2127) |
32#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(11(x1))))))))))))))))) | → | 32#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(11(x1))))))))))))))))) | (2128) |
32#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(12(x1))))))))))))))))) | → | 32#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(12(x1))))))))))))))))) | (2129) |
32#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(13(x1))))))))))))))))) | → | 32#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(13(x1))))))))))))))))) | (2130) |
32#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(14(x1))))))))))))))))) | → | 32#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(14(x1))))))))))))))))) | (2131) |
32#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(15(x1))))))))))))))))) | → | 32#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(15(x1))))))))))))))))) | (2132) |
22#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(10(x1))))))))))))))))) | → | 22#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(10(x1))))))))))))))))) | (2133) |
22#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(11(x1))))))))))))))))) | → | 22#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(11(x1))))))))))))))))) | (2134) |
22#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(12(x1))))))))))))))))) | → | 22#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(12(x1))))))))))))))))) | (2135) |
22#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(13(x1))))))))))))))))) | → | 22#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(13(x1))))))))))))))))) | (2136) |
22#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(14(x1))))))))))))))))) | → | 22#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(14(x1))))))))))))))))) | (2137) |
22#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(15(x1))))))))))))))))) | → | 22#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(15(x1))))))))))))))))) | (2138) |
12#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(10(x1))))))))))))))))) | → | 12#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(10(x1))))))))))))))))) | (2139) |
12#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(11(x1))))))))))))))))) | → | 12#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(11(x1))))))))))))))))) | (2140) |
12#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(12(x1))))))))))))))))) | → | 12#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(12(x1))))))))))))))))) | (2141) |
12#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(13(x1))))))))))))))))) | → | 12#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(13(x1))))))))))))))))) | (2142) |
12#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(14(x1))))))))))))))))) | → | 12#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(14(x1))))))))))))))))) | (2143) |
12#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(15(x1))))))))))))))))) | → | 12#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(15(x1))))))))))))))))) | (2144) |
02#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(10(x1))))))))))))))))) | → | 02#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(10(x1))))))))))))))))) | (2145) |
02#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(11(x1))))))))))))))))) | → | 02#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(11(x1))))))))))))))))) | (2146) |
02#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(12(x1))))))))))))))))) | → | 02#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(12(x1))))))))))))))))) | (2147) |
02#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(13(x1))))))))))))))))) | → | 02#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(13(x1))))))))))))))))) | (2148) |
02#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(14(x1))))))))))))))))) | → | 02#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(14(x1))))))))))))))))) | (2149) |
02#(34(14(13(21(43(20(55(01(41(40(51(44(12(31(44(15(x1))))))))))))))))) | → | 02#(34(14(13(21(43(20(55(01(40(51(41(44(12(31(44(15(x1))))))))))))))))) | (2150) |
The dependency pairs are split into 0 components.