The relative rewrite relation R/S is considered where R is the following TRS
0(0(0(0(1(2(1(2(2(1(1(2(0(x1))))))))))))) | → | 0(0(0(0(1(2(2(2(2(2(2(2(2(2(1(2(0(x1))))))))))))))))) | (1) |
0(0(0(2(1(0(2(1(1(2(0(2(1(x1))))))))))))) | → | 0(0(0(1(0(1(2(2(2(2(2(2(2(2(1(2(2(x1))))))))))))))))) | (2) |
0(0(0(2(2(1(0(2(2(0(1(1(0(x1))))))))))))) | → | 0(1(2(0(0(0(0(0(0(0(0(0(0(0(2(1(1(x1))))))))))))))))) | (3) |
0(0(1(0(1(0(0(2(0(2(1(0(1(x1))))))))))))) | → | 0(0(0(0(0(1(2(1(0(0(0(0(1(2(2(2(0(x1))))))))))))))))) | (4) |
0(0(1(1(1(0(2(1(2(0(2(1(2(x1))))))))))))) | → | 0(0(0(1(0(0(0(0(0(1(2(2(0(2(1(2(1(x1))))))))))))))))) | (5) |
0(0(2(0(1(1(0(2(1(1(0(2(2(x1))))))))))))) | → | 0(0(0(2(0(2(2(2(2(2(2(1(0(2(2(0(2(x1))))))))))))))))) | (6) |
0(0(2(1(1(2(1(0(2(2(1(0(0(x1))))))))))))) | → | 1(0(0(0(0(0(1(2(2(2(0(2(2(2(2(2(0(x1))))))))))))))))) | (7) |
0(0(2(2(0(0(2(2(1(0(2(0(0(x1))))))))))))) | → | 2(0(1(0(0(0(0(0(0(0(0(0(1(2(2(0(0(x1))))))))))))))))) | (8) |
0(1(0(0(1(1(1(1(2(1(0(1(1(x1))))))))))))) | → | 0(1(0(1(1(0(0(0(2(2(0(2(2(2(2(0(0(x1))))))))))))))))) | (9) |
0(1(0(1(0(1(1(1(1(0(0(1(2(x1))))))))))))) | → | 0(0(2(2(2(2(2(0(2(1(0(0(0(1(2(2(2(x1))))))))))))))))) | (10) |
0(1(0(1(1(0(2(0(2(2(1(0(2(x1))))))))))))) | → | 0(2(2(0(2(2(2(2(0(2(2(2(2(0(2(2(2(x1))))))))))))))))) | (11) |
0(1(0(1(1(1(2(2(2(1(1(0(2(x1))))))))))))) | → | 0(0(1(0(0(0(0(2(1(0(0(0(0(0(0(1(0(x1))))))))))))))))) | (12) |
0(1(1(0(1(2(2(0(1(1(0(1(0(x1))))))))))))) | → | 0(0(0(0(0(0(1(2(2(1(0(0(0(1(2(0(0(x1))))))))))))))))) | (13) |
0(1(1(0(2(1(0(0(1(2(1(1(2(x1))))))))))))) | → | 1(0(0(1(0(1(2(0(2(2(2(2(2(2(2(2(2(x1))))))))))))))))) | (14) |
0(1(1(2(2(2(1(1(2(2(2(2(1(x1))))))))))))) | → | 1(2(2(2(2(0(2(2(2(0(2(2(2(2(2(0(2(x1))))))))))))))))) | (15) |
0(1(2(0(0(1(0(0(1(2(1(2(1(x1))))))))))))) | → | 0(0(1(2(0(2(2(2(2(2(2(2(0(1(0(0(2(x1))))))))))))))))) | (16) |
0(1(2(0(1(2(2(2(1(1(2(0(2(x1))))))))))))) | → | 0(0(0(0(0(0(0(0(0(1(2(0(2(0(0(2(2(x1))))))))))))))))) | (17) |
0(1(2(2(0(2(0(2(1(0(1(1(1(x1))))))))))))) | → | 0(0(1(2(2(0(2(0(0(0(0(0(0(0(0(0(1(x1))))))))))))))))) | (18) |
0(2(0(1(0(2(2(1(0(0(2(2(0(x1))))))))))))) | → | 0(0(0(0(1(2(0(0(0(0(0(0(0(0(1(2(0(x1))))))))))))))))) | (19) |
0(2(0(1(1(0(2(2(1(0(2(2(0(x1))))))))))))) | → | 2(0(0(0(2(2(2(2(2(2(2(2(1(0(0(0(1(x1))))))))))))))))) | (20) |
0(2(0(1(1(1(2(1(0(2(0(1(1(x1))))))))))))) | → | 0(2(0(2(2(2(0(1(0(0(1(0(0(0(0(1(0(x1))))))))))))))))) | (21) |
0(2(1(0(1(2(0(1(0(0(0(1(1(x1))))))))))))) | → | 2(1(2(2(2(2(2(2(2(2(0(2(2(0(2(1(0(x1))))))))))))))))) | (22) |
0(2(1(0(2(1(2(2(2(1(0(0(2(x1))))))))))))) | → | 0(0(0(0(0(0(0(0(0(0(0(1(0(2(0(1(2(x1))))))))))))))))) | (23) |
0(2(1(2(1(2(2(0(2(0(1(1(0(x1))))))))))))) | → | 2(0(1(0(0(0(1(2(0(0(0(0(0(0(0(2(0(x1))))))))))))))))) | (24) |
1(0(0(0(1(1(1(1(0(1(0(0(1(x1))))))))))))) | → | 2(2(0(1(0(0(0(0(0(0(0(0(0(0(1(2(0(x1))))))))))))))))) | (25) |
1(0(0(1(0(2(1(2(1(0(1(2(0(x1))))))))))))) | → | 0(0(2(0(0(0(0(0(1(0(0(0(0(0(2(2(0(x1))))))))))))))))) | (26) |
1(0(0(2(0(0(2(2(1(2(1(1(1(x1))))))))))))) | → | 0(1(0(2(1(0(0(0(0(0(0(1(2(0(2(0(0(x1))))))))))))))))) | (27) |
1(0(0(2(0(1(2(2(1(0(0(1(2(x1))))))))))))) | → | 0(0(0(0(0(0(0(0(0(0(0(0(0(2(0(0(2(x1))))))))))))))))) | (28) |
1(0(0(2(1(1(0(1(2(0(0(2(1(x1))))))))))))) | → | 1(0(0(2(0(0(0(1(2(2(2(0(2(2(2(0(1(x1))))))))))))))))) | (29) |
1(0(0(2(2(0(0(1(1(0(2(1(1(x1))))))))))))) | → | 1(2(0(2(2(2(2(2(2(0(2(2(0(2(0(0(1(x1))))))))))))))))) | (30) |
1(0(1(2(1(2(0(2(0(1(2(1(0(x1))))))))))))) | → | 2(0(0(1(0(0(0(0(0(1(2(2(2(2(1(2(0(x1))))))))))))))))) | (31) |
1(0(2(0(1(1(1(0(0(0(1(0(1(x1))))))))))))) | → | 1(0(0(0(0(1(0(0(0(0(0(1(2(2(1(2(0(x1))))))))))))))))) | (32) |
1(0(2(0(2(0(1(0(1(1(1(1(1(x1))))))))))))) | → | 1(1(0(2(2(2(2(2(2(0(2(0(2(1(0(0(1(x1))))))))))))))))) | (33) |
1(0(2(1(1(0(0(2(1(0(2(0(1(x1))))))))))))) | → | 0(1(0(0(0(0(0(0(0(0(1(1(2(2(1(1(1(x1))))))))))))))))) | (34) |
1(0(2(1(2(1(0(1(0(0(2(1(0(x1))))))))))))) | → | 2(1(0(0(0(0(0(1(2(2(2(1(0(0(2(0(0(x1))))))))))))))))) | (35) |
1(0(2(1(2(1(1(1(0(2(0(1(2(x1))))))))))))) | → | 1(1(0(0(0(0(1(0(0(0(0(2(0(0(2(0(2(x1))))))))))))))))) | (36) |
1(0(2(1(2(2(0(0(0(1(2(2(0(x1))))))))))))) | → | 0(0(2(2(2(2(2(2(2(2(2(2(2(0(1(0(2(x1))))))))))))))))) | (37) |
1(1(0(0(1(0(1(1(2(1(0(1(2(x1))))))))))))) | → | 1(0(0(0(0(0(0(1(2(2(0(0(1(0(2(0(2(x1))))))))))))))))) | (38) |
1(1(0(1(1(0(2(2(1(0(2(0(0(x1))))))))))))) | → | 0(1(0(0(0(0(1(2(2(2(2(1(2(0(0(0(1(x1))))))))))))))))) | (39) |
1(1(0(2(0(1(0(2(1(0(2(1(2(x1))))))))))))) | → | 1(2(2(2(2(2(2(1(1(2(2(2(2(2(2(1(2(x1))))))))))))))))) | (40) |
1(1(0(2(0(1(1(0(0(2(2(1(2(x1))))))))))))) | → | 0(2(1(0(0(0(0(0(1(2(2(0(0(0(0(0(2(x1))))))))))))))))) | (41) |
1(1(1(0(0(0(1(1(0(1(1(0(2(x1))))))))))))) | → | 0(0(0(2(2(2(2(2(0(2(2(0(2(2(2(1(2(x1))))))))))))))))) | (42) |
1(1(1(0(0(2(0(2(1(0(2(0(2(x1))))))))))))) | → | 1(0(2(0(1(2(2(2(2(0(2(2(0(2(2(2(2(x1))))))))))))))))) | (43) |
1(1(1(2(2(2(2(1(0(0(2(1(2(x1))))))))))))) | → | 0(0(0(0(0(0(1(0(0(0(0(1(2(2(1(1(2(x1))))))))))))))))) | (44) |
1(1(2(0(2(0(2(0(1(0(0(2(0(x1))))))))))))) | → | 2(0(1(0(0(0(0(1(2(2(2(0(2(2(2(2(1(x1))))))))))))))))) | (45) |
1(1(2(1(0(0(0(1(0(2(0(2(2(x1))))))))))))) | → | 1(0(2(1(0(0(0(0(0(0(0(1(2(2(2(2(2(x1))))))))))))))))) | (46) |
1(1(2(2(0(0(2(0(1(1(1(1(0(x1))))))))))))) | → | 2(0(0(0(0(1(2(1(0(1(2(2(2(2(1(0(0(x1))))))))))))))))) | (47) |
1(2(0(0(1(1(2(2(1(2(2(0(0(x1))))))))))))) | → | 1(0(2(0(2(0(0(0(0(0(0(0(0(0(1(2(2(x1))))))))))))))))) | (48) |
1(2(0(0(2(1(0(2(2(2(0(0(1(x1))))))))))))) | → | 0(0(0(0(0(1(2(2(2(0(2(0(2(2(1(0(1(x1))))))))))))))))) | (49) |
1(2(0(1(0(0(1(1(1(1(0(1(1(x1))))))))))))) | → | 0(0(0(0(2(0(1(0(0(0(0(0(1(2(1(1(0(x1))))))))))))))))) | (50) |
1(2(0(1(2(1(2(2(1(0(1(0(0(x1))))))))))))) | → | 1(0(0(0(1(2(0(2(2(2(2(2(1(0(1(0(0(x1))))))))))))))))) | (51) |
1(2(1(1(2(0(0(2(2(1(0(0(1(x1))))))))))))) | → | 1(1(0(0(0(0(0(0(1(0(0(1(2(2(2(2(0(x1))))))))))))))))) | (52) |
1(2(2(0(0(1(2(0(2(1(0(0(1(x1))))))))))))) | → | 0(1(0(2(2(2(2(2(0(2(2(2(2(2(2(2(2(x1))))))))))))))))) | (53) |
1(2(2(0(1(2(2(2(0(1(2(1(1(x1))))))))))))) | → | 0(0(0(2(2(2(2(2(0(2(2(1(2(0(0(0(1(x1))))))))))))))))) | (54) |
2(0(0(0(0(1(1(2(0(0(1(0(2(x1))))))))))))) | → | 0(1(0(0(0(1(2(2(2(2(0(2(0(2(2(2(2(x1))))))))))))))))) | (55) |
2(0(0(2(1(2(1(0(1(0(1(1(1(x1))))))))))))) | → | 1(0(0(0(0(0(0(0(1(1(2(2(2(0(2(0(0(x1))))))))))))))))) | (56) |
2(0(1(0(1(0(0(0(2(0(1(2(1(x1))))))))))))) | → | 2(0(1(0(0(1(0(0(1(0(0(0(0(0(0(0(0(x1))))))))))))))))) | (57) |
2(0(2(0(1(1(0(0(2(1(1(0(2(x1))))))))))))) | → | 2(2(0(0(0(1(0(0(0(0(1(0(0(0(1(0(2(x1))))))))))))))))) | (58) |
2(0(2(2(0(2(2(0(2(1(2(0(1(x1))))))))))))) | → | 2(2(2(2(0(0(0(0(0(0(0(0(0(1(2(2(0(x1))))))))))))))))) | (59) |
2(1(0(2(1(2(1(2(1(2(2(2(1(x1))))))))))))) | → | 2(1(0(0(0(1(2(0(2(0(0(0(0(0(1(2(1(x1))))))))))))))))) | (60) |
2(1(1(2(1(1(2(0(1(0(1(0(2(x1))))))))))))) | → | 2(2(0(2(0(0(1(2(0(2(2(2(2(2(2(1(2(x1))))))))))))))))) | (61) |
2(1(1(2(2(0(2(0(0(2(0(1(0(x1))))))))))))) | → | 2(0(1(0(1(2(2(2(2(2(2(2(0(2(2(0(0(x1))))))))))))))))) | (62) |
2(1(2(0(0(2(2(0(2(0(1(2(2(x1))))))))))))) | → | 2(0(0(0(0(2(0(0(1(2(2(2(2(2(2(0(2(x1))))))))))))))))) | (63) |
2(1(2(0(2(2(2(1(1(0(0(1(2(x1))))))))))))) | → | 1(2(2(0(0(2(2(2(2(2(0(2(2(2(2(2(2(x1))))))))))))))))) | (64) |
2(1(2(1(0(1(0(0(2(1(2(2(0(x1))))))))))))) | → | 2(2(1(1(0(0(0(0(0(0(1(2(1(0(0(0(1(x1))))))))))))))))) | (65) |
2(1(2(2(1(2(2(2(2(1(2(1(0(x1))))))))))))) | → | 2(0(0(2(0(0(0(0(1(0(0(0(0(0(0(0(0(x1))))))))))))))))) | (66) |
2(2(0(0(1(2(1(0(2(2(1(0(0(x1))))))))))))) | → | 2(2(2(2(2(2(2(0(2(2(0(2(2(0(2(2(0(x1))))))))))))))))) | (67) |
2(2(0(0(2(1(2(1(2(0(1(2(0(x1))))))))))))) | → | 2(2(2(2(2(2(0(1(0(0(0(0(1(0(0(2(1(x1))))))))))))))))) | (68) |
2(2(0(2(2(0(1(1(2(1(0(1(0(x1))))))))))))) | → | 2(2(2(2(2(2(2(2(2(2(1(0(0(2(0(0(1(x1))))))))))))))))) | (69) |
2(2(0(2(2(1(2(1(2(2(0(2(0(x1))))))))))))) | → | 2(2(2(2(0(2(2(2(0(2(2(0(1(0(0(0(1(x1))))))))))))))))) | (70) |
2(2(1(0(2(1(1(2(2(0(1(0(1(x1))))))))))))) | → | 2(2(2(2(0(1(0(0(0(1(0(0(0(0(0(1(2(x1))))))))))))))))) | (71) |
2(2(1(1(2(1(0(1(1(2(0(0(2(x1))))))))))))) | → | 2(2(2(0(0(0(0(1(2(0(0(0(2(2(2(2(2(x1))))))))))))))))) | (72) |
and S is the following TRS.
2(1(2(2(1(2(0(2(0(0(2(1(0(x1))))))))))))) | → | 1(1(2(0(2(2(2(0(2(2(2(2(2(2(1(2(0(x1))))))))))))))))) | (73) |
0(2(1(1(2(2(1(2(1(0(0(0(0(x1))))))))))))) | → | 0(2(1(2(2(2(2(2(2(2(2(2(1(0(0(0(0(x1))))))))))))))))) | (74) |
1(2(0(2(1(1(2(0(1(2(0(0(0(x1))))))))))))) | → | 2(2(1(2(2(2(2(2(2(2(2(1(0(1(0(0(0(x1))))))))))))))))) | (75) |
0(1(1(0(2(2(0(1(2(2(0(0(0(x1))))))))))))) | → | 1(1(2(0(0(0(0(0(0(0(0(0(0(0(2(1(0(x1))))))))))))))))) | (76) |
1(0(1(2(0(2(0(0(1(0(1(0(0(x1))))))))))))) | → | 0(2(2(2(1(0(0(0(0(1(2(1(0(0(0(0(0(x1))))))))))))))))) | (77) |
2(1(2(0(2(1(2(0(1(1(1(0(0(x1))))))))))))) | → | 1(2(1(2(0(2(2(1(0(0(0(0(0(1(0(0(0(x1))))))))))))))))) | (78) |
2(2(0(1(1(2(0(1(1(0(2(0(0(x1))))))))))))) | → | 2(0(2(2(0(1(2(2(2(2(2(2(0(2(0(0(0(x1))))))))))))))))) | (79) |
0(0(1(2(2(0(1(2(1(1(2(0(0(x1))))))))))))) | → | 0(2(2(2(2(2(0(2(2(2(1(0(0(0(0(0(1(x1))))))))))))))))) | (80) |
0(0(2(0(1(2(2(0(0(2(2(0(0(x1))))))))))))) | → | 0(0(2(2(1(0(0(0(0(0(0(0(0(0(1(0(2(x1))))))))))))))))) | (81) |
1(1(0(1(2(1(1(1(1(0(0(1(0(x1))))))))))))) | → | 0(0(2(2(2(2(0(2(2(0(0(0(1(1(0(1(0(x1))))))))))))))))) | (82) |
2(1(0(0(1(1(1(1(0(1(0(1(0(x1))))))))))))) | → | 2(2(2(1(0(0(0(1(2(0(2(2(2(2(2(0(0(x1))))))))))))))))) | (83) |
2(0(1(2(2(0(2(0(1(1(0(1(0(x1))))))))))))) | → | 2(2(2(0(2(2(2(2(0(2(2(2(2(0(2(2(0(x1))))))))))))))))) | (84) |
2(0(1(1(2(2(2(1(1(1(0(1(0(x1))))))))))))) | → | 0(1(0(0(0(0(0(0(1(2(0(0(0(0(1(0(0(x1))))))))))))))))) | (85) |
0(1(0(1(1(0(2(2(1(0(1(1(0(x1))))))))))))) | → | 0(0(2(1(0(0(0(1(2(2(1(0(0(0(0(0(0(x1))))))))))))))))) | (86) |
2(1(1(2(1(0(0(1(2(0(1(1(0(x1))))))))))))) | → | 2(2(2(2(2(2(2(2(2(0(2(1(0(1(0(0(1(x1))))))))))))))))) | (87) |
1(2(2(2(2(1(1(2(2(2(1(1(0(x1))))))))))))) | → | 2(0(2(2(2(2(2(0(2(2(2(0(2(2(2(2(1(x1))))))))))))))))) | (88) |
1(2(1(2(1(0(0(1(0(0(2(1(0(x1))))))))))))) | → | 2(0(0(1(0(2(2(2(2(2(2(2(0(2(1(0(0(x1))))))))))))))))) | (89) |
2(0(2(1(1(2(2(2(1(0(2(1(0(x1))))))))))))) | → | 2(2(0(0(2(0(2(1(0(0(0(0(0(0(0(0(0(x1))))))))))))))))) | (90) |
1(1(1(0(1(2(0(2(0(2(2(1(0(x1))))))))))))) | → | 1(0(0(0(0(0(0(0(0(0(2(0(2(2(1(0(0(x1))))))))))))))))) | (91) |
0(2(2(0(0(1(2(2(0(1(0(2(0(x1))))))))))))) | → | 0(2(1(0(0(0(0(0(0(0(0(2(1(0(0(0(0(x1))))))))))))))))) | (92) |
0(2(2(0(1(2(2(0(1(1(0(2(0(x1))))))))))))) | → | 1(0(0(0(1(2(2(2(2(2(2(2(2(0(0(0(2(x1))))))))))))))))) | (93) |
1(1(0(2(0(1(2(1(1(1(0(2(0(x1))))))))))))) | → | 0(1(0(0(0(0(1(0(0(1(0(2(2(2(0(2(0(x1))))))))))))))))) | (94) |
1(1(0(0(0(1(0(2(1(0(1(2(0(x1))))))))))))) | → | 0(1(2(0(2(2(0(2(2(2(2(2(2(2(2(1(2(x1))))))))))))))))) | (95) |
2(0(0(1(2(2(2(1(2(0(1(2(0(x1))))))))))))) | → | 2(1(0(2(0(1(0(0(0(0(0(0(0(0(0(0(0(x1))))))))))))))))) | (96) |
0(1(1(0(2(0(2(2(1(2(1(2(0(x1))))))))))))) | → | 0(2(0(0(0(0(0(0(0(2(1(0(0(0(1(0(2(x1))))))))))))))))) | (97) |
1(0(0(1(0(1(1(1(1(0(0(0(1(x1))))))))))))) | → | 0(2(1(0(0(0(0(0(0(0(0(0(0(1(0(2(2(x1))))))))))))))))) | (98) |
0(2(1(0(1(2(1(2(0(1(0(0(1(x1))))))))))))) | → | 0(2(2(0(0(0(0(0(1(0(0(0(0(0(2(0(0(x1))))))))))))))))) | (99) |
1(1(1(2(1(2(2(0(0(2(0(0(1(x1))))))))))))) | → | 0(0(2(0(2(1(0(0(0(0(0(0(1(2(0(1(0(x1))))))))))))))))) | (100) |
2(1(0(0(1(2(2(1(0(2(0(0(1(x1))))))))))))) | → | 2(0(0(2(0(0(0(0(0(0(0(0(0(0(0(0(0(x1))))))))))))))))) | (101) |
1(2(0(0(2(1(0(1(1(2(0(0(1(x1))))))))))))) | → | 1(0(2(2(2(0(2(2(2(1(0(0(0(2(0(0(1(x1))))))))))))))))) | (102) |
1(1(2(0(1(1(0(0(2(2(0(0(1(x1))))))))))))) | → | 1(0(0(2(0(2(2(0(2(2(2(2(2(2(0(2(1(x1))))))))))))))))) | (103) |
0(1(2(1(0(2(0(2(1(2(1(0(1(x1))))))))))))) | → | 0(2(1(2(2(2(2(1(0(0(0(0(0(1(0(0(2(x1))))))))))))))))) | (104) |
1(0(1(0(0(0(1(1(1(0(2(0(1(x1))))))))))))) | → | 0(2(1(2(2(1(0(0(0(0(0(1(0(0(0(0(1(x1))))))))))))))))) | (105) |
1(1(1(1(1(0(1(0(2(0(2(0(1(x1))))))))))))) | → | 1(0(0(1(2(0(2(0(2(2(2(2(2(2(0(1(1(x1))))))))))))))))) | (106) |
1(0(2(0(1(2(0(0(1(1(2(0(1(x1))))))))))))) | → | 1(1(1(2(2(1(1(0(0(0(0(0(0(0(0(1(0(x1))))))))))))))))) | (107) |
0(1(2(0(0(1(0(1(2(1(2(0(1(x1))))))))))))) | → | 0(0(2(0(0(1(2(2(2(1(0(0(0(0(0(1(2(x1))))))))))))))))) | (108) |
2(1(0(2(0(1(1(1(2(1(2(0(1(x1))))))))))))) | → | 2(0(2(0(0(2(0(0(0(0(1(0(0(0(0(1(1(x1))))))))))))))))) | (109) |
0(2(2(1(0(0(0(2(2(1(2(0(1(x1))))))))))))) | → | 2(0(1(0(2(2(2(2(2(2(2(2(2(2(2(0(0(x1))))))))))))))))) | (110) |
2(1(0(1(2(1(1(0(1(0(0(1(1(x1))))))))))))) | → | 2(0(2(0(1(0(0(2(2(1(0(0(0(0(0(0(1(x1))))))))))))))))) | (111) |
0(0(2(0(1(2(2(0(1(1(0(1(1(x1))))))))))))) | → | 1(0(0(0(2(1(2(2(2(2(1(0(0(0(0(1(0(x1))))))))))))))))) | (112) |
2(1(2(0(1(2(0(1(0(2(0(1(1(x1))))))))))))) | → | 2(1(2(2(2(2(2(2(1(1(2(2(2(2(2(2(1(x1))))))))))))))))) | (113) |
2(1(2(2(0(0(1(1(0(2(0(1(1(x1))))))))))))) | → | 2(0(0(0(0(0(2(2(1(0(0(0(0(0(1(2(0(x1))))))))))))))))) | (114) |
2(0(1(1(0(1(1(0(0(0(1(1(1(x1))))))))))))) | → | 2(1(2(2(2(0(2(2(0(2(2(2(2(2(0(0(0(x1))))))))))))))))) | (115) |
2(0(2(0(1(2(0(2(0(0(1(1(1(x1))))))))))))) | → | 2(2(2(2(0(2(2(0(2(2(2(2(1(0(2(0(1(x1))))))))))))))))) | (116) |
2(1(2(0(0(1(2(2(2(2(1(1(1(x1))))))))))))) | → | 2(1(1(2(2(1(0(0(0(0(1(0(0(0(0(0(0(x1))))))))))))))))) | (117) |
0(2(0(0(1(0(2(0(2(0(2(1(1(x1))))))))))))) | → | 1(2(2(2(2(0(2(2(2(1(0(0(0(0(1(0(2(x1))))))))))))))))) | (118) |
2(2(0(2(0(1(0(0(0(1(2(1(1(x1))))))))))))) | → | 2(2(2(2(2(1(0(0(0(0(0(0(0(1(2(0(1(x1))))))))))))))))) | (119) |
0(1(1(1(1(0(2(0(0(2(2(1(1(x1))))))))))))) | → | 0(0(1(2(2(2(2(1(0(1(2(1(0(0(0(0(2(x1))))))))))))))))) | (120) |
0(0(2(2(1(2(2(1(1(0(0(2(1(x1))))))))))))) | → | 2(2(1(0(0(0(0(0(0(0(0(0(2(0(2(0(1(x1))))))))))))))))) | (121) |
1(0(0(2(2(2(0(1(2(0(0(2(1(x1))))))))))))) | → | 1(0(1(2(2(0(2(0(2(2(2(1(0(0(0(0(0(x1))))))))))))))))) | (122) |
1(1(0(1(1(1(1(0(0(1(0(2(1(x1))))))))))))) | → | 0(1(1(2(1(0(0(0(0(0(1(0(2(0(0(0(0(x1))))))))))))))))) | (123) |
0(0(1(0(1(2(2(1(2(1(0(2(1(x1))))))))))))) | → | 0(0(1(0(1(2(2(2(2(2(0(2(1(0(0(0(1(x1))))))))))))))))) | (124) |
1(0(0(1(2(2(0(0(2(1(1(2(1(x1))))))))))))) | → | 0(2(2(2(2(1(0(0(1(0(0(0(0(0(0(1(1(x1))))))))))))))))) | (125) |
1(0(0(1(2(0(2(1(0(0(2(2(1(x1))))))))))))) | → | 2(2(2(2(2(2(2(2(0(2(2(2(2(2(0(1(0(x1))))))))))))))))) | (126) |
1(1(2(1(0(2(2(2(1(0(2(2(1(x1))))))))))))) | → | 1(0(0(0(2(1(2(2(0(2(2(2(2(2(0(0(0(x1))))))))))))))))) | (127) |
2(0(1(0(0(2(1(1(0(0(0(0(2(x1))))))))))))) | → | 2(2(2(2(0(2(0(2(2(2(2(1(0(0(0(1(0(x1))))))))))))))))) | (128) |
1(1(1(0(1(0(1(2(1(2(0(0(2(x1))))))))))))) | → | 0(0(2(0(2(2(2(1(1(0(0(0(0(0(0(0(1(x1))))))))))))))))) | (129) |
1(2(1(0(2(0(0(0(1(0(1(0(2(x1))))))))))))) | → | 0(0(0(0(0(0(0(0(1(0(0(1(0(0(1(0(2(x1))))))))))))))))) | (130) |
2(0(1(1(2(0(0(1(1(0(2(0(2(x1))))))))))))) | → | 2(0(1(0(0(0(1(0(0(0(0(1(0(0(0(2(2(x1))))))))))))))))) | (131) |
1(0(2(1(2(0(2(2(0(2(2(0(2(x1))))))))))))) | → | 0(2(2(1(0(0(0(0(0(0(0(0(0(2(2(2(2(x1))))))))))))))))) | (132) |
1(2(2(2(1(2(1(2(1(2(0(1(2(x1))))))))))))) | → | 1(2(1(0(0(0(0(0(2(0(2(1(0(0(0(1(2(x1))))))))))))))))) | (133) |
2(0(1(0(1(0(2(1(1(2(1(1(2(x1))))))))))))) | → | 2(1(2(2(2(2(2(2(0(2(1(0(0(2(0(2(2(x1))))))))))))))))) | (134) |
0(1(0(2(0(0(2(0(2(2(1(1(2(x1))))))))))))) | → | 0(0(2(2(0(2(2(2(2(2(2(2(1(0(1(0(2(x1))))))))))))))))) | (135) |
2(2(1(0(2(0(2(2(0(0(2(1(2(x1))))))))))))) | → | 2(0(2(2(2(2(2(2(1(0(0(2(0(0(0(0(2(x1))))))))))))))))) | (136) |
2(1(0(0(1(1(2(2(2(0(2(1(2(x1))))))))))))) | → | 2(2(2(2(2(2(0(2(2(2(2(2(0(0(2(2(1(x1))))))))))))))))) | (137) |
0(2(2(1(2(0(0(1(0(1(2(1(2(x1))))))))))))) | → | 1(0(0(0(1(2(1(0(0(0(0(0(0(1(1(2(2(x1))))))))))))))))) | (138) |
0(1(2(1(2(2(2(2(1(2(2(1(2(x1))))))))))))) | → | 0(0(0(0(0(0(0(0(1(0(0(0(0(2(0(0(2(x1))))))))))))))))) | (139) |
0(0(1(2(2(0(1(2(1(0(0(2(2(x1))))))))))))) | → | 0(2(2(0(2(2(0(2(2(0(2(2(2(2(2(2(2(x1))))))))))))))))) | (140) |
0(2(1(0(2(1(2(1(2(0(0(2(2(x1))))))))))))) | → | 1(2(0(0(1(0(0(0(0(1(0(2(2(2(2(2(2(x1))))))))))))))))) | (141) |
0(1(0(1(2(1(1(0(2(2(0(2(2(x1))))))))))))) | → | 1(0(0(2(0(0(1(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))) | (142) |
0(2(0(2(2(1(2(1(2(2(0(2(2(x1))))))))))))) | → | 1(0(0(0(1(0(2(2(0(2(2(2(0(2(2(2(2(x1))))))))))))))))) | (143) |
1(0(1(0(2(2(1(1(2(0(1(2(2(x1))))))))))))) | → | 2(1(0(0(0(0(0(1(0(0(0(1(0(2(2(2(2(x1))))))))))))))))) | (144) |
2(0(0(2(1(1(0(1(2(1(1(2(2(x1))))))))))))) | → | 2(2(2(2(2(0(0(0(2(1(0(0(0(0(2(2(2(x1))))))))))))))))) | (145) |
0(1(2(0(0(2(0(2(1(2(2(1(2(x1))))))))))))) | → | 0(2(1(2(2(2(2(2(2(0(2(2(2(0(2(1(1(x1))))))))))))))))) | (146) |
{0(☐), 2(☐), 1(☐)}
We obtain the transformed TRSThere are 131 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRSThere are 393 ruless (increase limit for explicit display).
[02(x1)] | = | 1 + 1 · x1 |
[21(x1)] | = | 1 + 1 · x1 |
[11(x1)] | = | 1 + 1 · x1 |
[12(x1)] | = | 1 + 1 · x1 |
[22(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 + 1 · x1 |
[20(x1)] | = | 1 · x1 |
There are 377 ruless (increase limit for explicit display).
[00(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 + 1 · x1 |
[12(x1)] | = | 1 + 1 · x1 |
[22(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 + 1 · x1 |
00(02(20(01(12(22(20(00(02(22(20(00(00(x1))))))))))))) | → | 00(02(22(21(10(00(00(00(00(00(00(00(00(01(10(02(20(x1))))))))))))))))) | (243) |
00(02(20(01(12(22(20(00(02(22(20(00(01(x1))))))))))))) | → | 00(02(22(21(10(00(00(00(00(00(00(00(00(01(10(02(21(x1))))))))))))))))) | (245) |
10(00(02(22(22(20(01(12(20(00(02(21(12(x1))))))))))))) | → | 10(01(12(22(20(02(20(02(22(22(21(10(00(00(00(00(02(x1))))))))))))))))) | (325) |
20(01(10(00(02(21(11(10(00(00(00(02(22(x1))))))))))))) | → | 22(22(22(20(02(20(02(22(22(22(21(10(00(00(01(10(02(x1))))))))))))))))) | (334) |
00(01(11(10(02(22(20(01(12(22(20(00(00(00(x1)))))))))))))) | → | 01(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(00(x1)))))))))))))))))) | (372) |
00(01(11(10(02(22(20(01(12(22(20(00(00(02(x1)))))))))))))) | → | 01(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(02(x1)))))))))))))))))) | (373) |
00(01(11(10(02(22(20(01(12(22(20(00(00(01(x1)))))))))))))) | → | 01(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(01(x1)))))))))))))))))) | (374) |
20(01(11(10(02(22(20(01(12(22(20(00(00(00(x1)))))))))))))) | → | 21(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(00(x1)))))))))))))))))) | (375) |
20(01(11(10(02(22(20(01(12(22(20(00(00(02(x1)))))))))))))) | → | 21(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(02(x1)))))))))))))))))) | (376) |
20(01(11(10(02(22(20(01(12(22(20(00(00(01(x1)))))))))))))) | → | 21(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(01(x1)))))))))))))))))) | (377) |
10(01(11(10(02(22(20(01(12(22(20(00(00(00(x1)))))))))))))) | → | 11(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(00(x1)))))))))))))))))) | (378) |
10(01(11(10(02(22(20(01(12(22(20(00(00(02(x1)))))))))))))) | → | 11(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(02(x1)))))))))))))))))) | (379) |
10(01(11(10(02(22(20(01(12(22(20(00(00(01(x1)))))))))))))) | → | 11(11(12(20(00(00(00(00(00(00(00(00(00(00(02(21(10(01(x1)))))))))))))))))) | (380) |
01(12(20(00(02(20(02(21(12(22(21(12(22(x1))))))))))))) | → | 02(21(12(22(22(22(22(22(20(02(22(22(20(02(21(11(12(x1))))))))))))))))) | (625) |
Root-labeling is applied.
We obtain the labeled TRS1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1010(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0010(x1))))))))))))))))) | (627) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1000(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0000(x1))))))))))))))))) | (628) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1002(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0002(x1))))))))))))))))) | (629) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1022(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0022(x1))))))))))))))))) | (630) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1020(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0020(x1))))))))))))))))) | (631) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1001(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0001(x1))))))))))))))))) | (632) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1012(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0012(x1))))))))))))))))) | (633) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1021(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0021(x1))))))))))))))))) | (634) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1011(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0011(x1))))))))))))))))) | (635) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1110(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0110(x1))))))))))))))))) | (636) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1100(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0100(x1))))))))))))))))) | (637) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1102(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0102(x1))))))))))))))))) | (638) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1122(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0122(x1))))))))))))))))) | (639) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1120(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0120(x1))))))))))))))))) | (640) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1101(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0101(x1))))))))))))))))) | (641) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1112(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0112(x1))))))))))))))))) | (642) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1121(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0121(x1))))))))))))))))) | (643) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1111(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0111(x1))))))))))))))))) | (644) |
[1000(x1)] | = | 1 · x1 |
[0002(x1)] | = | 1 · x1 |
[0222(x1)] | = | 1 · x1 |
[2222(x1)] | = | 1 · x1 |
[2220(x1)] | = | 1 · x1 |
[2001(x1)] | = | 1 · x1 + 1 |
[0112(x1)] | = | 1 · x1 |
[1220(x1)] | = | 1 · x1 |
[2000(x1)] | = | 1 · x1 |
[0221(x1)] | = | 1 · x1 |
[2110(x1)] | = | 1 · x1 |
[1010(x1)] | = | 1 · x1 |
[1001(x1)] | = | 1 · x1 |
[1222(x1)] | = | 1 · x1 |
[2002(x1)] | = | 1 · x1 |
[0220(x1)] | = | 1 · x1 |
[2221(x1)] | = | 1 · x1 |
[0000(x1)] | = | 1 · x1 |
[0010(x1)] | = | 1 · x1 |
[1002(x1)] | = | 1 · x1 |
[1022(x1)] | = | 1 · x1 |
[0022(x1)] | = | 1 · x1 |
[1020(x1)] | = | 1 · x1 |
[0020(x1)] | = | 1 · x1 |
[0001(x1)] | = | 1 · x1 |
[1012(x1)] | = | 1 · x1 |
[0012(x1)] | = | 1 · x1 |
[1021(x1)] | = | 1 · x1 |
[0021(x1)] | = | 1 · x1 |
[1011(x1)] | = | 1 · x1 |
[0011(x1)] | = | 1 · x1 |
[2111(x1)] | = | 1 · x1 |
[1110(x1)] | = | 1 · x1 |
[0110(x1)] | = | 1 · x1 |
[1100(x1)] | = | 1 · x1 |
[0100(x1)] | = | 1 · x1 |
[1102(x1)] | = | 1 · x1 |
[0102(x1)] | = | 1 · x1 |
[1122(x1)] | = | 1 · x1 |
[0122(x1)] | = | 1 · x1 |
[1120(x1)] | = | 1 · x1 |
[0120(x1)] | = | 1 · x1 |
[1101(x1)] | = | 1 · x1 |
[0101(x1)] | = | 1 · x1 |
[1112(x1)] | = | 1 · x1 |
[1121(x1)] | = | 1 · x1 |
[0121(x1)] | = | 1 · x1 |
[1111(x1)] | = | 1 · x1 |
[0111(x1)] | = | 1 · x1 |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1010(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0010(x1))))))))))))))))) | (627) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1000(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0000(x1))))))))))))))))) | (628) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1002(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0002(x1))))))))))))))))) | (629) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1022(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0022(x1))))))))))))))))) | (630) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1020(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0020(x1))))))))))))))))) | (631) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1001(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0001(x1))))))))))))))))) | (632) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1012(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0012(x1))))))))))))))))) | (633) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1021(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0021(x1))))))))))))))))) | (634) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2110(1011(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0000(0011(x1))))))))))))))))) | (635) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1110(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0110(x1))))))))))))))))) | (636) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1100(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0100(x1))))))))))))))))) | (637) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1102(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0102(x1))))))))))))))))) | (638) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1122(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0122(x1))))))))))))))))) | (639) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1120(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0120(x1))))))))))))))))) | (640) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1101(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0101(x1))))))))))))))))) | (641) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1112(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0112(x1))))))))))))))))) | (642) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1121(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0121(x1))))))))))))))))) | (643) |
1000(0002(0222(2222(2220(2001(0112(1220(2000(0002(0221(2111(1111(x1))))))))))))) | → | 1001(0112(1222(2220(2002(0220(2002(0222(2222(2221(2110(1000(0000(0000(0000(0001(0111(x1))))))))))))))))) | (644) |
There are no rules in the TRS. Hence, it is terminating.