Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26896)

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)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
649
[4(x1)] = x1 +
491
[3(x1)] = x1 +
774
[2(x1)] = x1 +
685
[1(x1)] = x1 +
774
[0(x1)] = x1 +
721
all of the following rules can be deleted.
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)

1.1 Closure Under Flat Contexts

Using the flat contexts

{5(), 4(), 3(), 2(), 1(), 0()}

We obtain the transformed TRS

There are 288 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

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

We obtain the labeled TRS

There are 1728 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
205
[51(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
209
[54(x1)] = x1 +
20
[55(x1)] = x1 +
0
[40(x1)] = x1 +
20
[41(x1)] = x1 +
209
[42(x1)] = x1 +
225
[43(x1)] = x1 +
124
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
42
[33(x1)] = x1 +
0
[34(x1)] = x1 +
205
[35(x1)] = x1 +
205
[20(x1)] = x1 +
41
[21(x1)] = x1 +
206
[22(x1)] = x1 +
205
[23(x1)] = x1 +
123
[24(x1)] = x1 +
1
[25(x1)] = x1 +
4
[10(x1)] = x1 +
205
[11(x1)] = x1 +
164
[12(x1)] = x1 +
0
[13(x1)] = x1 +
86
[14(x1)] = x1 +
168
[15(x1)] = x1 +
205
[00(x1)] = x1 +
4
[01(x1)] = x1 +
205
[02(x1)] = x1 +
205
[03(x1)] = x1 +
165
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
all of the following rules can be deleted.

There are 1692 ruless (increase limit for explicit display).

1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
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)

1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.