Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/138254)

The rewrite relation of the following TRS is considered.

0(0(4(2(5(0(1(4(2(1(0(1(x1)))))))))))) → 2(2(5(5(2(0(0(5(3(1(5(4(1(2(5(5(5(1(x1)))))))))))))))))) (1)
0(1(1(1(4(0(4(5(0(4(3(1(x1)))))))))))) → 5(2(5(2(5(5(5(0(4(4(3(1(5(2(2(5(3(x1))))))))))))))))) (2)
0(1(4(0(0(3(2(4(3(1(0(4(x1)))))))))))) → 2(5(5(3(1(2(2(5(4(3(1(1(5(3(5(x1))))))))))))))) (3)
0(2(4(3(3(1(4(0(1(3(2(2(x1)))))))))))) → 3(2(4(4(3(5(1(5(5(3(3(1(0(2(2(1(x1)))))))))))))))) (4)
0(3(2(4(0(4(5(3(4(1(2(4(x1)))))))))))) → 2(1(5(1(0(3(0(5(1(2(3(5(1(5(5(1(x1)))))))))))))))) (5)
0(3(4(2(1(4(1(4(4(4(4(0(x1)))))))))))) → 3(2(1(0(5(0(3(5(4(0(2(3(1(0(5(0(x1)))))))))))))))) (6)
0(3(4(5(2(1(4(2(3(4(4(3(x1)))))))))))) → 0(5(3(5(3(0(1(0(5(0(5(1(3(5(4(2(x1)))))))))))))))) (7)
0(4(0(4(0(4(4(5(0(1(5(2(x1)))))))))))) → 3(1(5(1(3(3(4(1(5(5(4(1(3(3(x1)))))))))))))) (8)
0(4(2(3(5(4(4(4(1(2(2(4(x1)))))))))))) → 0(4(2(0(3(0(5(0(2(1(2(5(1(5(5(4(x1)))))))))))))))) (9)
0(4(2(4(1(1(3(0(0(4(1(4(x1)))))))))))) → 2(3(1(5(4(5(2(0(2(1(5(1(3(1(x1)))))))))))))) (10)
0(4(4(1(0(3(2(2(3(4(3(4(x1)))))))))))) → 5(1(5(0(2(5(5(2(3(2(4(3(1(2(2(5(x1)))))))))))))))) (11)
0(4(4(1(5(3(4(2(4(0(2(5(x1)))))))))))) → 5(2(0(2(5(3(0(1(0(0(2(0(3(5(1(5(x1)))))))))))))))) (12)
0(5(2(2(1(3(4(0(1(3(5(4(x1)))))))))))) → 1(0(2(2(5(2(1(1(5(5(5(5(5(3(1(x1))))))))))))))) (13)
0(5(3(2(1(3(4(0(4(4(0(0(x1)))))))))))) → 4(2(5(5(5(2(2(5(5(3(2(5(5(0(5(x1))))))))))))))) (14)
1(0(2(1(0(3(1(4(4(4(4(5(x1)))))))))))) → 3(1(3(3(5(1(3(1(5(5(3(2(5(3(2(x1))))))))))))))) (15)
1(0(5(0(5(2(4(0(4(2(1(1(x1)))))))))))) → 5(1(1(0(0(5(5(5(0(2(1(0(2(5(5(4(3(x1))))))))))))))))) (16)
1(2(1(4(0(1(4(0(1(5(1(1(x1)))))))))))) → 2(2(2(3(1(5(2(2(2(0(1(3(3(5(5(0(x1)))))))))))))))) (17)
1(2(3(0(4(0(3(0(4(4(3(4(x1)))))))))))) → 2(3(5(3(0(5(0(2(3(1(4(5(0(0(x1)))))))))))))) (18)
1(3(2(1(2(4(4(2(1(3(2(2(x1)))))))))))) → 1(3(5(3(0(5(2(2(5(3(5(5(5(3(5(1(x1)))))))))))))))) (19)
1(3(4(4(4(3(0(3(5(5(1(2(x1)))))))))))) → 5(2(2(5(2(2(1(5(3(2(1(2(5(5(5(5(5(x1))))))))))))))))) (20)
1(3(5(4(1(0(4(0(3(4(0(4(x1)))))))))))) → 5(1(0(5(3(1(5(1(5(0(0(2(2(1(3(0(5(x1))))))))))))))))) (21)
1(4(2(5(1(4(0(1(3(0(4(0(x1)))))))))))) → 3(1(3(2(0(2(0(0(2(2(5(1(3(5(5(1(x1)))))))))))))))) (22)
1(4(3(1(0(1(1(1(2(3(4(4(x1)))))))))))) → 5(3(4(1(2(2(2(2(5(0(5(1(5(1(5(3(5(x1))))))))))))))))) (23)
1(4(3(3(0(1(2(1(0(3(3(5(x1)))))))))))) → 5(0(2(5(5(5(2(5(3(2(4(5(0(5(x1)))))))))))))) (24)
2(1(1(3(4(4(3(4(4(0(4(3(x1)))))))))))) → 2(3(3(1(0(0(1(2(2(2(5(1(1(2(4(1(2(3(x1)))))))))))))))))) (25)
2(2(1(3(5(2(5(0(4(2(5(0(x1)))))))))))) → 2(2(5(5(2(5(5(2(0(2(5(5(1(1(5(x1))))))))))))))) (26)
2(2(2(4(2(0(4(1(3(4(4(4(x1)))))))))))) → 5(4(3(5(1(4(5(3(0(3(5(1(3(2(x1)))))))))))))) (27)
2(2(3(3(1(5(4(0(4(2(4(3(x1)))))))))))) → 5(5(5(1(1(2(5(2(0(5(1(5(3(0(3(0(5(3(x1)))))))))))))))))) (28)
2(2(3(4(3(4(3(4(2(4(4(0(x1)))))))))))) → 2(5(4(5(3(4(0(5(4(1(2(5(0(5(5(x1))))))))))))))) (29)
2(2(4(0(2(1(5(3(3(2(4(4(x1)))))))))))) → 5(3(3(0(3(3(5(5(0(2(2(5(0(0(x1)))))))))))))) (30)
2(2(4(4(2(3(4(3(4(2(4(5(x1)))))))))))) → 2(3(0(3(3(5(1(3(1(5(1(5(1(1(5(5(0(2(x1)))))))))))))))))) (31)
2(3(4(3(0(0(4(2(4(1(1(4(x1)))))))))))) → 5(0(3(1(1(0(3(3(3(3(5(4(1(2(5(x1))))))))))))))) (32)
2(3(5(0(3(1(4(0(1(3(4(4(x1)))))))))))) → 5(2(2(5(5(0(2(0(5(3(0(4(1(0(2(0(3(x1))))))))))))))))) (33)
2(4(0(3(4(4(0(3(4(0(5(0(x1)))))))))))) → 0(3(1(3(5(5(5(0(2(2(2(0(4(5(1(3(3(x1))))))))))))))))) (34)
2(4(0(4(0(1(2(0(1(3(4(1(x1)))))))))))) → 5(1(4(5(3(3(1(1(5(2(5(5(5(4(1(x1))))))))))))))) (35)
2(4(0(4(1(4(1(1(1(1(3(1(x1)))))))))))) → 4(2(0(3(2(0(0(2(3(1(2(2(2(0(5(5(x1)))))))))))))))) (36)
2(4(1(1(4(2(4(0(4(5(0(4(x1)))))))))))) → 3(1(5(1(5(5(5(5(5(5(1(3(1(5(5(5(0(5(x1)))))))))))))))))) (37)
2(4(3(3(3(4(0(0(4(0(0(1(x1)))))))))))) → 2(0(2(4(1(2(5(0(0(2(1(2(5(5(5(1(0(x1))))))))))))))))) (38)
2(4(3(4(0(0(1(3(0(1(4(1(x1)))))))))))) → 2(5(2(2(3(3(3(1(1(5(5(1(5(4(0(2(x1)))))))))))))))) (39)
2(5(2(2(1(4(2(1(4(1(4(4(x1)))))))))))) → 5(5(1(5(5(2(4(3(0(5(1(5(0(3(x1)))))))))))))) (40)
2(5(5(2(2(4(4(4(5(4(3(4(x1)))))))))))) → 0(5(0(2(2(2(5(1(5(5(5(3(3(1(2(5(5(3(x1)))))))))))))))))) (41)
3(0(2(1(1(4(3(1(4(2(1(0(x1)))))))))))) → 5(2(0(3(0(1(2(5(4(5(5(5(4(0(0(x1))))))))))))))) (42)
3(0(3(4(4(0(4(4(3(4(4(1(x1)))))))))))) → 5(2(0(2(5(2(0(1(2(2(4(1(0(4(4(5(4(1(x1)))))))))))))))))) (43)
3(0(4(0(3(4(4(4(4(4(4(1(x1)))))))))))) → 3(1(5(1(4(5(2(1(4(5(0(1(4(5(5(x1))))))))))))))) (44)
3(1(0(4(0(3(2(1(4(0(5(4(x1)))))))))))) → 0(5(4(5(1(0(3(5(3(0(3(1(1(2(x1)))))))))))))) (45)
3(1(3(1(4(3(4(3(1(3(4(4(x1)))))))))))) → 5(5(3(2(3(1(1(0(0(5(1(1(5(2(5(0(2(x1))))))))))))))))) (46)
3(1(3(4(0(1(0(3(1(3(4(4(x1)))))))))))) → 5(3(3(5(3(2(4(2(2(3(1(1(0(2(1(x1))))))))))))))) (47)
3(2(0(3(4(4(2(4(2(3(4(0(x1)))))))))))) → 0(1(3(5(5(3(2(5(2(3(5(3(4(3(3(x1))))))))))))))) (48)
3(2(3(4(4(0(5(3(4(4(4(0(x1)))))))))))) → 5(1(2(5(1(3(0(5(5(3(2(5(1(2(5(1(0(0(x1)))))))))))))))))) (49)
3(2(4(3(2(4(0(1(1(4(1(3(x1)))))))))))) → 0(0(5(5(1(0(5(5(0(2(3(4(5(0(2(0(5(x1))))))))))))))))) (50)
3(3(1(3(4(0(1(5(5(3(4(1(x1)))))))))))) → 1(5(4(5(5(1(5(1(2(1(5(4(4(2(x1)))))))))))))) (51)
3(3(1(5(0(4(2(0(4(2(1(2(x1)))))))))))) → 5(5(1(2(5(4(1(5(5(5(5(3(2(0(0(3(3(x1))))))))))))))))) (52)
3(3(2(3(3(3(5(3(0(3(4(2(x1)))))))))))) → 2(5(4(1(5(5(2(2(5(5(5(5(1(1(0(x1))))))))))))))) (53)
3(3(3(3(5(1(3(4(0(3(0(2(x1)))))))))))) → 5(5(5(5(4(5(3(3(3(3(5(0(0(1(5(0(x1)))))))))))))))) (54)
3(4(0(0(1(5(2(4(2(3(2(2(x1)))))))))))) → 1(5(5(5(2(1(3(2(5(1(4(5(2(5(0(x1))))))))))))))) (55)
3(4(1(4(4(2(0(4(0(3(4(1(x1)))))))))))) → 3(4(0(2(2(0(5(4(3(1(1(3(5(1(5(x1))))))))))))))) (56)
3(4(1(5(4(3(4(4(4(2(4(4(x1)))))))))))) → 5(5(5(5(0(5(4(0(3(5(0(3(1(3(2(x1))))))))))))))) (57)
3(4(2(3(3(5(2(4(0(2(2(5(x1)))))))))))) → 3(2(1(2(1(4(5(3(3(3(2(5(2(5(x1)))))))))))))) (58)
3(4(2(4(0(2(4(2(3(4(0(3(x1)))))))))))) → 2(5(2(1(5(5(3(5(5(5(5(0(3(5(x1)))))))))))))) (59)
3(4(3(0(3(1(2(1(1(1(4(0(x1)))))))))))) → 2(1(2(0(0(5(5(1(3(5(5(3(5(1(2(0(2(0(x1)))))))))))))))))) (60)
3(4(3(4(0(1(0(5(2(3(4(1(x1)))))))))))) → 5(2(4(4(1(5(3(2(5(0(2(5(2(2(1(x1))))))))))))))) (61)
3(4(3(4(3(0(4(4(2(1(4(5(x1)))))))))))) → 0(4(5(4(4(1(0(0(2(1(0(2(1(2(5(1(3(x1))))))))))))))))) (62)
3(4(3(4(5(2(3(2(3(4(3(0(x1)))))))))))) → 2(5(5(4(1(5(5(3(0(1(2(1(0(5(3(3(0(x1))))))))))))))))) (63)
3(4(4(0(1(5(1(4(0(3(3(0(x1)))))))))))) → 2(3(2(1(1(0(2(1(2(2(2(0(5(3(1(x1))))))))))))))) (64)
3(4(4(0(4(2(3(4(0(3(3(5(x1)))))))))))) → 5(1(5(4(0(0(5(3(0(1(1(2(3(5(2(5(1(x1))))))))))))))))) (65)
3(4(4(2(5(1(1(0(4(2(0(3(x1)))))))))))) → 5(5(5(2(3(1(3(3(1(5(2(1(5(3(x1)))))))))))))) (66)
3(4(4(3(3(4(3(4(2(0(2(4(x1)))))))))))) → 3(2(0(5(5(0(0(3(1(4(1(5(4(5(2(x1))))))))))))))) (67)
3(4(4(4(0(4(4(4(4(2(5(1(x1)))))))))))) → 1(1(2(4(5(2(0(5(1(3(2(2(5(1(5(5(x1)))))))))))))))) (68)
3(4(4(5(2(3(4(4(4(3(0(0(x1)))))))))))) → 2(0(0(0(1(1(2(5(5(4(1(5(1(3(1(0(x1)))))))))))))))) (69)
4(0(1(3(1(4(1(4(3(4(4(0(x1)))))))))))) → 1(3(1(5(0(3(5(5(4(5(4(1(1(4(1(1(x1)))))))))))))))) (70)
4(0(3(4(3(0(2(5(3(4(0(5(x1)))))))))))) → 1(2(0(5(3(5(5(1(2(5(1(3(5(5(5(5(0(x1))))))))))))))))) (71)
4(0(4(4(4(4(1(0(4(2(1(3(x1)))))))))))) → 1(4(5(3(3(3(5(4(1(5(5(3(5(3(x1)))))))))))))) (72)
4(1(1(1(3(0(4(4(0(3(4(1(x1)))))))))))) → 1(0(0(3(3(1(2(5(3(3(1(4(0(1(x1)))))))))))))) (73)
4(1(3(4(3(4(0(3(3(2(3(2(x1)))))))))))) → 0(2(5(0(2(3(0(1(0(2(5(0(1(2(x1)))))))))))))) (74)
4(1(5(1(4(3(4(0(1(5(4(0(x1)))))))))))) → 2(5(5(4(1(5(1(2(5(0(0(5(5(2(5(2(2(x1))))))))))))))))) (75)
4(2(1(1(5(0(2(1(2(1(4(4(x1)))))))))))) → 4(3(3(3(2(1(0(2(0(0(5(0(0(2(x1)))))))))))))) (76)
4(2(1(3(0(4(4(4(1(1(3(0(x1)))))))))))) → 5(4(1(0(2(5(3(1(2(5(2(5(2(2(5(5(2(x1))))))))))))))))) (77)
4(2(3(4(3(4(1(3(0(3(3(4(x1)))))))))))) → 1(5(4(2(0(2(2(5(5(5(1(0(2(1(0(2(5(4(x1)))))))))))))))))) (78)
4(2(5(0(5(2(1(1(3(1(3(0(x1)))))))))))) → 1(4(0(5(5(2(5(5(3(3(5(5(5(5(1(0(5(x1))))))))))))))))) (79)
4(2(5(1(1(3(3(2(1(4(0(2(x1)))))))))))) → 5(3(3(5(1(0(2(1(5(5(0(0(2(3(5(5(5(0(x1)))))))))))))))))) (80)
4(3(0(4(0(3(4(2(3(5(1(1(x1)))))))))))) → 4(4(0(0(5(0(2(0(2(1(1(0(0(5(x1)))))))))))))) (81)
4(3(2(4(3(2(4(0(2(0(4(5(x1)))))))))))) → 4(0(0(2(5(3(0(5(5(3(3(5(2(0(5(2(5(x1))))))))))))))))) (82)
4(3(4(2(4(0(3(3(1(4(3(0(x1)))))))))))) → 1(4(3(2(5(0(2(1(0(2(5(2(0(2(5(2(1(x1))))))))))))))))) (83)
5(0(2(4(4(0(4(4(3(4(3(1(x1)))))))))))) → 3(1(3(3(5(5(5(1(1(4(5(5(0(0(2(1(0(x1))))))))))))))))) (84)
5(0(3(4(4(0(3(1(0(3(3(2(x1)))))))))))) → 1(5(3(1(4(1(5(4(1(1(1(5(0(0(2(5(x1)))))))))))))))) (85)
5(0(3(5(2(3(4(5(3(3(4(1(x1)))))))))))) → 2(4(0(2(5(1(5(5(5(2(2(2(5(0(x1)))))))))))))) (86)
5(0(4(3(4(3(2(1(4(2(4(0(x1)))))))))))) → 5(5(0(0(2(2(2(4(0(1(0(5(3(5(5(4(1(1(x1)))))))))))))))))) (87)
5(0(5(4(2(3(4(4(4(5(4(4(x1)))))))))))) → 2(0(5(1(3(3(3(1(1(2(3(5(0(3(x1)))))))))))))) (88)
5(1(3(4(2(3(0(4(0(0(3(0(x1)))))))))))) → 0(3(1(5(1(0(0(2(5(5(3(5(1(0(2(5(2(2(x1)))))))))))))))))) (89)
5(2(1(3(4(1(1(1(4(2(3(0(x1)))))))))))) → 1(0(3(1(5(5(5(2(2(5(0(0(5(1(5(4(5(0(x1)))))))))))))))))) (90)
5(2(3(4(4(0(4(0(2(4(0(2(x1)))))))))))) → 5(4(2(5(4(5(0(0(1(5(5(5(2(0(2(3(2(5(x1)))))))))))))))))) (91)
5(3(2(4(3(4(5(1(2(3(4(1(x1)))))))))))) → 5(5(1(5(1(0(2(0(5(0(5(0(1(2(2(x1))))))))))))))) (92)
5(3(4(4(4(2(0(1(1(1(3(3(x1)))))))))))) → 3(0(3(1(2(0(2(5(3(5(1(5(2(2(5(1(2(x1))))))))))))))))) (93)
5(4(0(3(0(4(2(1(4(4(1(1(x1)))))))))))) → 4(1(3(1(5(2(1(5(5(0(2(3(1(5(5(0(x1)))))))))))))))) (94)
5(4(2(0(0(0(4(0(1(1(0(4(x1)))))))))))) → 5(1(4(5(2(0(2(4(1(5(3(0(2(2(4(x1))))))))))))))) (95)
5(5(0(1(4(3(4(2(5(4(3(4(x1)))))))))))) → 1(2(3(3(5(1(2(3(5(0(1(0(3(1(x1)))))))))))))) (96)

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 +
0
[4(x1)] = x1 +
1
[3(x1)] = x1 +
1/5
[2(x1)] = x1 +
0
[1(x1)] = x1 +
1/5
[0(x1)] = x1 +
2/5
all of the following rules can be deleted.
0(0(4(2(5(0(1(4(2(1(0(1(x1)))))))))))) → 2(2(5(5(2(0(0(5(3(1(5(4(1(2(5(5(5(1(x1)))))))))))))))))) (1)
0(1(1(1(4(0(4(5(0(4(3(1(x1)))))))))))) → 5(2(5(2(5(5(5(0(4(4(3(1(5(2(2(5(3(x1))))))))))))))))) (2)
0(1(4(0(0(3(2(4(3(1(0(4(x1)))))))))))) → 2(5(5(3(1(2(2(5(4(3(1(1(5(3(5(x1))))))))))))))) (3)
0(3(2(4(0(4(5(3(4(1(2(4(x1)))))))))))) → 2(1(5(1(0(3(0(5(1(2(3(5(1(5(5(1(x1)))))))))))))))) (5)
0(3(4(2(1(4(1(4(4(4(4(0(x1)))))))))))) → 3(2(1(0(5(0(3(5(4(0(2(3(1(0(5(0(x1)))))))))))))))) (6)
0(3(4(5(2(1(4(2(3(4(4(3(x1)))))))))))) → 0(5(3(5(3(0(1(0(5(0(5(1(3(5(4(2(x1)))))))))))))))) (7)
0(4(0(4(0(4(4(5(0(1(5(2(x1)))))))))))) → 3(1(5(1(3(3(4(1(5(5(4(1(3(3(x1)))))))))))))) (8)
0(4(2(3(5(4(4(4(1(2(2(4(x1)))))))))))) → 0(4(2(0(3(0(5(0(2(1(2(5(1(5(5(4(x1)))))))))))))))) (9)
0(4(2(4(1(1(3(0(0(4(1(4(x1)))))))))))) → 2(3(1(5(4(5(2(0(2(1(5(1(3(1(x1)))))))))))))) (10)
0(4(4(1(0(3(2(2(3(4(3(4(x1)))))))))))) → 5(1(5(0(2(5(5(2(3(2(4(3(1(2(2(5(x1)))))))))))))))) (11)
0(4(4(1(5(3(4(2(4(0(2(5(x1)))))))))))) → 5(2(0(2(5(3(0(1(0(0(2(0(3(5(1(5(x1)))))))))))))))) (12)
0(5(2(2(1(3(4(0(1(3(5(4(x1)))))))))))) → 1(0(2(2(5(2(1(1(5(5(5(5(5(3(1(x1))))))))))))))) (13)
0(5(3(2(1(3(4(0(4(4(0(0(x1)))))))))))) → 4(2(5(5(5(2(2(5(5(3(2(5(5(0(5(x1))))))))))))))) (14)
1(0(2(1(0(3(1(4(4(4(4(5(x1)))))))))))) → 3(1(3(3(5(1(3(1(5(5(3(2(5(3(2(x1))))))))))))))) (15)
1(0(5(0(5(2(4(0(4(2(1(1(x1)))))))))))) → 5(1(1(0(0(5(5(5(0(2(1(0(2(5(5(4(3(x1))))))))))))))))) (16)
1(2(1(4(0(1(4(0(1(5(1(1(x1)))))))))))) → 2(2(2(3(1(5(2(2(2(0(1(3(3(5(5(0(x1)))))))))))))))) (17)
1(2(3(0(4(0(3(0(4(4(3(4(x1)))))))))))) → 2(3(5(3(0(5(0(2(3(1(4(5(0(0(x1)))))))))))))) (18)
1(3(2(1(2(4(4(2(1(3(2(2(x1)))))))))))) → 1(3(5(3(0(5(2(2(5(3(5(5(5(3(5(1(x1)))))))))))))))) (19)
1(3(4(4(4(3(0(3(5(5(1(2(x1)))))))))))) → 5(2(2(5(2(2(1(5(3(2(1(2(5(5(5(5(5(x1))))))))))))))))) (20)
1(3(5(4(1(0(4(0(3(4(0(4(x1)))))))))))) → 5(1(0(5(3(1(5(1(5(0(0(2(2(1(3(0(5(x1))))))))))))))))) (21)
1(4(2(5(1(4(0(1(3(0(4(0(x1)))))))))))) → 3(1(3(2(0(2(0(0(2(2(5(1(3(5(5(1(x1)))))))))))))))) (22)
1(4(3(1(0(1(1(1(2(3(4(4(x1)))))))))))) → 5(3(4(1(2(2(2(2(5(0(5(1(5(1(5(3(5(x1))))))))))))))))) (23)
1(4(3(3(0(1(2(1(0(3(3(5(x1)))))))))))) → 5(0(2(5(5(5(2(5(3(2(4(5(0(5(x1)))))))))))))) (24)
2(1(1(3(4(4(3(4(4(0(4(3(x1)))))))))))) → 2(3(3(1(0(0(1(2(2(2(5(1(1(2(4(1(2(3(x1)))))))))))))))))) (25)
2(2(1(3(5(2(5(0(4(2(5(0(x1)))))))))))) → 2(2(5(5(2(5(5(2(0(2(5(5(1(1(5(x1))))))))))))))) (26)
2(2(2(4(2(0(4(1(3(4(4(4(x1)))))))))))) → 5(4(3(5(1(4(5(3(0(3(5(1(3(2(x1)))))))))))))) (27)
2(2(3(3(1(5(4(0(4(2(4(3(x1)))))))))))) → 5(5(5(1(1(2(5(2(0(5(1(5(3(0(3(0(5(3(x1)))))))))))))))))) (28)
2(2(3(4(3(4(3(4(2(4(4(0(x1)))))))))))) → 2(5(4(5(3(4(0(5(4(1(2(5(0(5(5(x1))))))))))))))) (29)
2(2(4(0(2(1(5(3(3(2(4(4(x1)))))))))))) → 5(3(3(0(3(3(5(5(0(2(2(5(0(0(x1)))))))))))))) (30)
2(2(4(4(2(3(4(3(4(2(4(5(x1)))))))))))) → 2(3(0(3(3(5(1(3(1(5(1(5(1(1(5(5(0(2(x1)))))))))))))))))) (31)
2(3(4(3(0(0(4(2(4(1(1(4(x1)))))))))))) → 5(0(3(1(1(0(3(3(3(3(5(4(1(2(5(x1))))))))))))))) (32)
2(3(5(0(3(1(4(0(1(3(4(4(x1)))))))))))) → 5(2(2(5(5(0(2(0(5(3(0(4(1(0(2(0(3(x1))))))))))))))))) (33)
2(4(0(3(4(4(0(3(4(0(5(0(x1)))))))))))) → 0(3(1(3(5(5(5(0(2(2(2(0(4(5(1(3(3(x1))))))))))))))))) (34)
2(4(0(4(0(1(2(0(1(3(4(1(x1)))))))))))) → 5(1(4(5(3(3(1(1(5(2(5(5(5(4(1(x1))))))))))))))) (35)
2(4(0(4(1(4(1(1(1(1(3(1(x1)))))))))))) → 4(2(0(3(2(0(0(2(3(1(2(2(2(0(5(5(x1)))))))))))))))) (36)
2(4(1(1(4(2(4(0(4(5(0(4(x1)))))))))))) → 3(1(5(1(5(5(5(5(5(5(1(3(1(5(5(5(0(5(x1)))))))))))))))))) (37)
2(4(3(3(3(4(0(0(4(0(0(1(x1)))))))))))) → 2(0(2(4(1(2(5(0(0(2(1(2(5(5(5(1(0(x1))))))))))))))))) (38)
2(4(3(4(0(0(1(3(0(1(4(1(x1)))))))))))) → 2(5(2(2(3(3(3(1(1(5(5(1(5(4(0(2(x1)))))))))))))))) (39)
2(5(2(2(1(4(2(1(4(1(4(4(x1)))))))))))) → 5(5(1(5(5(2(4(3(0(5(1(5(0(3(x1)))))))))))))) (40)
2(5(5(2(2(4(4(4(5(4(3(4(x1)))))))))))) → 0(5(0(2(2(2(5(1(5(5(5(3(3(1(2(5(5(3(x1)))))))))))))))))) (41)
3(0(3(4(4(0(4(4(3(4(4(1(x1)))))))))))) → 5(2(0(2(5(2(0(1(2(2(4(1(0(4(4(5(4(1(x1)))))))))))))))))) (43)
3(0(4(0(3(4(4(4(4(4(4(1(x1)))))))))))) → 3(1(5(1(4(5(2(1(4(5(0(1(4(5(5(x1))))))))))))))) (44)
3(1(0(4(0(3(2(1(4(0(5(4(x1)))))))))))) → 0(5(4(5(1(0(3(5(3(0(3(1(1(2(x1)))))))))))))) (45)
3(1(3(1(4(3(4(3(1(3(4(4(x1)))))))))))) → 5(5(3(2(3(1(1(0(0(5(1(1(5(2(5(0(2(x1))))))))))))))))) (46)
3(1(3(4(0(1(0(3(1(3(4(4(x1)))))))))))) → 5(3(3(5(3(2(4(2(2(3(1(1(0(2(1(x1))))))))))))))) (47)
3(2(0(3(4(4(2(4(2(3(4(0(x1)))))))))))) → 0(1(3(5(5(3(2(5(2(3(5(3(4(3(3(x1))))))))))))))) (48)
3(2(3(4(4(0(5(3(4(4(4(0(x1)))))))))))) → 5(1(2(5(1(3(0(5(5(3(2(5(1(2(5(1(0(0(x1)))))))))))))))))) (49)
3(2(4(3(2(4(0(1(1(4(1(3(x1)))))))))))) → 0(0(5(5(1(0(5(5(0(2(3(4(5(0(2(0(5(x1))))))))))))))))) (50)
3(3(1(5(0(4(2(0(4(2(1(2(x1)))))))))))) → 5(5(1(2(5(4(1(5(5(5(5(3(2(0(0(3(3(x1))))))))))))))))) (52)
3(3(2(3(3(3(5(3(0(3(4(2(x1)))))))))))) → 2(5(4(1(5(5(2(2(5(5(5(5(1(1(0(x1))))))))))))))) (53)
3(4(0(0(1(5(2(4(2(3(2(2(x1)))))))))))) → 1(5(5(5(2(1(3(2(5(1(4(5(2(5(0(x1))))))))))))))) (55)
3(4(1(4(4(2(0(4(0(3(4(1(x1)))))))))))) → 3(4(0(2(2(0(5(4(3(1(1(3(5(1(5(x1))))))))))))))) (56)
3(4(1(5(4(3(4(4(4(2(4(4(x1)))))))))))) → 5(5(5(5(0(5(4(0(3(5(0(3(1(3(2(x1))))))))))))))) (57)
3(4(2(3(3(5(2(4(0(2(2(5(x1)))))))))))) → 3(2(1(2(1(4(5(3(3(3(2(5(2(5(x1)))))))))))))) (58)
3(4(2(4(0(2(4(2(3(4(0(3(x1)))))))))))) → 2(5(2(1(5(5(3(5(5(5(5(0(3(5(x1)))))))))))))) (59)
3(4(3(0(3(1(2(1(1(1(4(0(x1)))))))))))) → 2(1(2(0(0(5(5(1(3(5(5(3(5(1(2(0(2(0(x1)))))))))))))))))) (60)
3(4(3(4(0(1(0(5(2(3(4(1(x1)))))))))))) → 5(2(4(4(1(5(3(2(5(0(2(5(2(2(1(x1))))))))))))))) (61)
3(4(3(4(3(0(4(4(2(1(4(5(x1)))))))))))) → 0(4(5(4(4(1(0(0(2(1(0(2(1(2(5(1(3(x1))))))))))))))))) (62)
3(4(3(4(5(2(3(2(3(4(3(0(x1)))))))))))) → 2(5(5(4(1(5(5(3(0(1(2(1(0(5(3(3(0(x1))))))))))))))))) (63)
3(4(4(0(1(5(1(4(0(3(3(0(x1)))))))))))) → 2(3(2(1(1(0(2(1(2(2(2(0(5(3(1(x1))))))))))))))) (64)
3(4(4(0(4(2(3(4(0(3(3(5(x1)))))))))))) → 5(1(5(4(0(0(5(3(0(1(1(2(3(5(2(5(1(x1))))))))))))))))) (65)
3(4(4(2(5(1(1(0(4(2(0(3(x1)))))))))))) → 5(5(5(2(3(1(3(3(1(5(2(1(5(3(x1)))))))))))))) (66)
3(4(4(3(3(4(3(4(2(0(2(4(x1)))))))))))) → 3(2(0(5(5(0(0(3(1(4(1(5(4(5(2(x1))))))))))))))) (67)
3(4(4(4(0(4(4(4(4(2(5(1(x1)))))))))))) → 1(1(2(4(5(2(0(5(1(3(2(2(5(1(5(5(x1)))))))))))))))) (68)
3(4(4(5(2(3(4(4(4(3(0(0(x1)))))))))))) → 2(0(0(0(1(1(2(5(5(4(1(5(1(3(1(0(x1)))))))))))))))) (69)
4(0(1(3(1(4(1(4(3(4(4(0(x1)))))))))))) → 1(3(1(5(0(3(5(5(4(5(4(1(1(4(1(1(x1)))))))))))))))) (70)
4(0(3(4(3(0(2(5(3(4(0(5(x1)))))))))))) → 1(2(0(5(3(5(5(1(2(5(1(3(5(5(5(5(0(x1))))))))))))))))) (71)
4(0(4(4(4(4(1(0(4(2(1(3(x1)))))))))))) → 1(4(5(3(3(3(5(4(1(5(5(3(5(3(x1)))))))))))))) (72)
4(1(1(1(3(0(4(4(0(3(4(1(x1)))))))))))) → 1(0(0(3(3(1(2(5(3(3(1(4(0(1(x1)))))))))))))) (73)
4(1(3(4(3(4(0(3(3(2(3(2(x1)))))))))))) → 0(2(5(0(2(3(0(1(0(2(5(0(1(2(x1)))))))))))))) (74)
4(1(5(1(4(3(4(0(1(5(4(0(x1)))))))))))) → 2(5(5(4(1(5(1(2(5(0(0(5(5(2(5(2(2(x1))))))))))))))))) (75)
4(2(1(1(5(0(2(1(2(1(4(4(x1)))))))))))) → 4(3(3(3(2(1(0(2(0(0(5(0(0(2(x1)))))))))))))) (76)
4(2(1(3(0(4(4(4(1(1(3(0(x1)))))))))))) → 5(4(1(0(2(5(3(1(2(5(2(5(2(2(5(5(2(x1))))))))))))))))) (77)
4(2(3(4(3(4(1(3(0(3(3(4(x1)))))))))))) → 1(5(4(2(0(2(2(5(5(5(1(0(2(1(0(2(5(4(x1)))))))))))))))))) (78)
4(2(5(0(5(2(1(1(3(1(3(0(x1)))))))))))) → 1(4(0(5(5(2(5(5(3(3(5(5(5(5(1(0(5(x1))))))))))))))))) (79)
4(2(5(1(1(3(3(2(1(4(0(2(x1)))))))))))) → 5(3(3(5(1(0(2(1(5(5(0(0(2(3(5(5(5(0(x1)))))))))))))))))) (80)
4(3(2(4(3(2(4(0(2(0(4(5(x1)))))))))))) → 4(0(0(2(5(3(0(5(5(3(3(5(2(0(5(2(5(x1))))))))))))))))) (82)
4(3(4(2(4(0(3(3(1(4(3(0(x1)))))))))))) → 1(4(3(2(5(0(2(1(0(2(5(2(0(2(5(2(1(x1))))))))))))))))) (83)
5(0(2(4(4(0(4(4(3(4(3(1(x1)))))))))))) → 3(1(3(3(5(5(5(1(1(4(5(5(0(0(2(1(0(x1))))))))))))))))) (84)
5(0(3(5(2(3(4(5(3(3(4(1(x1)))))))))))) → 2(4(0(2(5(1(5(5(5(2(2(2(5(0(x1)))))))))))))) (86)
5(0(4(3(4(3(2(1(4(2(4(0(x1)))))))))))) → 5(5(0(0(2(2(2(4(0(1(0(5(3(5(5(4(1(1(x1)))))))))))))))))) (87)
5(0(5(4(2(3(4(4(4(5(4(4(x1)))))))))))) → 2(0(5(1(3(3(3(1(1(2(3(5(0(3(x1)))))))))))))) (88)
5(1(3(4(2(3(0(4(0(0(3(0(x1)))))))))))) → 0(3(1(5(1(0(0(2(5(5(3(5(1(0(2(5(2(2(x1)))))))))))))))))) (89)
5(2(1(3(4(1(1(1(4(2(3(0(x1)))))))))))) → 1(0(3(1(5(5(5(2(2(5(0(0(5(1(5(4(5(0(x1)))))))))))))))))) (90)
5(2(3(4(4(0(4(0(2(4(0(2(x1)))))))))))) → 5(4(2(5(4(5(0(0(1(5(5(5(2(0(2(3(2(5(x1)))))))))))))))))) (91)
5(3(2(4(3(4(5(1(2(3(4(1(x1)))))))))))) → 5(5(1(5(1(0(2(0(5(0(5(0(1(2(2(x1))))))))))))))) (92)
5(3(4(4(4(2(0(1(1(1(3(3(x1)))))))))))) → 3(0(3(1(2(0(2(5(3(5(1(5(2(2(5(1(2(x1))))))))))))))))) (93)
5(4(0(3(0(4(2(1(4(4(1(1(x1)))))))))))) → 4(1(3(1(5(2(1(5(5(0(2(3(1(5(5(0(x1)))))))))))))))) (94)
5(4(2(0(0(0(4(0(1(1(0(4(x1)))))))))))) → 5(1(4(5(2(0(2(4(1(5(3(0(2(2(4(x1))))))))))))))) (95)
5(5(0(1(4(3(4(2(5(4(3(4(x1)))))))))))) → 1(2(3(3(5(1(2(3(5(0(1(0(3(1(x1)))))))))))))) (96)

1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
2(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 1(2(2(0(1(3(3(5(5(1(5(3(4(4(2(3(x1)))))))))))))))) (97)
0(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0(0(4(5(5(5(4(5(2(1(0(3(0(2(5(x1))))))))))))))) (98)
1(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 2(4(4(5(1(2(1(5(1(5(5(4(5(1(x1)))))))))))))) (99)
2(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0(5(1(0(0(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))))))) (100)
1(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 5(0(0(1(1(2(0(2(0(5(0(0(4(4(x1)))))))))))))) (101)
2(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 5(2(0(0(5(1(1(1(4(5(1(4(1(3(5(1(x1)))))))))))))))) (102)

1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 2#(0(0(5(1(1(1(4(5(1(4(1(3(5(1(x1))))))))))))))) (103)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(x1) (104)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(4(5(1(4(1(3(5(1(x1))))))))) (105)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(4(1(3(5(1(x1)))))) (106)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(3(5(1(x1)))) (107)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(1(4(5(1(4(1(3(5(1(x1)))))))))) (108)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(1(1(4(5(1(4(1(3(5(1(x1))))))))))) (109)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 0#(5(1(1(1(4(5(1(4(1(3(5(1(x1))))))))))))) (110)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 0#(0(5(1(1(1(4(5(1(4(1(3(5(1(x1)))))))))))))) (111)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 2#(3(x1)) (112)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 2#(2(0(1(3(3(5(5(1(5(3(4(4(2(3(x1))))))))))))))) (113)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 2#(0(1(3(3(5(5(1(5(3(4(4(2(3(x1)))))))))))))) (114)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 1#(5(3(4(4(2(3(x1))))))) (115)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 1#(3(3(5(5(1(5(3(4(4(2(3(x1)))))))))))) (116)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 1#(2(2(0(1(3(3(5(5(1(5(3(4(4(2(3(x1)))))))))))))))) (117)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 0#(1(3(3(5(5(1(5(3(4(4(2(3(x1))))))))))))) (118)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 1#(0(0(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))))) (119)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0#(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))) (120)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0#(5(1(0(0(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))))))) (121)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0#(0(5(3(3(3(3(5(4(5(5(5(5(x1))))))))))))) (122)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 2#(4(4(5(1(2(1(5(1(5(5(4(5(1(x1)))))))))))))) (123)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 2#(1(5(1(5(5(4(5(1(x1))))))))) (124)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(x1) (125)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(5(5(4(5(1(x1)))))) (126)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(5(1(5(5(4(5(1(x1)))))))) (127)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(2(1(5(1(5(5(4(5(1(x1)))))))))) (128)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 2#(0(5(0(0(4(4(x1))))))) (129)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 2#(0(2(0(5(0(0(4(4(x1))))))))) (130)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 1#(2(0(2(0(5(0(0(4(4(x1)))))))))) (131)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 1#(1(2(0(2(0(5(0(0(4(4(x1))))))))))) (132)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(5(0(0(4(4(x1)))))) (133)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(4(4(x1))) (134)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(2(0(5(0(0(4(4(x1)))))))) (135)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(1(1(2(0(2(0(5(0(0(4(4(x1)))))))))))) (136)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(0(4(4(x1)))) (137)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(0(1(1(2(0(2(0(5(0(0(4(4(x1))))))))))))) (138)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 2#(5(x1)) (139)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 2#(1(0(3(0(2(5(x1))))))) (140)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 1#(0(3(0(2(5(x1)))))) (141)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0#(4(5(5(5(4(5(2(1(0(3(0(2(5(x1)))))))))))))) (142)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0#(3(0(2(5(x1))))) (143)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0#(2(5(x1))) (144)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0#(0(4(5(5(5(4(5(2(1(0(3(0(2(5(x1))))))))))))))) (145)

1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
0
[4(x1)] = x1 +
1
[3(x1)] = x1 +
1/5
[2(x1)] = x1 +
0
[1(x1)] = x1 +
1/5
[0(x1)] = x1 +
2/5
[2#(x1)] = x1 +
4/5
[1#(x1)] = x1 +
1
[0#(x1)] = x1 +
0
together with the usable rules
2(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 1(2(2(0(1(3(3(5(5(1(5(3(4(4(2(3(x1)))))))))))))))) (97)
0(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0(0(4(5(5(5(4(5(2(1(0(3(0(2(5(x1))))))))))))))) (98)
1(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 2(4(4(5(1(2(1(5(1(5(5(4(5(1(x1)))))))))))))) (99)
2(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0(5(1(0(0(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))))))) (100)
1(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 5(0(0(1(1(2(0(2(0(5(0(0(4(4(x1)))))))))))))) (101)
2(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 5(2(0(0(5(1(1(1(4(5(1(4(1(3(5(1(x1)))))))))))))))) (102)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(x1) (104)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(4(5(1(4(1(3(5(1(x1))))))))) (105)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(4(1(3(5(1(x1)))))) (106)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(3(5(1(x1)))) (107)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(1(4(5(1(4(1(3(5(1(x1)))))))))) (108)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 1#(1(1(4(5(1(4(1(3(5(1(x1))))))))))) (109)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 0#(5(1(1(1(4(5(1(4(1(3(5(1(x1))))))))))))) (110)
2#(3(3(0(1(3(0(4(4(3(0(5(x1)))))))))))) → 0#(0(5(1(1(1(4(5(1(4(1(3(5(1(x1)))))))))))))) (111)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 2#(3(x1)) (112)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 2#(2(0(1(3(3(5(5(1(5(3(4(4(2(3(x1))))))))))))))) (113)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 2#(0(1(3(3(5(5(1(5(3(4(4(2(3(x1)))))))))))))) (114)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 1#(5(3(4(4(2(3(x1))))))) (115)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 1#(3(3(5(5(1(5(3(4(4(2(3(x1)))))))))))) (116)
2#(2(3(1(0(4(1(3(3(4(2(0(x1)))))))))))) → 0#(1(3(3(5(5(1(5(3(4(4(2(3(x1))))))))))))) (118)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 1#(0(0(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))))) (119)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0#(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))) (120)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0#(5(1(0(0(5(3(3(3(3(5(4(5(5(5(5(x1)))))))))))))))) (121)
2#(0(3(0(4(3(1(5(3(3(3(3(x1)))))))))))) → 0#(0(5(3(3(3(3(5(4(5(5(5(5(x1))))))))))))) (122)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 2#(1(5(1(5(5(4(5(1(x1))))))))) (124)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(x1) (125)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(5(5(4(5(1(x1)))))) (126)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(5(1(5(5(4(5(1(x1)))))))) (127)
1#(4(3(5(5(1(0(4(3(1(3(3(x1)))))))))))) → 1#(2(1(5(1(5(5(4(5(1(x1)))))))))) (128)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 2#(0(5(0(0(4(4(x1))))))) (129)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 2#(0(2(0(5(0(0(4(4(x1))))))))) (130)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 1#(2(0(2(0(5(0(0(4(4(x1)))))))))) (131)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 1#(1(2(0(2(0(5(0(0(4(4(x1))))))))))) (132)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(5(0(0(4(4(x1)))))) (133)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(4(4(x1))) (134)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(2(0(5(0(0(4(4(x1)))))))) (135)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(1(1(2(0(2(0(5(0(0(4(4(x1)))))))))))) (136)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(0(4(4(x1)))) (137)
1#(1(5(3(2(4(3(0(4(0(3(4(x1)))))))))))) → 0#(0(1(1(2(0(2(0(5(0(0(4(4(x1))))))))))))) (138)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 2#(5(x1)) (139)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 2#(1(0(3(0(2(5(x1))))))) (140)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 1#(0(3(0(2(5(x1)))))) (141)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0#(4(5(5(5(4(5(2(1(0(3(0(2(5(x1)))))))))))))) (142)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0#(3(0(2(5(x1))))) (143)
0#(1(2(4(1(3(4(1(1(2(0(3(x1)))))))))))) → 0#(2(5(x1))) (144)
and no rules could be deleted.

1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.