Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/132611)

The rewrite relation of the following TRS is considered.

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

1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 3#(0(5(4(4(2(x1)))))) (97)
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 2#(x1) (98)
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 2#(1(3(0(5(4(4(2(x1)))))))) (99)
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 1#(3(0(5(4(4(2(x1))))))) (100)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 3#(4(4(5(4(1(3(1(4(4(0(5(4(3(2(0(2(x1))))))))))))))))) (101)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 3#(2(0(2(x1)))) (102)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 3#(1(4(4(0(5(4(3(2(0(2(x1))))))))))) (103)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 2#(x1) (104)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 2#(0(2(x1))) (105)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 1#(4(4(0(5(4(3(2(0(2(x1)))))))))) (106)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 1#(3(1(4(4(0(5(4(3(2(0(2(x1)))))))))))) (107)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 2#(x1) (108)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 2#(4(0(1(2(x1))))) (109)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 1#(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))) (110)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 1#(2(x1)) (111)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 3#(4(1(4(4(3(4(1(4(4(0(3(x1)))))))))))) (112)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 3#(4(1(4(4(0(3(x1))))))) (113)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 2#(4(3(4(1(4(4(3(4(1(4(4(0(3(x1)))))))))))))) (114)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 2#(0(1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))))) (115)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 1#(4(4(3(4(1(4(4(0(3(x1)))))))))) (116)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 1#(4(4(0(3(x1))))) (117)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 1#(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))) (118)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 3#(5(x1)) (119)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 3#(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))) (120)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 3#(4(4(3(5(x1))))) (121)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 2#(2(0(1(3(4(4(3(5(x1))))))))) (122)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 2#(0(1(3(4(4(3(5(x1)))))))) (123)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 1#(3(4(4(3(5(x1)))))) (124)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 3#(4(5(3(4(5(2(x1))))))) (125)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 3#(4(5(2(x1)))) (126)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 2#(x1) (127)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 1#(5(4(1(4(3(4(5(3(4(5(2(x1)))))))))))) (128)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 1#(4(3(4(5(3(4(5(2(x1))))))))) (129)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(5(2(1(5(4(1(5(2(5(x1)))))))))) (130)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1))))))))))))))))) (131)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(3(5(2(1(5(4(1(5(2(5(x1))))))))))) (132)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))) (133)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 2#(5(x1)) (134)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 2#(1(5(4(1(5(2(5(x1)))))))) (135)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 1#(5(4(1(5(2(5(x1))))))) (136)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 1#(5(2(5(x1)))) (137)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 1#(3(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))))))))) (138)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) (139)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))) (140)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(4(x1)) (141)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(0(2(4(0(2(3(4(x1)))))))) (142)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 2#(4(0(2(3(4(x1)))))) (143)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 2#(3(4(x1))) (144)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 2#(3(0(2(4(0(2(3(4(x1))))))))) (145)

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 +
0
[3(x1)] = x1 +
2
[2(x1)] = x1 +
2
[1(x1)] = x1 +
2
[0(x1)] = x1 +
2
[3#(x1)] = x1 +
1
[2#(x1)] = x1 +
2
[1#(x1)] = x1 +
2
together with the usable rules
1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) (22)
1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 1(3(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))))))))) (35)
2(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 0(0(0(5(4(1(5(4(1(4(3(4(5(3(4(5(2(x1))))))))))))))))) (38)
2(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 4(4(3(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))))) (48)
2(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 2(0(1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))))) (57)
2(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 0(4(1(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))))) (65)
3(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 3(4(4(5(4(1(3(1(4(4(0(5(4(3(2(0(2(x1))))))))))))))))) (85)
3(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 0(0(4(5(4(5(2(1(3(0(5(4(4(2(x1)))))))))))))) (88)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 3#(0(5(4(4(2(x1)))))) (97)
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 2#(x1) (98)
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 2#(1(3(0(5(4(4(2(x1)))))))) (99)
3#(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) → 1#(3(0(5(4(4(2(x1))))))) (100)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 3#(2(0(2(x1)))) (102)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 3#(1(4(4(0(5(4(3(2(0(2(x1))))))))))) (103)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 2#(x1) (104)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 2#(0(2(x1))) (105)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 1#(4(4(0(5(4(3(2(0(2(x1)))))))))) (106)
3#(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) → 1#(3(1(4(4(0(5(4(3(2(0(2(x1)))))))))))) (107)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 2#(x1) (108)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 2#(4(0(1(2(x1))))) (109)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 1#(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))) (110)
2#(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) → 1#(2(x1)) (111)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 3#(4(1(4(4(3(4(1(4(4(0(3(x1)))))))))))) (112)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 3#(4(1(4(4(0(3(x1))))))) (113)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 2#(4(3(4(1(4(4(3(4(1(4(4(0(3(x1)))))))))))))) (114)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 1#(4(4(3(4(1(4(4(0(3(x1)))))))))) (116)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 1#(4(4(0(3(x1))))) (117)
2#(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) → 1#(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))) (118)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 3#(5(x1)) (119)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 3#(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))) (120)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 3#(4(4(3(5(x1))))) (121)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 2#(2(0(1(3(4(4(3(5(x1))))))))) (122)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 2#(0(1(3(4(4(3(5(x1)))))))) (123)
2#(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) → 1#(3(4(4(3(5(x1)))))) (124)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 3#(4(5(3(4(5(2(x1))))))) (125)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 3#(4(5(2(x1)))) (126)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 2#(x1) (127)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 1#(5(4(1(4(3(4(5(3(4(5(2(x1)))))))))))) (128)
2#(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) → 1#(4(3(4(5(3(4(5(2(x1))))))))) (129)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(5(2(1(5(4(1(5(2(5(x1)))))))))) (130)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1))))))))))))))))) (131)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(3(5(2(1(5(4(1(5(2(5(x1))))))))))) (132)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 3#(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))) (133)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 2#(5(x1)) (134)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 2#(1(5(4(1(5(2(5(x1)))))))) (135)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 1#(5(4(1(5(2(5(x1))))))) (136)
1#(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) → 1#(5(2(5(x1)))) (137)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) (139)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))) (140)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(4(x1)) (141)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 3#(0(2(4(0(2(3(4(x1)))))))) (142)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 2#(4(0(2(3(4(x1)))))) (143)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 2#(3(4(x1))) (144)
1#(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) → 2#(3(0(2(4(0(2(3(4(x1))))))))) (145)
and no rules could be deleted.

1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.