Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26903)

The rewrite relation of the following TRS is considered.

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

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 +
108
[4(x1)] = x1 +
109
[3(x1)] = x1 +
108
[2(x1)] = x1 +
72
[1(x1)] = x1 +
113
[0(x1)] = x1 +
91
all of the following rules can be deleted.
1(3(1(1(4(0(4(0(5(4(x1)))))))))) 1(3(1(5(5(3(2(3(1(3(x1)))))))))) (8)
0(0(4(0(2(1(4(3(3(4(5(x1))))))))))) 3(4(3(2(1(3(2(5(5(5(x1)))))))))) (12)
0(1(1(4(4(4(0(5(0(3(5(x1))))))))))) 1(3(5(0(2(4(4(0(2(0(x1)))))))))) (13)
0(3(1(3(4(1(3(4(4(3(5(x1))))))))))) 0(4(4(2(3(4(1(4(0(4(x1)))))))))) (14)
0(3(5(4(4(5(1(5(4(1(5(x1))))))))))) 5(4(1(3(3(4(4(3(1(1(x1)))))))))) (15)
0(5(1(2(5(0(3(5(2(5(1(x1))))))))))) 4(2(3(5(2(0(0(3(2(0(x1)))))))))) (16)
1(0(4(5(5(0(0(1(2(5(2(x1))))))))))) 4(0(5(0(5(5(5(0(4(0(x1)))))))))) (17)
1(0(5(2(4(4(2(0(2(5(4(x1))))))))))) 2(1(0(4(3(2(2(4(2(2(x1)))))))))) (18)
1(1(2(3(1(3(2(1(1(0(5(x1))))))))))) 3(1(1(4(2(0(0(0(2(3(x1)))))))))) (19)
1(1(3(0(5(1(5(2(2(3(1(x1))))))))))) 0(3(0(3(0(1(2(2(5(2(x1)))))))))) (20)
1(1(4(2(0(1(3(3(4(4(2(x1))))))))))) 2(3(5(3(2(4(5(2(1(0(x1)))))))))) (21)
1(2(1(1(1(2(5(2(5(0(2(x1))))))))))) 0(2(5(0(2(2(3(2(2(1(x1)))))))))) (22)
1(2(2(3(3(1(3(3(2(0(0(x1))))))))))) 1(3(0(2(0(5(5(3(5(0(x1)))))))))) (23)
1(4(0(1(5(3(3(1(1(4(0(x1))))))))))) 4(5(5(3(4(4(5(5(1(5(x1)))))))))) (24)
1(4(3(0(2(2(4(4(3(0(1(x1))))))))))) 1(3(0(1(0(5(3(4(3(5(x1)))))))))) (25)
1(5(5(1(2(1(3(5(0(0(0(x1))))))))))) 4(0(3(2(5(1(0(5(3(2(x1)))))))))) (26)
2(1(4(1(4(4(0(5(4(3(2(x1))))))))))) 3(0(3(0(4(5(2(0(0(4(x1)))))))))) (27)
2(3(2(2(5(1(5(2(1(2(2(x1))))))))))) 5(5(0(4(4(5(0(2(1(2(x1)))))))))) (28)
2(4(3(3(0(0(4(0(3(5(0(x1))))))))))) 3(5(3(4(4(3(0(2(5(3(x1)))))))))) (29)
2(5(1(4(3(5(5(5(0(0(0(x1))))))))))) 4(1(3(0(4(4(0(5(2(5(x1)))))))))) (30)
2(5(4(0(0(2(3(3(1(4(1(x1))))))))))) 0(3(2(0(4(3(5(5(4(3(x1)))))))))) (31)
3(3(4(2(3(4(2(5(4(4(3(x1))))))))))) 4(4(2(0(0(3(2(0(5(3(x1)))))))))) (32)
3(4(2(0(5(4(0(1(1(2(2(x1))))))))))) 3(4(5(1(1(3(3(2(3(4(x1)))))))))) (33)
3(4(2(5(4(0(1(4(2(0(3(x1))))))))))) 2(1(4(0(3(5(0(3(1(2(x1)))))))))) (34)
3(4(3(4(0(0(4(1(5(4(0(x1))))))))))) 5(4(3(5(4(2(2(1(2(1(x1)))))))))) (35)
3(5(1(1(2(1(0(4(2(4(3(x1))))))))))) 2(2(3(5(0(4(5(4(2(1(x1)))))))))) (36)
4(0(2(3(3(2(3(5(2(0(2(x1))))))))))) 3(4(2(4(2(5(0(5(5(2(x1)))))))))) (37)
4(2(3(4(4(4(0(0(1(2(1(x1))))))))))) 5(2(1(1(0(4(0(5(5(1(x1)))))))))) (38)
4(2(4(0(4(3(2(5(5(0(1(x1))))))))))) 0(1(5(5(4(4(3(5(2(4(x1)))))))))) (39)
4(3(3(2(2(4(0(2(4(1(3(x1))))))))))) 5(4(2(2(1(0(2(5(2(0(x1)))))))))) (40)
5(1(1(1(4(4(1(1(5(3(2(x1))))))))))) 1(4(2(0(4(0(1(4(3(5(x1)))))))))) (42)
5(1(1(3(1(1(2(1(0(3(3(x1))))))))))) 2(5(1(2(1(2(2(4(3(4(x1)))))))))) (43)
5(2(3(1(2(5(1(4(1(3(0(x1))))))))))) 4(3(2(2(3(5(1(4(5(2(x1)))))))))) (44)
5(2(3(3(0(3(4(5(1(2(4(x1))))))))))) 2(4(0(1(1(3(1(0(5(4(x1)))))))))) (45)
5(2(4(3(1(3(4(2(3(4(4(x1))))))))))) 0(0(3(3(1(2(3(1(1(3(x1)))))))))) (46)
5(2(5(0(0(3(5(4(3(5(1(x1))))))))))) 3(1(2(1(5(4(0(0(2(5(x1)))))))))) (47)
5(2(5(4(2(5(0(0(2(3(0(x1))))))))))) 5(3(3(3(0(2(1(0(3(1(x1)))))))))) (48)
5(3(1(2(1(1(5(3(0(3(4(x1))))))))))) 1(5(1(4(3(4(0(1(0(0(x1)))))))))) (49)
5(5(1(5(1(0(1(2(4(1(0(x1))))))))))) 1(0(2(2(2(1(5(1(2(1(x1)))))))))) (50)
0(0(4(5(0(2(5(1(2(5(5(5(x1)))))))))))) 4(5(2(0(3(3(1(0(0(2(x1)))))))))) (51)
0(1(3(5(5(3(0(3(3(5(3(3(x1)))))))))))) 0(4(3(2(2(4(1(2(5(1(x1)))))))))) (52)
0(3(1(3(3(2(2(1(4(2(1(3(x1)))))))))))) 2(4(4(2(0(4(2(5(5(5(x1)))))))))) (53)
2(4(4(5(1(2(0(0(5(0(3(4(x1)))))))))))) 1(1(5(1(0(0(1(4(1(2(x1)))))))))) (56)
2(5(5(2(5(2(0(4(5(0(2(3(x1)))))))))))) 0(2(5(4(2(4(1(1(4(1(x1)))))))))) (58)
3(3(3(2(2(3(3(3(1(1(3(5(x1)))))))))))) 2(5(1(2(0(2(0(1(2(5(x1)))))))))) (59)
3(3(3(3(3(4(4(3(3(3(1(1(x1)))))))))))) 0(4(5(1(2(4(1(4(4(4(x1)))))))))) (60)
4(3(5(3(5(3(2(1(0(5(3(2(x1)))))))))))) 1(3(4(2(4(3(0(0(1(1(x1)))))))))) (61)
4(4(3(4(3(1(3(3(4(5(2(5(x1)))))))))))) 2(4(2(2(3(3(4(4(0(0(x1)))))))))) (62)
4(5(1(5(1(3(3(1(3(3(2(3(x1)))))))))))) 2(3(4(2(2(5(1(2(3(0(x1)))))))))) (63)
5(3(3(1(1(5(0(1(4(1(0(0(x1)))))))))))) 0(3(1(2(1(2(2(1(4(3(x1)))))))))) (64)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 264 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 1584 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 +
13
[51(x1)] = x1 +
0
[52(x1)] = x1 +
14
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
13
[40(x1)] = x1 +
0
[41(x1)] = x1 +
13
[42(x1)] = x1 +
1
[43(x1)] = x1 +
3
[44(x1)] = x1 +
3
[45(x1)] = x1 +
13
[30(x1)] = x1 +
14
[31(x1)] = x1 +
16
[32(x1)] = x1 +
13
[33(x1)] = x1 +
1
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
13
[21(x1)] = x1 +
13
[22(x1)] = x1 +
0
[23(x1)] = x1 +
3
[24(x1)] = x1 +
13
[25(x1)] = x1 +
0
[10(x1)] = x1 +
3
[11(x1)] = x1 +
0
[12(x1)] = x1 +
13
[13(x1)] = x1 +
13
[14(x1)] = x1 +
14
[15(x1)] = x1 +
16
[00(x1)] = x1 +
13
[01(x1)] = x1 +
0
[02(x1)] = x1 +
16
[03(x1)] = x1 +
13
[04(x1)] = x1 +
13
[05(x1)] = x1 +
3
all of the following rules can be deleted.

There are 1548 ruless (increase limit for explicit display).

1.1.1.1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1943)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1944)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1945)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1946)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1947)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1948)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1949)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1950)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1951)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1952)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1953)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1954)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1955)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1956)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1957)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1958)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1959)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1960)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1961)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1962)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1963)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1964)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1965)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1966)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1967)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1968)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1969)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1970)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1971)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1972)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1973)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1974)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1975)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1976)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1977)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1978)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 108 ruless (increase limit for explicit display).

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
1
[51(x1)] = x1 +
0
[53(x1)] = x1 +
0
[54(x1)] = x1 +
1
[40(x1)] = x1 +
0
[30(x1)] = x1 +
0
[35(x1)] = x1 +
1
[20(x1)] = x1 +
1
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[13(x1)] = x1 +
1
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[02(x1)] = x1 +
1
[03(x1)] = x1 +
1
[20#(x1)] = x1 +
0
[21#(x1)] = x1 +
1
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
1
[24#(x1)] = x1 +
1
[25#(x1)] = x1 +
1
together with the usable rules
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1943)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1944)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1945)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1946)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1947)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1)))))))))))))))))))) (1948)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1949)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1950)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1951)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1952)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1953)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1)))))))))))))))))))) (1954)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1955)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1956)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1957)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1958)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1959)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1)))))))))))))))))))) (1960)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1961)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1962)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1963)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1964)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1965)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1)))))))))))))))))))) (1966)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1967)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1968)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1969)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1970)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1971)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1)))))))))))))))))))) (1972)
25(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 25(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1973)
24(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 24(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1974)
23(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 23(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1975)
22(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 22(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1976)
21(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 21(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1977)
20(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20(13(54(20(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1)))))))))))))))))))) (1978)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(50(x1))))))))) (1979)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1))))))))))))))))) (1981)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(40(x1))))))))) (1982)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1))))))))))))))))) (1984)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(30(x1))))))))) (1985)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1))))))))))))))))) (1987)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(20(x1))))))))) (1988)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1))))))))))))))))) (1990)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(10(x1))))))))) (1991)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1))))))))))))))))) (1993)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(00(x1))))))))) (1994)
20#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1))))))))))))))))) (1996)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(50(x1))))))))) (1997)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1))))))))))))))))) (1998)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(40(x1))))))))) (2000)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1))))))))))))))))) (2001)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(30(x1))))))))) (2003)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1))))))))))))))))) (2004)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(20(x1))))))))) (2006)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1))))))))))))))))) (2007)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(10(x1))))))))) (2009)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1))))))))))))))))) (2010)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(00(x1))))))))) (2012)
21#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1))))))))))))))))) (2013)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(50(x1))))))))) (2015)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1))))))))))))))))) (2016)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(40(x1))))))))) (2018)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1))))))))))))))))) (2019)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(30(x1))))))))) (2021)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1))))))))))))))))) (2022)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(20(x1))))))))) (2024)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1))))))))))))))))) (2025)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(10(x1))))))))) (2027)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1))))))))))))))))) (2028)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(00(x1))))))))) (2030)
22#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1))))))))))))))))) (2031)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(50(x1))))))))) (2033)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1))))))))))))))))) (2034)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(40(x1))))))))) (2036)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1))))))))))))))))) (2037)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(30(x1))))))))) (2039)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1))))))))))))))))) (2040)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(20(x1))))))))) (2042)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1))))))))))))))))) (2043)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(10(x1))))))))) (2045)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1))))))))))))))))) (2046)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(00(x1))))))))) (2048)
23#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1))))))))))))))))) (2049)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(50(x1))))))))) (2051)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1))))))))))))))))) (2052)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(40(x1))))))))) (2054)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1))))))))))))))))) (2055)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(30(x1))))))))) (2057)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1))))))))))))))))) (2058)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(20(x1))))))))) (2060)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1))))))))))))))))) (2061)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(10(x1))))))))) (2063)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1))))))))))))))))) (2064)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(00(x1))))))))) (2066)
24#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1))))))))))))))))) (2067)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(50(x1))))))))) (2069)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(50(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(50(x1))))))))))))))))) (2070)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(40(x1))))))))) (2072)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(40(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(40(x1))))))))))))))))) (2073)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(30(x1))))))))) (2075)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(30(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(30(x1))))))))))))))))) (2076)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(20(x1))))))))) (2078)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(20(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(20(x1))))))))))))))))) (2079)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(10(x1))))))))) (2081)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(10(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(10(x1))))))))))))))))) (2082)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(53(50(40(51(40(21(53(00(x1))))))))) (2084)
25#(13(54(20(03(35(02(15(54(50(50(20(53(40(51(50(40(21(53(00(x1)))))))))))))))))))) 20#(03(35(02(15(54(50(50(20(53(50(40(51(40(21(53(00(x1))))))))))))))))) (2085)
and no rules could be deleted.

1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.