Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/27001)

The rewrite relation of the following TRS is considered.

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

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 +
22
[4(x1)] = x1 +
21
[3(x1)] = x1 +
21
[2(x1)] = x1 +
21
[1(x1)] = x1 +
15
[0(x1)] = x1 +
21
all of the following rules can be deleted.
0(0(4(2(1(3(2(0(4(1(2(x1))))))))))) 1(2(2(1(1(5(0(0(3(5(x1)))))))))) (4)
0(2(1(3(4(4(2(3(5(4(4(x1))))))))))) 4(1(1(4(2(2(5(0(2(0(x1)))))))))) (5)
0(3(2(0(0(5(5(0(5(0(2(x1))))))))))) 5(0(4(0(1(4(0(2(0(0(x1)))))))))) (6)
0(4(1(4(5(4(4(5(2(3(4(x1))))))))))) 1(3(4(4(2(2(4(4(5(3(x1)))))))))) (7)
0(4(3(4(3(0(1(0(0(3(2(x1))))))))))) 4(3(1(1(4(4(3(0(5(5(x1)))))))))) (8)
0(4(5(1(3(1(1(4(0(2(1(x1))))))))))) 4(4(5(0(1(3(1(1(2(3(x1)))))))))) (9)
0(5(0(2(4(5(2(3(2(2(1(x1))))))))))) 1(5(5(0(4(5(5(2(3(1(x1)))))))))) (10)
0(5(1(1(4(2(3(0(3(1(3(x1))))))))))) 1(3(4(1(3(1(4(0(1(1(x1)))))))))) (11)
0(5(2(3(5(1(4(5(1(1(2(x1))))))))))) 3(0(2(4(3(5(5(2(3(0(x1)))))))))) (12)
0(5(4(5(1(0(5(5(2(2(0(x1))))))))))) 3(1(2(3(5(4(3(1(0(5(x1)))))))))) (13)
1(0(0(2(0(4(2(4(1(5(3(x1))))))))))) 1(4(4(0(1(2(0(3(0(4(x1)))))))))) (14)
1(0(1(1(0(1(4(5(0(3(1(x1))))))))))) 0(3(0(3(5(1(2(1(3(0(x1)))))))))) (15)
1(0(3(1(5(2(3(2(0(2(5(x1))))))))))) 4(0(3(4(2(2(4(2(5(0(x1)))))))))) (16)
1(2(0(5(5(5(0(5(4(0(2(x1))))))))))) 5(5(2(4(3(3(1(4(5(0(x1)))))))))) (17)
1(3(0(4(1(4(4(3(5(5(2(x1))))))))))) 1(4(2(0(1(2(5(5(4(0(x1)))))))))) (18)
1(3(4(2(2(3(2(3(5(1(0(x1))))))))))) 5(4(3(1(5(3(2(4(4(1(x1)))))))))) (19)
2(0(1(5(3(4(2(3(1(3(1(x1))))))))))) 3(0(0(4(4(3(3(4(4(5(x1)))))))))) (20)
2(0(2(4(5(4(5(5(5(0(1(x1))))))))))) 3(5(5(5(3(1(0(2(3(2(x1)))))))))) (21)
2(2(4(2(5(4(2(0(4(3(3(x1))))))))))) 2(1(1(2(1(5(3(2(1(1(x1)))))))))) (22)
2(4(3(0(4(0(2(1(4(0(5(x1))))))))))) 0(4(2(4(1(4(1(5(5(0(x1)))))))))) (23)
2(4(4(2(0(5(5(1(2(2(4(x1))))))))))) 2(3(5(5(0(5(5(0(0(1(x1)))))))))) (24)
2(5(5(2(2(3(5(4(0(4(0(x1))))))))))) 2(4(3(1(4(3(3(2(2(0(x1)))))))))) (25)
3(1(3(2(5(5(2(2(2(1(3(x1))))))))))) 0(2(0(1(3(1(4(4(0(1(x1)))))))))) (26)
3(4(0(5(0(3(5(2(4(4(0(x1))))))))))) 3(4(4(3(3(3(5(2(5(1(x1)))))))))) (27)
3(4(1(2(2(0(2(1(3(4(1(x1))))))))))) 0(0(0(1(3(0(2(3(2(4(x1)))))))))) (28)
3(4(2(0(1(0(1(0(2(0(2(x1))))))))))) 3(5(5(2(1(4(3(2(3(3(x1)))))))))) (29)
4(0(0(1(2(0(2(4(5(0(5(x1))))))))))) 3(0(2(5(5(3(4(2(1(4(x1)))))))))) (30)
4(0(3(0(4(0(0(4(5(4(3(x1))))))))))) 5(1(2(3(5(1(5(5(5(0(x1)))))))))) (31)
4(0(5(5(3(2(4(1(3(0(4(x1))))))))))) 4(5(2(4(5(1(0(1(5(1(x1)))))))))) (32)
4(1(2(5(1(4(4(1(1(3(3(x1))))))))))) 0(5(2(0(3(4(5(5(1(1(x1)))))))))) (33)
4(1(3(0(2(0(3(2(5(5(4(x1))))))))))) 5(0(4(0(1(5(4(3(4(5(x1)))))))))) (34)
4(2(4(5(0(4(5(5(0(3(2(x1))))))))))) 1(2(1(1(2(0(3(5(3(3(x1)))))))))) (35)
4(2(5(0(4(2(5(0(0(4(5(x1))))))))))) 0(0(2(5(3(1(0(2(2(1(x1)))))))))) (36)
4(3(0(2(1(1(5(5(3(5(0(x1))))))))))) 1(4(2(2(0(0(0(5(2(0(x1)))))))))) (37)
4(3(4(5(2(2(4(0(4(3(4(x1))))))))))) 1(1(3(4(1(1(1(4(4(3(x1)))))))))) (38)
4(4(0(0(5(0(5(5(0(2(4(x1))))))))))) 4(0(1(1(4(4(0(0(0(3(x1)))))))))) (39)
4(4(3(0(4(1(1(1(4(4(1(x1))))))))))) 2(2(4(4(4(4(1(1(3(1(x1)))))))))) (40)
4(5(4(3(2(5(4(3(4(1(0(x1))))))))))) 1(2(1(5(2(3(2(3(2(5(x1)))))))))) (41)
5(1(0(4(2(1(1(5(0(0(5(x1))))))))))) 5(2(3(3(5(1(5(1(0(2(x1)))))))))) (42)
5(2(1(0(1(3(1(2(4(3(3(x1))))))))))) 2(0(1(2(4(5(0(2(1(2(x1)))))))))) (43)
5(2(2(4(3(1(0(4(3(0(5(x1))))))))))) 5(1(4(1(4(2(4(0(2(3(x1)))))))))) (44)
5(2(4(5(3(5(1(0(1(4(1(x1))))))))))) 2(5(1(4(3(5(0(3(1(1(x1)))))))))) (46)
5(2(4(5(5(1(2(1(3(0(4(x1))))))))))) 4(2(2(3(5(4(5(5(0(2(x1)))))))))) (47)
5(3(1(3(4(5(3(1(4(1(3(x1))))))))))) 4(1(3(5(1(4(0(3(0(1(x1)))))))))) (48)
5(3(5(0(5(5(2(3(5(2(3(x1))))))))))) 5(1(3(5(4(5(3(2(4(5(x1)))))))))) (49)
5(4(4(5(0(3(0(2(4(2(4(x1))))))))))) 0(2(3(4(5(2(4(5(2(4(x1)))))))))) (50)
5(5(4(5(4(5(1(3(0(5(0(x1))))))))))) 2(5(2(0(5(4(1(2(4(0(x1)))))))))) (51)
0(3(2(3(2(2(0(1(3(5(4(3(x1)))))))))))) 1(2(5(1(5(4(1(0(2(4(x1)))))))))) (53)
3(4(5(0(1(5(1(5(5(1(1(3(x1)))))))))))) 2(4(2(1(5(5(5(1(0(1(x1)))))))))) (54)
4(5(2(3(5(2(5(1(5(1(2(1(x1)))))))))))) 5(4(4(4(2(3(4(0(5(4(x1)))))))))) (56)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 252 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 1512 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 +
0
[51(x1)] = x1 +
12
[52(x1)] = x1 +
8
[53(x1)] = x1 +
3
[54(x1)] = x1 +
0
[55(x1)] = x1 +
7
[40(x1)] = x1 +
8
[41(x1)] = x1 +
12
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
4
[30(x1)] = x1 +
4
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
1
[20(x1)] = x1 +
7
[21(x1)] = x1 +
0
[22(x1)] = x1 +
4
[23(x1)] = x1 +
0
[24(x1)] = x1 +
3
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
3
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
1
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
8
[02(x1)] = x1 +
1
[03(x1)] = x1 +
4
[04(x1)] = x1 +
0
[05(x1)] = x1 +
3
all of the following rules can be deleted.

There are 1440 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
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1857)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1858)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1859)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1860)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1861)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1862)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1863)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1864)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1865)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1866)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1867)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1868)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1869)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1870)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1871)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1872)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1873)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1874)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1875)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1876)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1877)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1878)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1879)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1880)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1881)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1882)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1883)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1884)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1885)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1886)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1887)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1888)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1889)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1890)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1891)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1892)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1893)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1894)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1895)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1896)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1897)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1898)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1899)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1900)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1901)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1902)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1903)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1904)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1905)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1906)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1907)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1908)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1909)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1910)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1911)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1912)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1913)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1914)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1915)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1916)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1917)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1918)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1919)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1920)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1921)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1922)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1923)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1924)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1925)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1926)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1927)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1928)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 216 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 +
1
[52(x1)] = x1 +
0
[53(x1)] = x1 +
1
[54(x1)] = x1 +
1
[55(x1)] = x1 +
0
[40(x1)] = x1 +
1
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
1
[35(x1)] = x1 +
0
[20(x1)] = x1 +
1
[21(x1)] = x1 +
0
[23(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
[50#(x1)] = x1 +
0
[51#(x1)] = x1 +
0
[52#(x1)] = x1 +
1
[53#(x1)] = x1 +
0
[54#(x1)] = x1 +
0
[55#(x1)] = x1 +
1
[00#(x1)] = x1 +
1
[01#(x1)] = x1 +
1
[02#(x1)] = x1 +
1
[03#(x1)] = x1 +
1
[04#(x1)] = x1 +
1
[05#(x1)] = x1 +
1
together with the usable rules
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1857)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1858)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1859)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1860)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1861)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(03(x1))))))))))))))))))))))) (1862)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1863)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1864)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1865)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1866)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1867)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(13(x1))))))))))))))))))))))) (1868)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1869)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1870)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1871)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1872)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1873)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(23(x1))))))))))))))))))))))) (1874)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1875)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1876)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1877)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1878)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1879)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(33(x1))))))))))))))))))))))) (1880)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1881)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1882)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1883)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1884)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1885)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(43(x1))))))))))))))))))))))) (1886)
05(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 05(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1887)
04(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 04(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1888)
03(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 03(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1889)
02(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 02(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1890)
01(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 01(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1891)
00(15(34(12(54(20(23(43(21(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) 00(15(34(12(54(20(43(21(23(13(34(02(25(33(32(52(20(23(43(31(42(21(53(x1))))))))))))))))))))))) (1892)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1893)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1894)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1895)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1896)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1897)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(00(x1)))))))))))))))))))))))))))) (1898)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1899)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1900)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1901)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1902)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1903)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(10(x1)))))))))))))))))))))))))))) (1904)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1905)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1906)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1907)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1908)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1909)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(20(x1)))))))))))))))))))))))))))) (1910)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1911)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1912)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1913)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1914)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1915)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(30(x1)))))))))))))))))))))))))))) (1916)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1917)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1918)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1919)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1920)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1921)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(40(x1)))))))))))))))))))))))))))) (1922)
55(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 55(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1923)
54(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 54(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1924)
53(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 53(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1925)
52(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 52(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1926)
51(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 51(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1927)
50(40(51(20(53(50(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) 50(40(51(50(20(53(10(34(02(45(01(35(42(11(04(25(23(03(35(12(14(04(55(50(20(23(53(50(x1)))))))))))))))))))))))))))) (1928)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 144 ruless (increase limit for explicit display).

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.