Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26969)

The rewrite relation of the following TRS is considered.

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

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 +
7
[51(x1)] = x1 +
7
[52(x1)] = x1 +
2
[53(x1)] = x1 +
0
[54(x1)] = x1 +
7
[55(x1)] = x1 +
0
[40(x1)] = x1 +
9
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
7
[44(x1)] = x1 +
1
[45(x1)] = x1 +
7
[30(x1)] = x1 +
0
[31(x1)] = x1 +
9
[32(x1)] = x1 +
7
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
8
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
7
[24(x1)] = x1 +
9
[25(x1)] = x1 +
2
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
7
[00(x1)] = x1 +
2
[01(x1)] = x1 +
0
[02(x1)] = x1 +
7
[03(x1)] = x1 +
0
[04(x1)] = x1 +
2
[05(x1)] = x1 +
0
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(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1857)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1858)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1859)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1860)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1861)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1862)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1863)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1864)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1865)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1866)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1867)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1868)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1869)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1870)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1871)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1872)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1873)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1874)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1875)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1876)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1877)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1878)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1879)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1880)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1881)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1882)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1883)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1884)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1885)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1886)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1887)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1888)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1889)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1890)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1891)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1892)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1893)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1894)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1895)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1896)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1897)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1898)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1899)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1900)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1901)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1902)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1903)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1904)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1905)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1906)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1907)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1908)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1909)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1910)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1911)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1912)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1913)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1914)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1915)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1916)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1917)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1918)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1919)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1920)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1921)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1922)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1923)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1924)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1925)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1926)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1927)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1928)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 720 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
[51(x1)] = x1 +
0
[53(x1)] = x1 +
1
[54(x1)] = x1 +
0
[55(x1)] = x1 +
1
[40(x1)] = x1 +
1
[41(x1)] = x1 +
0
[42(x1)] = x1 +
1
[44(x1)] = x1 +
1
[45(x1)] = x1 +
1
[30(x1)] = x1 +
1
[31(x1)] = x1 +
0
[32(x1)] = x1 +
1
[33(x1)] = x1 +
1
[34(x1)] = x1 +
1
[21(x1)] = x1 +
1
[22(x1)] = x1 +
1
[24(x1)] = x1 +
1
[10(x1)] = x1 +
1
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
1
[00(x1)] = x1 +
1
[01(x1)] = x1 +
0
[02(x1)] = x1 +
1
[03(x1)] = x1 +
1
[04(x1)] = x1 +
0
[05(x1)] = x1 +
1
[10#(x1)] = x1 +
0
[11#(x1)] = x1 +
0
[12#(x1)] = x1 +
1
[13#(x1)] = x1 +
1
[14#(x1)] = x1 +
0
[15#(x1)] = x1 +
0
[00#(x1)] = x1 +
0
[01#(x1)] = x1 +
1
[02#(x1)] = x1 +
0
[03#(x1)] = x1 +
0
[04#(x1)] = x1 +
1
[05#(x1)] = x1 +
0
together with the usable rules
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1857)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1858)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1859)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1860)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1861)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(04(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(04(x1)))))))))))))))))))))))))) (1862)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1863)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1864)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1865)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1866)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1867)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(14(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(14(x1)))))))))))))))))))))))))) (1868)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1869)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1870)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1871)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1872)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1873)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(24(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(24(x1)))))))))))))))))))))))))) (1874)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1875)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1876)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1877)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1878)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1879)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(34(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(34(x1)))))))))))))))))))))))))) (1880)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1881)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1882)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1883)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1884)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1885)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(44(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(44(x1)))))))))))))))))))))))))) (1886)
05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 05(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1887)
04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 04(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1888)
03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 03(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1889)
02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 02(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1890)
01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 01(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1891)
00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(51(10(14(24(13(14(54(x1)))))))))))))))))))))))))) 00(55(30(22(03(55(00(45(11(14(14(24(53(40(11(44(21(33(42(11(54(10(24(13(14(54(x1)))))))))))))))))))))))))) (1892)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1893)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1894)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1895)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1896)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1897)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(01(x1)))))))))))))))))))))))))) (1898)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1899)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1900)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1901)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1902)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1903)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(11(x1)))))))))))))))))))))))))) (1904)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1905)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1906)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1907)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1908)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1909)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(21(x1)))))))))))))))))))))))))) (1910)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1911)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1912)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1913)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1914)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1915)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(31(x1)))))))))))))))))))))))))) (1916)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1917)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1918)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1919)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1920)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1921)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(41(x1)))))))))))))))))))))))))) (1922)
15(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 15(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1923)
14(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 14(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1924)
13(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 13(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1925)
12(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 12(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1926)
11(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 11(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1927)
10(34(32(02(05(15(24(03(05(15(14(54(00(45(11(54(10(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) 10(34(32(02(05(15(24(03(05(15(14(54(00(45(51(10(14(44(01(45(51(30(12(54(40(51(x1)))))))))))))))))))))))))) (1928)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 648 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.