Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26974)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
5
[4(x1)] = x1 +
6
[3(x1)] = x1 +
6
[2(x1)] = x1 +
6
[1(x1)] = x1 +
5
[0(x1)] = x1 +
6
all of the following rules can be deleted.
0(3(1(2(0(0(3(0(4(3(x1)))))))))) 1(1(1(5(0(1(0(3(3(4(x1)))))))))) (5)
2(2(0(3(5(4(0(2(1(0(x1)))))))))) 2(1(1(5(5(1(0(3(0(4(x1)))))))))) (6)
3(5(4(4(2(1(4(0(5(4(x1)))))))))) 3(1(1(5(5(2(1(1(0(4(x1)))))))))) (7)
0(0(2(2(3(4(0(5(3(1(5(x1))))))))))) 0(1(1(2(0(1(4(1(2(0(x1)))))))))) (9)
0(1(2(4(0(1(2(2(3(2(5(x1))))))))))) 3(0(4(5(4(1(5(0(1(2(x1)))))))))) (10)
0(2(1(5(4(2(5(2(2(4(1(x1))))))))))) 0(5(5(4(3(2(4(1(5(1(x1)))))))))) (11)
0(3(1(1(5(0(4(4(3(0(3(x1))))))))))) 0(5(0(4(0(0(3(0(4(5(x1)))))))))) (12)
0(3(2(1(0(1(0(3(2(1(4(x1))))))))))) 0(1(3(3(1(4(5(2(2(5(x1)))))))))) (13)
0(3(2(1(3(3(4(2(1(2(2(x1))))))))))) 1(3(0(1(3(1(3(2(4(2(x1)))))))))) (14)
0(4(3(5(0(0(2(5(3(2(2(x1))))))))))) 2(3(5(0(5(2(2(4(2(4(x1)))))))))) (15)
0(4(4(4(1(1(4(1(4(5(3(x1))))))))))) 5(5(1(0(4(1(3(4(1(1(x1)))))))))) (16)
0(4(4(4(4(3(3(2(0(2(5(x1))))))))))) 0(2(4(3(5(2(5(5(2(1(x1)))))))))) (17)
0(5(3(1(2(3(3(2(2(4(2(x1))))))))))) 2(1(5(3(1(3(3(2(4(3(x1)))))))))) (18)
1(0(1(1(4(4(3(4(3(2(2(x1))))))))))) 4(4(4(1(4(1(4(2(2(5(x1)))))))))) (19)
1(1(3(1(3(0(3(4(4(3(0(x1))))))))))) 1(2(5(5(2(5(0(2(0(0(x1)))))))))) (20)
1(1(4(4(2(2(2(0(0(2(5(x1))))))))))) 4(4(3(4(0(0(3(4(3(0(x1)))))))))) (21)
1(3(4(2(3(0(0(2(1(0(1(x1))))))))))) 1(3(3(4(4(3(1(5(0(1(x1)))))))))) (25)
1(3(4(4(5(0(4(3(2(3(0(x1))))))))))) 3(4(1(4(0(3(1(2(2(5(x1)))))))))) (26)
1(5(4(0(4(4(3(3(2(2(4(x1))))))))))) 5(3(5(2(4(0(4(0(4(0(x1)))))))))) (27)
1(5(5(1(3(4(1(4(5(4(1(x1))))))))))) 2(1(1(1(0(0(1(0(5(3(x1)))))))))) (28)
2(1(0(4(3(3(5(1(2(5(2(x1))))))))))) 1(0(0(4(0(5(3(4(2(3(x1)))))))))) (29)
2(1(1(4(5(3(4(3(5(0(5(x1))))))))))) 2(5(0(0(4(1(5(2(2(1(x1)))))))))) (30)
2(2(0(2(3(5(4(5(2(3(1(x1))))))))))) 5(2(5(4(1(4(0(1(3(0(x1)))))))))) (31)
2(5(4(0(0(3(5(3(3(1(0(x1))))))))))) 1(2(4(2(1(3(2(5(4(4(x1)))))))))) (33)
3(0(0(5(0(3(4(4(5(5(4(x1))))))))))) 1(2(4(3(4(4(2(0(2(3(x1)))))))))) (34)
3(2(3(2(3(1(3(0(2(2(2(x1))))))))))) 1(3(1(5(5(5(0(5(4(0(x1)))))))))) (35)
3(3(0(5(3(3(5(3(3(3(2(x1))))))))))) 3(3(2(4(4(3(1(0(3(5(x1)))))))))) (36)
3(4(1(1(1(0(5(4(1(3(3(x1))))))))))) 5(1(3(0(3(2(1(3(2(0(x1)))))))))) (37)
3(5(2(2(0(4(3(1(1(4(5(x1))))))))))) 3(2(0(0(4(4(5(5(3(3(x1)))))))))) (38)
3(5(3(1(1(3(2(2(3(1(2(x1))))))))))) 0(3(4(2(4(3(1(5(3(5(x1)))))))))) (39)
3(5(4(0(4(0(4(4(4(2(1(x1))))))))))) 2(0(4(0(1(1(0(0(4(3(x1)))))))))) (40)
3(5(5(0(3(3(1(4(1(3(0(x1))))))))))) 2(0(2(1(2(2(3(1(2(1(x1)))))))))) (41)
4(0(4(2(1(0(2(3(4(1(5(x1))))))))))) 0(3(1(1(4(5(5(0(4(3(x1)))))))))) (42)
4(0(4(3(1(1(4(5(1(2(3(x1))))))))))) 5(2(5(2(2(4(5(1(3(3(x1)))))))))) (43)
4(0(5(1(0(3(5(1(3(1(5(x1))))))))))) 4(5(2(2(1(5(4(0(4(2(x1)))))))))) (44)
4(1(0(2(1(5(0(2(2(2(4(x1))))))))))) 4(0(2(0(5(4(5(2(4(2(x1)))))))))) (45)
4(1(2(3(2(1(0(2(2(0(4(x1))))))))))) 5(4(1(3(0(1(5(5(4(4(x1)))))))))) (46)
4(2(1(3(5(2(5(1(5(5(0(x1))))))))))) 2(2(4(1(2(5(2(2(5(3(x1)))))))))) (47)
4(2(2(5(3(2(4(2(0(2(0(x1))))))))))) 5(2(1(2(5(0(0(3(0(1(x1)))))))))) (48)
4(2(4(2(4(0(3(0(1(1(5(x1))))))))))) 3(0(0(2(3(4(5(1(5(4(x1)))))))))) (49)
4(2(4(3(2(1(1(3(4(3(1(x1))))))))))) 2(5(0(5(5(5(5(4(3(0(x1)))))))))) (50)
4(5(0(0(1(5(2(4(2(4(5(x1))))))))))) 5(3(2(1(0(2(0(1(0(2(x1)))))))))) (51)
4(5(2(1(5(1(4(2(0(0(3(x1))))))))))) 3(0(5(5(4(4(1(5(2(3(x1)))))))))) (52)
4(5(3(0(0(0(2(1(3(4(1(x1))))))))))) 2(4(3(5(5(3(3(4(4(3(x1)))))))))) (53)
5(2(2(5(1(3(2(3(4(4(5(x1))))))))))) 4(2(4(3(5(3(2(1(3(1(x1)))))))))) (54)
1(1(0(3(1(5(1(1(2(1(3(5(x1)))))))))))) 3(0(3(0(3(5(2(0(5(0(x1)))))))))) (55)
2(5(1(2(1(0(5(1(4(2(1(3(x1)))))))))))) 0(0(4(4(5(2(2(5(4(0(x1)))))))))) (57)
2(5(3(1(5(0(3(1(2(3(3(2(x1)))))))))))) 4(2(0(3(4(5(4(0(4(2(x1)))))))))) (58)
4(2(3(4(0(3(4(4(1(1(2(4(x1)))))))))))) 5(2(3(2(0(1(4(5(5(2(x1)))))))))) (59)
5(0(2(5(0(5(1(5(1(3(1(2(x1)))))))))))) 2(5(3(4(4(5(4(4(0(3(x1)))))))))) (60)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 264 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,5}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 6):

[5(x1)] = 6x1 + 0
[4(x1)] = 6x1 + 1
[3(x1)] = 6x1 + 2
[2(x1)] = 6x1 + 3
[1(x1)] = 6x1 + 4
[0(x1)] = 6x1 + 5

We obtain the labeled TRS

There are 1584 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[51(x1)] = x1 +
14
[52(x1)] = x1 +
17
[53(x1)] = x1 +
3
[54(x1)] = x1 +
3
[55(x1)] = x1 +
14
[40(x1)] = x1 +
14
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
1
[44(x1)] = x1 +
0
[45(x1)] = x1 +
14
[30(x1)] = x1 +
14
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
3
[34(x1)] = x1 +
14
[35(x1)] = x1 +
17
[20(x1)] = x1 +
31
[21(x1)] = x1 +
17
[22(x1)] = x1 +
14
[23(x1)] = x1 +
0
[24(x1)] = x1 +
1
[25(x1)] = x1 +
14
[10(x1)] = x1 +
0
[11(x1)] = x1 +
17
[12(x1)] = x1 +
3
[13(x1)] = x1 +
14
[14(x1)] = x1 +
14
[15(x1)] = x1 +
0
[00(x1)] = x1 +
3
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
14
[05(x1)] = x1 +
0
all of the following rules can be deleted.

There are 1512 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(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1943)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1944)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1945)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1946)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1947)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1948)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1949)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1950)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1951)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1952)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1953)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1954)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1955)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1956)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1957)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1958)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1959)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1960)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1961)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1962)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1963)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1964)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1965)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1966)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1967)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1968)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1969)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1970)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1971)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1972)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1973)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1974)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1975)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1976)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1977)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1978)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1979)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1980)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1981)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1982)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1983)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1984)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1985)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1986)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1987)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1988)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1989)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1990)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1991)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1992)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1993)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1994)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1995)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1996)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (1997)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (1998)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (1999)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (2000)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (2001)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (2002)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2003)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2004)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2005)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2006)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2007)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2008)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2009)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2010)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2011)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2012)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2013)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2014)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 288 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 +
1
[52(x1)] = x1 +
0
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
1
[40(x1)] = x1 +
1
[41(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
1
[31(x1)] = x1 +
1
[32(x1)] = x1 +
1
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
1
[22(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
1
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
1
[03(x1)] = x1 +
1
[04(x1)] = x1 +
1
[05(x1)] = x1 +
1
[00#(x1)] = x1 +
1
[01#(x1)] = x1 +
0
[02#(x1)] = x1 +
0
[03#(x1)] = x1 +
0
[04#(x1)] = x1 +
0
[05#(x1)] = x1 +
0
together with the usable rules
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1943)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1944)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1945)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1946)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1947)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(04(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(04(x1)))))))))))))))))) (1948)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1949)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1950)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1951)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1952)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1953)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(14(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(14(x1)))))))))))))))))) (1954)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1955)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1956)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1957)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1958)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1959)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(24(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(24(x1)))))))))))))))))) (1960)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1961)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1962)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1963)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1964)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1965)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(34(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(34(x1)))))))))))))))))) (1966)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1967)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1968)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1969)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1970)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1971)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(44(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(44(x1)))))))))))))))))) (1972)
05(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 05(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1973)
04(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 04(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1974)
03(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 03(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1975)
02(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 02(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1976)
01(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 01(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1977)
00(45(21(03(45(31(32(02(35(32(32(22(33(22(43(41(11(54(x1)))))))))))))))))) 00(45(21(03(45(31(32(32(02(35(32(22(33(22(43(41(11(54(x1)))))))))))))))))) (1978)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1979)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1980)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1981)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1982)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1983)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(04(x1))))))))))))))))))))))))))))))) (1984)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1985)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1986)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1987)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1988)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1989)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(14(x1))))))))))))))))))))))))))))))) (1990)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1991)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1992)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1993)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1994)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1995)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(24(x1))))))))))))))))))))))))))))))) (1996)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (1997)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (1998)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (1999)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (2000)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (2001)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(34(x1))))))))))))))))))))))))))))))) (2002)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2003)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2004)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2005)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2006)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2007)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(44(x1))))))))))))))))))))))))))))))) (2008)
05(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 05(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2009)
04(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 04(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2010)
03(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 03(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2011)
02(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 02(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2012)
01(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 01(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2013)
00(55(40(51(40(01(25(03(15(04(05(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) 00(55(40(51(40(01(25(03(05(15(04(35(22(53(20(43(11(14(34(52(10(14(54(10(24(03(45(41(21(13(54(x1))))))))))))))))))))))))))))))) (2014)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 216 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.