Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26940)

The rewrite relation of the following TRS is considered.

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

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 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 +
12
[51(x1)] = x1 +
2
[52(x1)] = x1 +
0
[53(x1)] = x1 +
10
[54(x1)] = x1 +
0
[55(x1)] = x1 +
10
[40(x1)] = x1 +
0
[41(x1)] = x1 +
10
[42(x1)] = x1 +
11
[43(x1)] = x1 +
2
[44(x1)] = x1 +
12
[45(x1)] = x1 +
10
[30(x1)] = x1 +
10
[31(x1)] = x1 +
1
[32(x1)] = x1 +
0
[33(x1)] = x1 +
10
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
11
[22(x1)] = x1 +
10
[23(x1)] = x1 +
0
[24(x1)] = x1 +
10
[25(x1)] = x1 +
2
[10(x1)] = x1 +
0
[11(x1)] = x1 +
10
[12(x1)] = x1 +
12
[13(x1)] = x1 +
2
[14(x1)] = x1 +
10
[15(x1)] = x1 +
0
[00(x1)] = x1 +
12
[01(x1)] = x1 +
2
[02(x1)] = x1 +
0
[03(x1)] = x1 +
10
[04(x1)] = x1 +
0
[05(x1)] = x1 +
10
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
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1943)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1944)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1945)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1946)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1947)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1948)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1949)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1950)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1951)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1952)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1953)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1954)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1955)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1956)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1957)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1958)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1959)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1960)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1961)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1962)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1963)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1964)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1965)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1966)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1967)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1968)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1969)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1970)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1971)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1972)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1973)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1974)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1975)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1976)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1977)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1978)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1979)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1980)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1981)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1982)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1983)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1984)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1985)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1986)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1987)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1988)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1989)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1990)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1991)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1992)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1993)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1994)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1995)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1996)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (1997)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (1998)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (1999)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (2000)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (2001)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (2002)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2003)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2004)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2005)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2006)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2007)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2008)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2009)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2010)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2011)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2012)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2013)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2014)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 252 ruless (increase limit for explicit display).

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
1
[51(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
1
[55(x1)] = x1 +
1
[40(x1)] = x1 +
1
[41(x1)] = x1 +
1
[43(x1)] = x1 +
0
[45(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
1
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
1
[24(x1)] = x1 +
0
[25(x1)] = x1 +
1
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
1
[01(x1)] = x1 +
1
[03(x1)] = x1 +
0
[04(x1)] = x1 +
1
[05(x1)] = x1 +
1
[20#(x1)] = x1 +
0
[21#(x1)] = x1 +
1
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
0
[24#(x1)] = x1 +
1
[25#(x1)] = x1 +
0
[10#(x1)] = x1 +
1
[11#(x1)] = x1 +
1
[12#(x1)] = x1 +
1
[13#(x1)] = x1 +
1
[14#(x1)] = x1 +
1
[15#(x1)] = x1 +
1
together with the usable rules
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1943)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1944)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1945)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1946)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1947)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(01(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(01(x1))))))))))))))))))) (1948)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1949)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1950)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1951)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1952)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1953)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(11(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(11(x1))))))))))))))))))) (1954)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1955)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1956)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1957)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1958)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1959)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(21(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(21(x1))))))))))))))))))) (1960)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1961)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1962)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1963)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1964)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1965)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(31(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(31(x1))))))))))))))))))) (1966)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1967)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1968)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1969)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1970)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1971)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(41(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(41(x1))))))))))))))))))) (1972)
15(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 15(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1973)
14(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 14(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1974)
13(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 13(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1975)
12(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 12(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1976)
11(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 11(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1977)
10(04(55(00(05(05(55(50(00(05(25(03(55(10(24(53(00(45(51(x1))))))))))))))))))) 10(04(55(00(05(05(55(50(00(25(03(05(55(10(24(53(00(45(51(x1))))))))))))))))))) (1978)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1979)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1980)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1981)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1982)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1983)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(05(x1))))))))))))))))))))))))))))) (1984)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1985)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1986)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1987)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1988)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1989)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(15(x1))))))))))))))))))))))))))))) (1990)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1991)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1992)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1993)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1994)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1995)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(25(x1))))))))))))))))))))))))))))) (1996)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (1997)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (1998)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (1999)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (2000)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (2001)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(35(x1))))))))))))))))))))))))))))) (2002)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2003)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2004)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2005)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2006)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2007)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(45(x1))))))))))))))))))))))))))))) (2008)
25(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 25(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2009)
24(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 24(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2010)
23(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 23(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2011)
22(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 22(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2012)
21(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 21(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2013)
20(53(20(53(40(41(41(01(55(50(20(23(53(20(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) 20(53(20(53(40(41(41(01(55(50(20(53(20(23(23(43(21(43(31(32(12(34(32(52(50(50(40(01(55(x1))))))))))))))))))))))))))))) (2014)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 180 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.