Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26943)

The rewrite relation of the following TRS is considered.

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

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 +
5
[2(x1)] = x1 +
5
[1(x1)] = x1 +
6
[0(x1)] = x1 +
5
all of the following rules can be deleted.
4(4(4(5(0(4(2(1(1(0(x1)))))))))) 3(2(2(0(5(5(2(4(2(0(x1)))))))))) (5)
0(2(0(3(5(1(0(5(4(0(3(x1))))))))))) 5(2(4(3(0(5(4(2(2(2(x1)))))))))) (6)
0(2(5(4(0(5(0(4(0(4(5(x1))))))))))) 2(4(2(4(1(2(5(0(5(4(x1)))))))))) (7)
0(4(1(3(4(2(4(3(0(2(4(x1))))))))))) 2(4(2(5(4(1(3(5(4(4(x1)))))))))) (8)
0(4(2(3(1(4(5(0(2(2(0(x1))))))))))) 1(0(1(4(3(2(1(5(3(3(x1)))))))))) (9)
0(4(3(4(3(3(4(5(5(2(0(x1))))))))))) 5(0(4(0(1(2(4(1(3(3(x1)))))))))) (10)
0(4(5(4(1(2(4(4(3(2(3(x1))))))))))) 5(5(0(5(0(4(4(5(0(3(x1)))))))))) (11)
0(5(2(5(5(1(5(5(0(2(2(x1))))))))))) 0(5(2(3(1(3(2(0(2(3(x1)))))))))) (12)
0(5(3(1(5(3(2(3(0(5(1(x1))))))))))) 4(3(0(4(0(2(5(5(5(1(x1)))))))))) (13)
1(0(1(1(4(2(3(4(1(1(3(x1))))))))))) 1(3(0(0(0(0(1(2(1(0(x1)))))))))) (14)
1(1(4(3(2(5(1(0(4(3(0(x1))))))))))) 5(3(2(0(4(5(2(4(4(3(x1)))))))))) (15)
1(3(0(5(4(1(2(2(5(4(1(x1))))))))))) 2(0(5(3(5(5(3(3(4(5(x1)))))))))) (16)
1(3(1(0(1(2(5(0(1(5(4(x1))))))))))) 0(4(1(2(5(3(3(2(0(3(x1)))))))))) (17)
1(3(1(5(0(1(4(0(3(3(4(x1))))))))))) 4(1(4(1(1(2(4(1(4(5(x1)))))))))) (18)
1(4(2(0(2(3(5(4(5(3(2(x1))))))))))) 2(5(4(1(1(1(3(1(5(4(x1)))))))))) (19)
1(4(3(3(2(4(5(4(4(1(2(x1))))))))))) 4(3(2(2(4(3(3(5(3(0(x1)))))))))) (20)
1(5(3(0(5(5(1(4(4(5(5(x1))))))))))) 4(4(0(1(1(1(0(0(4(4(x1)))))))))) (21)
2(0(5(5(0(3(2(4(3(3(3(x1))))))))))) 0(4(1(0(5(2(5(0(2(5(x1)))))))))) (22)
2(1(4(4(4(3(4(3(0(0(1(x1))))))))))) 5(2(1(1(1(3(0(2(2(1(x1)))))))))) (23)
2(2(0(5(1(5(3(5(5(0(1(x1))))))))))) 5(5(2(1(0(3(5(3(4(3(x1)))))))))) (24)
2(4(1(5(2(3(0(0(0(2(5(x1))))))))))) 2(2(4(1(5(0(0(3(1(1(x1)))))))))) (25)
2(4(4(0(3(2(1(4(5(3(5(x1))))))))))) 4(0(3(3(2(4(0(4(3(1(x1)))))))))) (26)
2(5(3(5(3(2(1(5(1(0(5(x1))))))))))) 3(2(1(3(1(4(4(0(4(2(x1)))))))))) (27)
3(1(0(4(4(1(0(1(3(4(3(x1))))))))))) 1(5(0(1(2(1(0(1(1(0(x1)))))))))) (28)
3(1(3(2(0(2(4(2(2(4(3(x1))))))))))) 0(2(2(1(5(1(5(3(2(0(x1)))))))))) (29)
3(2(5(1(3(4(1(1(2(4(1(x1))))))))))) 5(5(0(1(0(3(0(4(4(2(x1)))))))))) (30)
4(0(3(5(4(3(4(2(5(1(3(x1))))))))))) 4(4(5(0(4(5(1(4(3(3(x1)))))))))) (31)
4(1(1(1(1(4(2(4(1(3(4(x1))))))))))) 2(2(1(1(4(2(1(2(2(0(x1)))))))))) (32)
4(1(3(2(5(4(3(1(3(2(3(x1))))))))))) 2(1(5(5(5(5(5(1(1(5(x1)))))))))) (33)
4(1(3(3(1(2(4(2(1(2(4(x1))))))))))) 3(2(4(2(4(0(5(1(4(2(x1)))))))))) (34)
4(2(1(0(0(5(5(1(1(1(0(x1))))))))))) 3(4(4(0(5(1(2(1(3(3(x1)))))))))) (35)
4(3(5(2(2(2(1(3(5(0(0(x1))))))))))) 2(0(1(3(0(5(2(2(2(3(x1)))))))))) (36)
4(3(5(3(1(5(1(5(5(1(5(x1))))))))))) 4(1(0(4(1(1(1(3(5(2(x1)))))))))) (37)
4(4(3(0(5(2(1(1(5(1(2(x1))))))))))) 1(3(2(1(2(1(5(5(4(1(x1)))))))))) (38)
4(5(3(1(4(4(5(1(1(0(0(x1))))))))))) 3(5(3(5(4(4(4(5(3(5(x1)))))))))) (39)
4(5(4(0(0(3(1(2(5(4(2(x1))))))))))) 5(4(4(1(0(5(1(2(3(0(x1)))))))))) (40)
5(3(1(2(3(3(0(2(5(0(2(x1))))))))))) 3(1(3(4(0(0(4(4(1(5(x1)))))))))) (41)
5(4(1(4(0(4(2(1(3(1(4(x1))))))))))) 5(2(4(3(1(5(5(1(3(0(x1)))))))))) (42)
5(4(1(5(0(5(3(2(4(5(1(x1))))))))))) 1(5(5(2(3(1(2(1(5(3(x1)))))))))) (43)
5(5(2(1(1(0(5(1(5(4(0(x1))))))))))) 0(2(4(2(3(0(5(5(0(0(x1)))))))))) (44)
5(5(4(3(0(5(3(2(4(2(1(x1))))))))))) 0(0(5(4(1(5(1(0(5(3(x1)))))))))) (45)
5(5(5(2(4(0(2(2(1(2(3(x1))))))))))) 4(5(1(2(5(0(3(1(5(3(x1)))))))))) (46)
0(3(0(1(1(3(3(3(1(0(2(2(x1)))))))))))) 1(1(1(0(2(3(2(4(5(0(x1)))))))))) (47)
1(5(0(3(5(4(3(3(0(0(3(0(x1)))))))))))) 3(2(3(4(1(1(5(0(4(1(x1)))))))))) (48)
4(0(2(0(4(3(4(3(1(2(0(4(x1)))))))))))) 4(1(5(5(5(3(3(5(2(1(x1)))))))))) (51)
4(2(2(4(3(1(5(5(3(1(2(2(x1)))))))))))) 1(0(5(1(4(2(5(4(1(5(x1)))))))))) (52)
4(3(1(0(4(2(2(4(0(3(4(2(x1)))))))))))) 1(5(3(1(1(4(2(1(5(4(x1)))))))))) (53)
4(3(3(1(1(0(1(1(4(2(0(2(x1)))))))))))) 3(1(4(0(2(5(0(4(2(4(x1)))))))))) (54)
5(3(3(2(4(0(1(4(1(5(2(3(x1)))))))))))) 2(4(0(5(1(4(4(3(0(5(x1)))))))))) (55)
5(4(3(5(2(4(0(5(4(5(5(2(x1)))))))))))) 3(1(2(4(1(2(3(4(1(4(x1)))))))))) (56)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 228 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 1368 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 +
25/2
[52(x1)] = x1 +
23
[53(x1)] = x1 +
25/2
[54(x1)] = x1 +
0
[55(x1)] = x1 +
11
[40(x1)] = x1 +
25/2
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
12
[44(x1)] = x1 +
0
[45(x1)] = x1 +
3/2
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
11
[34(x1)] = x1 +
11
[35(x1)] = x1 +
25/2
[20(x1)] = x1 +
11
[21(x1)] = x1 +
3/2
[22(x1)] = x1 +
11
[23(x1)] = x1 +
0
[24(x1)] = x1 +
25/2
[25(x1)] = x1 +
11
[10(x1)] = x1 +
11
[11(x1)] = x1 +
1
[12(x1)] = x1 +
7
[13(x1)] = x1 +
11
[14(x1)] = x1 +
0
[15(x1)] = x1 +
11
[00(x1)] = x1 +
0
[01(x1)] = x1 +
11
[02(x1)] = x1 +
11
[03(x1)] = x1 +
3/2
[04(x1)] = x1 +
12
[05(x1)] = x1 +
0
all of the following rules can be deleted.

There are 1296 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(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1685)
14(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1686)
13(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1687)
12(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1688)
11(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1689)
10(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1690)
15(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1691)
14(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1692)
13(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1693)
12(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1694)
11(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1695)
10(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1696)
15(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1697)
14(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1698)
13(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1699)
12(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1700)
11(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1701)
10(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1702)
15(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1703)
14(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1704)
13(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1705)
12(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1706)
11(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1707)
10(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1708)
15(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1709)
14(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1710)
13(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1711)
12(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1712)
11(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1713)
10(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1714)
15(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1715)
14(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1716)
13(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1717)
12(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1718)
11(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1719)
10(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1720)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1721)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1722)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1723)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1724)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1725)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1726)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1727)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1728)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1729)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1730)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1731)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1732)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1733)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1734)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1735)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1736)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1737)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1738)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1739)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1740)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1741)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1742)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1743)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1744)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1745)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1746)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1747)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1748)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1749)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1750)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1751)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1752)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1753)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1754)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1755)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1756)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 468 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 +
0
[52(x1)] = x1 +
0
[54(x1)] = x1 +
1
[55(x1)] = x1 +
1
[42(x1)] = x1 +
0
[43(x1)] = x1 +
1
[44(x1)] = x1 +
0
[45(x1)] = x1 +
1
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
1
[35(x1)] = x1 +
0
[20(x1)] = x1 +
1
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
1
[24(x1)] = x1 +
1
[25(x1)] = x1 +
0
[10(x1)] = x1 +
1
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
1
[14(x1)] = x1 +
1
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
1
[20#(x1)] = x1 +
0
[21#(x1)] = x1 +
1
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
0
[24#(x1)] = x1 +
0
[25#(x1)] = x1 +
1
[10#(x1)] = x1 +
0
[11#(x1)] = x1 +
1
[12#(x1)] = x1 +
0
[13#(x1)] = x1 +
0
[14#(x1)] = x1 +
0
[15#(x1)] = x1 +
0
together with the usable rules
15(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1685)
14(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1686)
13(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1687)
12(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1688)
11(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1689)
10(54(10(54(50(10(54(30(42(31(22(33(12(04(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(04(x1)))))))))))))) (1690)
15(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1691)
14(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1692)
13(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1693)
12(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1694)
11(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1695)
10(54(10(54(50(10(54(30(42(31(22(33(12(14(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(14(x1)))))))))))))) (1696)
15(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1697)
14(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1698)
13(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1699)
12(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1700)
11(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1701)
10(54(10(54(50(10(54(30(42(31(22(33(12(24(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(24(x1)))))))))))))) (1702)
15(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1703)
14(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1704)
13(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1705)
12(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1706)
11(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1707)
10(54(10(54(50(10(54(30(42(31(22(33(12(34(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(34(x1)))))))))))))) (1708)
15(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1709)
14(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1710)
13(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1711)
12(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1712)
11(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1713)
10(54(10(54(50(10(54(30(42(31(22(33(12(44(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(44(x1)))))))))))))) (1714)
15(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 15(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1715)
14(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 14(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1716)
13(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 13(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1717)
12(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 12(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1718)
11(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 11(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1719)
10(54(10(54(50(10(54(30(42(31(22(33(12(54(x1)))))))))))))) 10(54(10(54(10(54(50(30(42(31(22(33(12(54(x1)))))))))))))) (1720)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1721)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1722)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1723)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1724)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1725)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(02(x1))))))))))))))))))))))))))))) (1726)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1727)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1728)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1729)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1730)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1731)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(12(x1))))))))))))))))))))))))))))) (1732)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1733)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1734)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1735)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1736)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1737)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(22(x1))))))))))))))))))))))))))))) (1738)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1739)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1740)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1741)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1742)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1743)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(32(x1))))))))))))))))))))))))))))) (1744)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1745)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1746)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1747)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1748)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1749)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(42(x1))))))))))))))))))))))))))))) (1750)
25(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 25(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1751)
24(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 24(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1752)
23(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 23(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1753)
22(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 22(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1754)
21(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 21(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1755)
20(13(14(04(55(20(23(43(01(45(01(15(34(12(24(13(14(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) 20(13(14(04(55(20(23(43(01(45(01(15(34(12(14(24(13(24(03(35(52(50(00(35(22(33(12(34(52(x1))))))))))))))))))))))))))))) (1756)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 396 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.