Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/25422)

The rewrite relation of the following TRS is considered.

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

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 +
4
[4(x1)] = x1 +
4
[3(x1)] = x1 +
5
[2(x1)] = x1 +
4
[1(x1)] = x1 +
4
[0(x1)] = x1 +
4
all of the following rules can be deleted.
0(4(4(3(3(1(1(4(3(3(x1)))))))))) 4(4(1(2(4(0(3(1(5(3(x1)))))))))) (7)
0(0(0(3(3(3(3(4(3(2(2(x1))))))))))) 1(3(3(3(0(5(5(3(4(3(x1)))))))))) (9)
0(1(3(4(3(2(0(3(2(1(3(x1))))))))))) 1(2(2(5(1(0(2(0(0(4(x1)))))))))) (10)
0(1(5(5(0(2(0(0(2(4(2(x1))))))))))) 0(4(3(0(1(0(2(2(2(0(x1)))))))))) (11)
0(3(3(4(2(5(4(5(1(2(5(x1))))))))))) 2(5(4(4(2(1(5(3(4(4(x1)))))))))) (12)
0(3(4(4(0(5(5(3(0(4(5(x1))))))))))) 3(4(5(5(2(3(2(3(0(4(x1)))))))))) (13)
0(4(5(0(1(2(0(0(0(4(3(x1))))))))))) 4(0(3(4(0(1(2(3(2(5(x1)))))))))) (14)
0(4(5(0(4(5(0(5(2(2(5(x1))))))))))) 1(5(4(3(1(0(3(3(4(0(x1)))))))))) (15)
0(5(4(5(4(0(4(2(1(1(5(x1))))))))))) 0(4(0(1(3(2(5(5(3(3(x1)))))))))) (16)
1(1(1(4(2(3(5(1(4(5(2(x1))))))))))) 0(3(3(5(2(3(4(2(5(4(x1)))))))))) (17)
2(0(2(4(1(4(2(5(2(3(2(x1))))))))))) 0(1(5(3(3(4(4(3(0(5(x1)))))))))) (18)
2(0(5(2(5(5(5(3(2(2(4(x1))))))))))) 4(5(1(2(2(1(3(5(0(1(x1)))))))))) (19)
2(1(2(5(2(0(0(3(0(5(0(x1))))))))))) 0(3(2(1(1(3(1(3(1(0(x1)))))))))) (20)
2(1(5(0(1(3(5(0(3(5(1(x1))))))))))) 4(2(4(1(5(3(2(5(5(2(x1)))))))))) (21)
2(3(2(3(0(1(0(3(0(5(2(x1))))))))))) 2(0(1(1(1(5(3(2(1(1(x1)))))))))) (22)
2(3(4(1(5(1(2(0(1(0(2(x1))))))))))) 1(2(5(4(2(1(1(1(3(3(x1)))))))))) (23)
2(3(4(3(0(0(4(0(4(3(3(x1))))))))))) 2(5(2(4(4(5(2(5(1(0(x1)))))))))) (24)
3(1(1(5(1(0(4(5(1(2(3(x1))))))))))) 2(4(3(4(2(5(5(3(0(1(x1)))))))))) (28)
3(1(3(5(0(3(0(1(3(3(3(x1))))))))))) 3(0(0(4(5(1(1(1(3(1(x1)))))))))) (29)
3(1(4(0(3(0(4(4(3(0(5(x1))))))))))) 1(2(4(3(1(0(0(1(0(0(x1)))))))))) (30)
3(2(1(5(1(4(2(0(1(2(2(x1))))))))))) 2(4(2(3(2(2(0(1(1(0(x1)))))))))) (31)
3(2(4(1(4(4(1(1(0(1(0(x1))))))))))) 3(4(4(5(2(0(3(0(1(5(x1)))))))))) (32)
3(2(5(0(2(4(0(4(3(0(2(x1))))))))))) 0(4(4(3(2(1(5(2(1(1(x1)))))))))) (33)
3(3(2(1(5(4(5(2(1(5(5(x1))))))))))) 1(3(0(4(2(2(3(1(1(3(x1)))))))))) (34)
3(4(0(0(5(0(2(1(2(0(0(x1))))))))))) 1(1(2(2(1(5(0(0(1(5(x1)))))))))) (35)
3(4(1(3(2(4(3(5(5(4(1(x1))))))))))) 5(0(0(5(1(4(4(3(4(5(x1)))))))))) (36)
3(4(3(5(2(1(2(1(1(4(2(x1))))))))))) 1(4(1(2(0(2(3(5(1(0(x1)))))))))) (37)
3(5(1(0(3(2(1(4(0(2(2(x1))))))))))) 0(3(0(4(4(5(5(5(5(2(x1)))))))))) (38)
4(0(2(1(0(4(1(3(2(2(1(x1))))))))))) 4(1(3(2(0(1(5(5(1(4(x1)))))))))) (39)
4(0(2(2(3(0(1(3(3(0(0(x1))))))))))) 0(3(0(3(1(1(5(1(3(1(x1)))))))))) (40)
4(0(5(1(2(4(3(5(2(3(0(x1))))))))))) 5(0(4(3(0(4(4(5(0(1(x1)))))))))) (41)
4(2(0(2(3(3(4(5(0(4(3(x1))))))))))) 4(3(1(1(3(0(4(4(4(5(x1)))))))))) (42)
4(2(4(1(3(0(4(5(0(3(0(x1))))))))))) 4(0(1(0(0(1(3(0(1(3(x1)))))))))) (43)
4(4(1(0(4(1(3(4(0(0(0(x1))))))))))) 2(0(4(0(0(0(1(2(3(2(x1)))))))))) (44)
5(0(3(0(2(2(2(1(4(5(1(x1))))))))))) 4(0(1(5(1(5(2(0(2(1(x1)))))))))) (46)
5(1(0(3(2(4(0(5(2(3(0(x1))))))))))) 1(3(0(3(4(2(0(2(2(0(x1)))))))))) (47)
5(1(0(5(5(0(2(1(1(2(1(x1))))))))))) 4(1(5(5(5(3(5(1(4(2(x1)))))))))) (48)
5(1(4(3(2(2(3(4(0(4(0(x1))))))))))) 2(2(2(4(3(1(4(3(5(5(x1)))))))))) (49)
5(2(3(1(3(3(3(2(1(2(0(x1))))))))))) 1(5(2(5(5(3(5(5(1(1(x1)))))))))) (50)
5(2(4(2(1(0(1(1(5(2(1(x1))))))))))) 3(4(0(1(2(0(0(1(0(2(x1)))))))))) (51)
5(2(4(2(5(5(2(4(3(4(2(x1))))))))))) 1(1(5(1(0(3(4(0(5(0(x1)))))))))) (52)
5(3(2(3(3(4(3(2(0(1(5(x1))))))))))) 0(5(1(4(5(5(1(5(0(5(x1)))))))))) (53)
5(3(2(4(5(1(1(2(3(1(1(x1))))))))))) 4(5(4(5(0(0(1(4(4(2(x1)))))))))) (54)
5(3(5(2(4(5(3(3(3(3(4(x1))))))))))) 4(5(5(4(5(2(5(1(1(4(x1)))))))))) (55)
5(4(1(3(2(1(0(4(5(2(4(x1))))))))))) 1(2(2(3(2(1(1(0(0(4(x1)))))))))) (56)
5(5(1(3(5(0(4(5(1(5(3(x1))))))))))) 5(3(2(0(2(2(2(3(1(0(x1)))))))))) (57)
1(1(5(4(3(5(1(1(4(4(4(3(x1)))))))))))) 5(2(2(4(3(1(4(2(1(5(x1)))))))))) (59)
1(5(4(4(0(0(0(0(0(0(3(4(x1)))))))))))) 3(0(2(0(3(3(2(1(4(1(x1)))))))))) (60)
2(5(5(3(5(3(2(5(5(1(4(3(x1)))))))))))) 1(2(0(5(5(0(3(2(1(0(x1)))))))))) (63)
4(1(4(2(1(2(4(5(2(0(3(4(x1)))))))))))) 0(0(1(3(4(0(0(5(0(2(x1)))))))))) (64)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 246 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 1476 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 +
1
[51(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
2
[54(x1)] = x1 +
0
[55(x1)] = x1 +
7
[40(x1)] = x1 +
0
[41(x1)] = x1 +
2
[42(x1)] = x1 +
15
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
2
[31(x1)] = x1 +
0
[32(x1)] = x1 +
7
[33(x1)] = x1 +
0
[34(x1)] = x1 +
7
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
1
[22(x1)] = x1 +
2
[23(x1)] = x1 +
0
[24(x1)] = x1 +
2
[25(x1)] = x1 +
2
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
7
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
7
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
15
[05(x1)] = x1 +
7
all of the following rules can be deleted.

There are 1404 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(40(41(51(40(11(34(02(45(01(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1814)
14(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1815)
13(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1816)
12(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1817)
11(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1818)
10(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1819)
15(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1820)
14(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1821)
13(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1822)
12(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1823)
11(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1824)
10(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1825)
15(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1826)
14(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1827)
13(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1828)
12(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1829)
11(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1830)
10(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1831)
15(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1832)
14(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1833)
13(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1834)
12(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1835)
11(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1836)
10(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1837)
15(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1838)
14(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1839)
13(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1840)
12(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1841)
11(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1842)
10(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1843)
15(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1844)
14(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1845)
13(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1846)
12(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1847)
11(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1848)
10(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1849)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1850)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1851)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1852)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1853)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1854)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1855)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1856)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1857)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1858)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1859)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1860)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1861)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1862)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1863)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1864)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1865)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1866)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1867)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1868)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1869)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1870)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1871)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1872)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1873)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1874)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1875)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1876)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1877)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1878)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1879)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1880)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1881)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1882)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1883)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1884)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1885)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 396 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
[53(x1)] = x1 +
1
[54(x1)] = x1 +
1
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[44(x1)] = x1 +
1
[45(x1)] = x1 +
0
[30(x1)] = x1 +
1
[31(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
0
[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 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[20#(x1)] = x1 +
1
[21#(x1)] = x1 +
1
[22#(x1)] = x1 +
1
[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
together with the usable rules
15(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1814)
14(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1815)
13(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1816)
12(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1817)
11(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1818)
10(54(40(41(51(40(11(34(02(45(01(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(01(x1))))))))))) (1819)
15(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1820)
14(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1821)
13(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1822)
12(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1823)
11(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1824)
10(54(40(41(51(40(11(34(02(45(11(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(11(x1))))))))))) (1825)
15(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1826)
14(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1827)
13(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1828)
12(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1829)
11(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1830)
10(54(40(41(51(40(11(34(02(45(21(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(21(x1))))))))))) (1831)
15(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1832)
14(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1833)
13(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1834)
12(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1835)
11(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1836)
10(54(40(41(51(40(11(34(02(45(31(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(31(x1))))))))))) (1837)
15(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1838)
14(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1839)
13(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1840)
12(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1841)
11(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1842)
10(54(40(41(51(40(11(34(02(45(41(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(41(x1))))))))))) (1843)
15(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 15(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1844)
14(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 14(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1845)
13(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 13(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1846)
12(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 12(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1847)
11(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 11(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1848)
10(54(40(41(51(40(11(34(02(45(51(x1))))))))))) 10(54(40(51(40(41(11(34(02(45(51(x1))))))))))) (1849)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1850)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1851)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1852)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1853)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1854)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(04(x1))))))))))))))))))))))))))))))) (1855)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1856)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1857)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1858)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1859)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1860)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(14(x1))))))))))))))))))))))))))))))) (1861)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1862)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1863)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1864)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1865)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1866)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(24(x1))))))))))))))))))))))))))))))) (1867)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1868)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1869)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1870)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1871)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1872)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(34(x1))))))))))))))))))))))))))))))) (1873)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1874)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1875)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1876)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1877)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1878)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(44(x1))))))))))))))))))))))))))))))) (1879)
25(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 25(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1880)
24(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 24(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1881)
23(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 23(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1882)
22(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 22(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1883)
21(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 21(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1884)
20(53(30(12(14(44(51(10(14(24(13(14(54(10(14(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) 20(53(30(12(14(44(51(10(14(24(13(14(14(54(10(14(44(51(20(03(25(23(53(40(01(35(12(54(40(11(54(x1))))))))))))))))))))))))))))))) (1885)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 324 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.