Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/27013)

The rewrite relation of the following TRS is considered.

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

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 +
0
[51(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
25
[54(x1)] = x1 +
2
[55(x1)] = x1 +
0
[40(x1)] = x1 +
82
[41(x1)] = x1 +
0
[42(x1)] = x1 +
25
[43(x1)] = x1 +
2
[44(x1)] = x1 +
1
[45(x1)] = x1 +
0
[30(x1)] = x1 +
8
[31(x1)] = x1 +
2
[32(x1)] = x1 +
2
[33(x1)] = x1 +
8
[34(x1)] = x1 +
0
[35(x1)] = x1 +
25
[20(x1)] = x1 +
25
[21(x1)] = x1 +
25
[22(x1)] = x1 +
0
[23(x1)] = x1 +
2
[24(x1)] = x1 +
25
[25(x1)] = x1 +
8
[10(x1)] = x1 +
0
[11(x1)] = x1 +
1
[12(x1)] = x1 +
8
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
2
[00(x1)] = x1 +
82
[01(x1)] = x1 +
0
[02(x1)] = x1 +
2
[03(x1)] = x1 +
0
[04(x1)] = x1 +
2
[05(x1)] = x1 +
2
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
25(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1814)
24(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1815)
23(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1816)
22(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1817)
21(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1818)
20(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1819)
25(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1820)
24(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1821)
23(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1822)
22(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1823)
21(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1824)
20(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1825)
25(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1826)
24(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1827)
23(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1828)
22(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1829)
21(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1830)
20(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1831)
25(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1832)
24(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1833)
23(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1834)
22(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1835)
21(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1836)
20(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1837)
25(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1838)
24(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1839)
23(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1840)
22(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1841)
21(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1842)
20(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1843)
25(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1844)
24(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1845)
23(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1846)
22(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1847)
21(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1848)
20(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1849)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1850)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1851)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1852)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1853)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1854)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1855)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1856)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1857)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1858)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1859)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1860)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1861)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1862)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1863)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1864)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1865)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1866)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1867)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1868)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1869)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1870)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1871)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1872)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1873)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1874)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1875)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1876)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1877)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1878)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1879)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1880)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1881)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1882)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1883)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1884)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1885)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 360 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
[51(x1)] = x1 +
0
[53(x1)] = x1 +
1
[54(x1)] = x1 +
0
[55(x1)] = x1 +
0
[41(x1)] = x1 +
0
[42(x1)] = x1 +
1
[43(x1)] = x1 +
1
[44(x1)] = x1 +
0
[45(x1)] = x1 +
1
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[35(x1)] = x1 +
1
[20(x1)] = x1 +
1
[21(x1)] = x1 +
1
[22(x1)] = x1 +
0
[23(x1)] = x1 +
1
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
1
[05(x1)] = x1 +
1
[20#(x1)] = x1 +
0
[21#(x1)] = x1 +
0
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
0
[24#(x1)] = x1 +
1
[25#(x1)] = x1 +
1
[00#(x1)] = x1 +
1
[01#(x1)] = x1 +
0
[02#(x1)] = x1 +
1
[03#(x1)] = x1 +
1
[04#(x1)] = x1 +
0
[05#(x1)] = x1 +
0
together with the usable rules
25(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1814)
24(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1815)
23(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1816)
22(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1817)
21(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1818)
20(43(21(23(53(20(33(32(22(03(15(04(05(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(05(x1))))))))))))) (1819)
25(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1820)
24(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1821)
23(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1822)
22(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1823)
21(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1824)
20(43(21(23(53(20(33(32(22(03(15(04(15(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(15(x1))))))))))))) (1825)
25(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1826)
24(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1827)
23(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1828)
22(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1829)
21(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1830)
20(43(21(23(53(20(33(32(22(03(15(04(25(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(25(x1))))))))))))) (1831)
25(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1832)
24(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1833)
23(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1834)
22(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1835)
21(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1836)
20(43(21(23(53(20(33(32(22(03(15(04(35(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(35(x1))))))))))))) (1837)
25(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1838)
24(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1839)
23(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1840)
22(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1841)
21(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1842)
20(43(21(23(53(20(33(32(22(03(15(04(45(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(45(x1))))))))))))) (1843)
25(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 25(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1844)
24(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 24(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1845)
23(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 23(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1846)
22(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 22(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1847)
21(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 21(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1848)
20(43(21(23(53(20(33(32(22(03(15(04(55(x1))))))))))))) 20(43(21(53(20(23(33(32(22(03(15(04(55(x1))))))))))))) (1849)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1850)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1851)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1852)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1853)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1854)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(01(x1)))))))))))))))))))))))))) (1855)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1856)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1857)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1858)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1859)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1860)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(11(x1)))))))))))))))))))))))))) (1861)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1862)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1863)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1864)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1865)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1866)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(21(x1)))))))))))))))))))))))))) (1867)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1868)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1869)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1870)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1871)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1872)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(31(x1)))))))))))))))))))))))))) (1873)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1874)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1875)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1876)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1877)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1878)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(41(x1)))))))))))))))))))))))))) (1879)
05(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 05(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1880)
04(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 04(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1881)
03(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 03(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1882)
02(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 02(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1883)
01(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 01(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1884)
00(15(04(35(42(01(45(01(15(04(05(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) 00(15(04(35(42(01(45(01(05(15(04(45(31(02(55(20(53(50(10(14(54(00(35(12(44(51(x1)))))))))))))))))))))))))) (1885)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 288 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.