Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26862)

The rewrite relation of the following TRS is considered.

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

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 +
10
[4(x1)] = x1 +
9
[3(x1)] = x1 +
9
[2(x1)] = x1 +
9
[1(x1)] = x1 +
13
[0(x1)] = x1 +
10
all of the following rules can be deleted.
0(5(0(5(3(5(5(1(5(5(x1)))))))))) 2(2(1(3(0(4(5(5(2(5(x1)))))))))) (6)
1(0(3(3(0(1(4(4(2(4(x1)))))))))) 0(2(1(3(3(4(2(3(3(0(x1)))))))))) (8)
3(5(1(4(0(0(1(4(1(4(x1)))))))))) 2(0(5(0(0(1(1(5(0(2(x1)))))))))) (9)
4(2(5(0(5(2(4(3(1(1(x1)))))))))) 5(0(2(3(3(0(2(5(0(2(x1)))))))))) (11)
0(1(4(2(3(4(4(1(0(3(0(x1))))))))))) 2(2(3(3(1(4(4(0(3(5(x1)))))))))) (14)
0(2(0(5(4(4(0(0(4(1(5(x1))))))))))) 4(3(1(5(0(2(3(5(0(1(x1)))))))))) (15)
0(2(4(1(4(4(2(2(3(4(1(x1))))))))))) 5(1(0(2(4(1(5(0(2(3(x1)))))))))) (16)
0(3(5(5(4(5(2(1(5(1(0(x1))))))))))) 1(5(1(3(4(4(1(5(1(0(x1)))))))))) (17)
0(5(3(0(1(0(3(3(4(1(0(x1))))))))))) 2(5(2(0(3(1(4(0(4(2(x1)))))))))) (18)
0(5(5(3(2(0(3(4(0(0(0(x1))))))))))) 5(2(0(5(5(3(4(0(4(3(x1)))))))))) (19)
1(1(0(0(2(3(5(2(2(1(0(x1))))))))))) 5(4(4(5(1(2(4(0(0(4(x1)))))))))) (20)
1(1(3(2(0(1(4(3(5(0(2(x1))))))))))) 5(5(5(0(4(3(1(4(4(2(x1)))))))))) (21)
1(1(3(4(3(2(2(3(1(4(1(x1))))))))))) 2(4(1(3(1(0(3(1(1(2(x1)))))))))) (22)
1(2(1(2(3(0(3(4(1(4(3(x1))))))))))) 5(0(3(2(1(3(4(3(3(3(x1)))))))))) (23)
1(3(4(1(3(1(3(2(1(2(0(x1))))))))))) 0(0(2(5(2(0(5(3(4(0(x1)))))))))) (24)
1(3(5(3(3(1(3(3(4(5(4(x1))))))))))) 4(5(2(2(5(0(3(5(0(5(x1)))))))))) (25)
1(4(0(0(3(1(0(2(4(1(1(x1))))))))))) 5(0(1(2(0(2(4(5(3(4(x1)))))))))) (26)
1(5(0(2(4(0(3(5(2(3(1(x1))))))))))) 5(2(2(0(5(1(2(3(4(1(x1)))))))))) (27)
1(5(1(1(2(0(2(5(1(3(4(x1))))))))))) 5(0(1(2(4(5(1(5(1(3(x1)))))))))) (28)
1(5(3(1(1(0(2(3(0(3(5(x1))))))))))) 5(0(5(3(2(4(3(1(1(4(x1)))))))))) (29)
2(0(1(1(0(1(3(4(5(1(2(x1))))))))))) 2(1(0(3(1(5(0(4(5(2(x1)))))))))) (30)
2(1(4(5(5(0(1(3(4(5(0(x1))))))))))) 4(1(5(5(2(0(4(0(1(1(x1)))))))))) (31)
2(2(1(4(1(3(3(5(1(5(0(x1))))))))))) 1(0(1(3(2(4(0(0(4(2(x1)))))))))) (32)
2(3(4(2(0(1(4(4(0(0(3(x1))))))))))) 2(5(5(0(5(0(0(2(2(5(x1)))))))))) (33)
2(5(2(0(2(2(3(4(2(5(1(x1))))))))))) 2(5(3(4(1(2(1(2(0(5(x1)))))))))) (34)
3(1(0(4(4(2(1(2(5(5(5(x1))))))))))) 0(3(1(2(5(0(5(4(0(3(x1)))))))))) (35)
3(3(3(4(3(0(4(1(4(4(0(x1))))))))))) 1(2(2(5(4(5(0(0(2(3(x1)))))))))) (36)
3(3(3(4(4(0(2(0(5(2(2(x1))))))))))) 4(1(5(2(2(4(3(0(3(2(x1)))))))))) (37)
3(3(3(5(2(4(5(1(5(5(1(x1))))))))))) 3(5(0(5(2(4(0(5(1(4(x1)))))))))) (38)
3(4(2(1(4(1(1(1(3(1(0(x1))))))))))) 4(4(5(3(5(0(4(1(0(1(x1)))))))))) (39)
3(5(4(4(0(2(1(5(3(0(0(x1))))))))))) 1(5(5(5(5(2(2(5(1(3(x1)))))))))) (40)
4(0(4(1(0(1(0(0(0(2(1(x1))))))))))) 5(1(3(2(2(5(2(4(2(3(x1)))))))))) (41)
4(1(5(0(3(2(0(1(2(3(0(x1))))))))))) 5(4(5(4(2(3(5(1(3(1(x1)))))))))) (42)
4(3(0(4(2(2(1(1(1(5(4(x1))))))))))) 4(5(0(0(3(5(5(3(0(2(x1)))))))))) (43)
4(4(5(1(2(0(2(3(5(0(3(x1))))))))))) 0(4(4(4(4(1(2(4(4(0(x1)))))))))) (44)
5(0(3(1(4(2(5(4(3(5(0(x1))))))))))) 2(0(2(4(0(5(5(5(5(3(x1)))))))))) (45)
5(1(2(1(4(1(2(4(2(0(5(x1))))))))))) 0(1(1(1(4(3(4(2(3(5(x1)))))))))) (46)
5(2(1(3(5(2(5(1(1(4(4(x1))))))))))) 1(5(2(4(4(1(3(3(5(0(x1)))))))))) (47)
5(2(2(2(1(4(0(3(4(3(5(x1))))))))))) 0(4(0(3(2(3(3(3(4(1(x1)))))))))) (48)
0(0(2(2(5(3(0(3(5(2(5(5(x1)))))))))))) 5(5(5(4(2(3(4(1(5(0(x1)))))))))) (49)
1(3(3(2(3(0(1(2(5(4(4(3(x1)))))))))))) 0(1(0(1(4(3(5(4(3(0(x1)))))))))) (50)
1(4(4(5(5(5(2(4(5(0(1(4(x1)))))))))))) 1(1(0(1(1(3(4(0(4(5(x1)))))))))) (51)
3(0(4(1(2(2(1(4(5(2(3(0(x1)))))))))))) 1(1(0(1(5(4(0(4(2(1(x1)))))))))) (53)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 252 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 1512 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 +
1
[52(x1)] = x1 +
3
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
3
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
3
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
1
[31(x1)] = x1 +
0
[32(x1)] = x1 +
10
[33(x1)] = x1 +
0
[34(x1)] = x1 +
3
[35(x1)] = x1 +
0
[20(x1)] = x1 +
3
[21(x1)] = x1 +
0
[22(x1)] = x1 +
10
[23(x1)] = x1 +
0
[24(x1)] = x1 +
3
[25(x1)] = x1 +
10
[10(x1)] = x1 +
0
[11(x1)] = x1 +
3
[12(x1)] = x1 +
0
[13(x1)] = x1 +
10
[14(x1)] = x1 +
1
[15(x1)] = x1 +
0
[00(x1)] = x1 +
22
[01(x1)] = x1 +
10
[02(x1)] = x1 +
22
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
all of the following rules can be deleted.

There are 1440 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
35(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1850)
34(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1851)
33(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1852)
32(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1853)
31(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1854)
30(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1855)
35(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1856)
34(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1857)
33(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1858)
32(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1859)
31(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1860)
30(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1861)
35(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1862)
34(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1863)
33(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1864)
32(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1865)
31(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1866)
30(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1867)
35(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1868)
34(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1869)
33(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1870)
32(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1871)
31(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1872)
30(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1873)
35(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1874)
34(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1875)
33(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1876)
32(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1877)
31(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1878)
30(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1879)
35(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1880)
34(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1881)
33(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1882)
32(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1883)
31(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1884)
30(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1885)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1886)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1887)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1888)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1889)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1890)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1891)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1892)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1893)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1894)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1895)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1896)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1897)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1898)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1899)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1900)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1901)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1902)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1903)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1904)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1905)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1906)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1907)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1908)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1909)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1910)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1911)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1912)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1913)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1914)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1915)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1916)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1917)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1918)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1919)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1920)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1921)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 288 ruless (increase limit for explicit display).

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[51(x1)] = x1 +
1
[52(x1)] = x1 +
1
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[40(x1)] = x1 +
0
[42(x1)] = x1 +
1
[43(x1)] = x1 +
0
[44(x1)] = x1 +
1
[45(x1)] = x1 +
0
[30(x1)] = x1 +
1
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
1
[35(x1)] = x1 +
1
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
1
[11(x1)] = x1 +
1
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
1
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
[30#(x1)] = x1 +
0
[31#(x1)] = x1 +
1
[32#(x1)] = x1 +
1
[33#(x1)] = x1 +
1
[34#(x1)] = x1 +
0
[35#(x1)] = x1 +
0
[10#(x1)] = x1 +
0
[11#(x1)] = x1 +
0
[12#(x1)] = x1 +
1
[13#(x1)] = x1 +
1
[14#(x1)] = x1 +
1
[15#(x1)] = x1 +
1
together with the usable rules
35(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1850)
34(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1851)
33(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1852)
32(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1853)
31(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1854)
30(52(10(34(52(20(53(20(23(43(21(03(25(03(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(03(x1)))))))))))))) (1855)
35(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1856)
34(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1857)
33(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1858)
32(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1859)
31(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1860)
30(52(10(34(52(20(53(20(23(43(21(03(25(13(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(13(x1)))))))))))))) (1861)
35(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1862)
34(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1863)
33(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1864)
32(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1865)
31(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1866)
30(52(10(34(52(20(53(20(23(43(21(03(25(23(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(23(x1)))))))))))))) (1867)
35(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1868)
34(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1869)
33(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1870)
32(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1871)
31(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1872)
30(52(10(34(52(20(53(20(23(43(21(03(25(33(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(33(x1)))))))))))))) (1873)
35(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1874)
34(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1875)
33(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1876)
32(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1877)
31(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1878)
30(52(10(34(52(20(53(20(23(43(21(03(25(43(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(43(x1)))))))))))))) (1879)
35(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 35(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1880)
34(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 34(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1881)
33(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 33(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1882)
32(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 32(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1883)
31(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 31(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1884)
30(52(10(34(52(20(53(20(23(43(21(03(25(53(x1)))))))))))))) 30(52(10(34(52(20(23(53(20(43(21(03(25(53(x1)))))))))))))) (1885)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1886)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1887)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1888)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1889)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1890)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(04(x1)))))))))))))))))))))))) (1891)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1892)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1893)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1894)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1895)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1896)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(14(x1)))))))))))))))))))))))) (1897)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1898)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1899)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1900)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1901)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1902)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(24(x1)))))))))))))))))))))))) (1903)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1904)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1905)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1906)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1907)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1908)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(34(x1)))))))))))))))))))))))) (1909)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1910)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1911)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1912)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1913)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1914)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(44(x1)))))))))))))))))))))))) (1915)
15(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 15(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1916)
14(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 14(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1917)
13(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 13(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1918)
12(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 12(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1919)
11(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 11(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1920)
10(44(01(35(02(35(42(51(30(42(11(04(45(01(05(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) 10(44(01(35(02(35(42(51(30(42(11(04(05(45(01(25(13(44(31(22(53(40(11(54(x1)))))))))))))))))))))))) (1921)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 216 ruless (increase limit for explicit display).

and no rules could be deleted.

1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.