Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26886)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
4
[4(x1)] = x1 +
4
[3(x1)] = x1 +
4
[2(x1)] = x1 +
5
[1(x1)] = x1 +
4
[0(x1)] = x1 +
4
all of the following rules can be deleted.
1(0(5(4(4(2(3(1(2(0(x1)))))))))) 4(5(4(5(5(0(0(0(2(0(x1)))))))))) (3)
1(3(5(0(1(2(5(2(1(2(x1)))))))))) 0(0(0(1(3(0(1(1(1(1(x1)))))))))) (4)
1(5(2(2(1(2(0(1(5(0(x1)))))))))) 0(4(5(4(0(4(4(1(4(3(x1)))))))))) (5)
3(4(4(2(2(2(3(3(3(0(x1)))))))))) 0(0(0(0(3(1(3(5(4(1(x1)))))))))) (7)
4(2(5(1(3(0(3(2(5(2(x1)))))))))) 5(4(3(1(5(3(4(4(0(5(x1)))))))))) (8)
0(0(2(0(3(1(3(4(5(0(3(x1))))))))))) 5(5(0(5(4(3(1(1(4(4(x1)))))))))) (9)
0(1(0(0(4(0(1(5(4(0(3(x1))))))))))) 3(0(3(5(2(4(2(3(4(3(x1)))))))))) (10)
0(1(2(5(4(0(4(1(1(4(2(x1))))))))))) 3(4(5(3(4(3(2(3(0(5(x1)))))))))) (11)
0(1(5(5(4(0(4(3(2(4(5(x1))))))))))) 5(1(1(2(4(3(2(1(3(4(x1)))))))))) (12)
0(2(2(4(5(5(0(2(0(1(1(x1))))))))))) 0(5(4(2(0(5(3(4(2(2(x1)))))))))) (13)
0(2(4(0(3(0(5(0(0(3(2(x1))))))))))) 0(4(4(1(1(1(0(4(2(4(x1)))))))))) (14)
0(3(1(4(2(4(3(2(2(4(5(x1))))))))))) 5(4(2(2(1(4(3(5(2(4(x1)))))))))) (15)
1(0(4(0(1(1(5(3(3(2(4(x1))))))))))) 5(2(4(2(4(2(3(3(5(3(x1)))))))))) (17)
1(0(4(4(5(0(5(2(3(4(4(x1))))))))))) 0(0(3(5(3(3(5(1(5(1(x1)))))))))) (18)
1(1(1(4(3(5(1(0(0(2(5(x1))))))))))) 3(1(5(2(1(2(5(3(4(2(x1)))))))))) (19)
1(1(4(1(1(5(0(0(3(4(1(x1))))))))))) 5(3(0(3(3(1(0(5(5(2(x1)))))))))) (20)
1(2(0(5(5(4(3(5(2(4(3(x1))))))))))) 5(3(5(0(1(5(4(3(2(5(x1)))))))))) (21)
1(3(1(0(1(5(2(3(5(5(3(x1))))))))))) 1(5(0(2(4(5(5(5(2(3(x1)))))))))) (22)
1(3(1(0(1(5(3(2(2(4(3(x1))))))))))) 1(5(3(3(2(0(5(2(3(2(x1)))))))))) (23)
1(3(5(3(3(3(0(1(5(5(2(x1))))))))))) 4(5(1(4(1(4(0(1(1(4(x1)))))))))) (24)
1(5(2(1(4(2(5(4(1(5(2(x1))))))))))) 2(2(4(5(1(0(4(5(0(2(x1)))))))))) (25)
1(5(2(4(1(0(3(5(0(4(5(x1))))))))))) 1(0(3(1(1(0(4(0(5(3(x1)))))))))) (26)
2(1(0(1(5(2(0(4(3(4(4(x1))))))))))) 3(3(0(4(0(2(4(3(0(0(x1)))))))))) (27)
2(1(5(3(0(3(4(0(5(1(0(x1))))))))))) 0(3(5(4(4(2(3(4(1(3(x1)))))))))) (28)
2(2(1(0(3(3(5(4(1(1(4(x1))))))))))) 1(5(5(1(0(2(4(1(5(5(x1)))))))))) (29)
2(2(1(5(4(3(3(1(0(0(5(x1))))))))))) 0(4(3(2(4(3(2(0(2(5(x1)))))))))) (30)
2(2(4(2(4(4(3(5(2(5(4(x1))))))))))) 0(5(3(2(3(3(2(5(3(2(x1)))))))))) (31)
2(2(5(5(1(0(0(2(3(3(1(x1))))))))))) 1(3(4(1(3(2(0(1(3(2(x1)))))))))) (32)
2(3(1(0(4(0(1(2(2(4(0(x1))))))))))) 4(4(0(1(1(3(1(4(0(2(x1)))))))))) (33)
2(5(1(2(4(4(4(3(2(1(3(x1))))))))))) 4(4(1(1(2(0(1(2(2(0(x1)))))))))) (34)
2(5(2(4(0(1(4(3(5(0(5(x1))))))))))) 1(1(0(2(5(4(3(0(3(1(x1)))))))))) (35)
3(0(0(5(1(5(0(2(2(4(5(x1))))))))))) 0(0(2(1(5(5(5(3(0(1(x1)))))))))) (36)
3(0(3(2(4(5(0(3(1(5(5(x1))))))))))) 0(1(4(4(2(5(4(3(2(5(x1)))))))))) (37)
3(2(5(0(4(5(3(4(3(4(2(x1))))))))))) 1(2(0(3(5(1(2(4(1(1(x1)))))))))) (38)
3(3(5(5(4(3(1(1(2(2(3(x1))))))))))) 2(3(1(5(5(4(2(3(0(5(x1)))))))))) (39)
3(4(4(0(3(2(5(2(4(2(3(x1))))))))))) 1(1(5(3(0(2(5(2(2(4(x1)))))))))) (40)
3(4(5(0(3(4(3(1(2(5(2(x1))))))))))) 5(5(0(0(3(3(5(2(4(0(x1)))))))))) (41)
3(5(0(5(3(2(3(0(5(5(0(x1))))))))))) 5(1(3(2(1(3(2(1(0(3(x1)))))))))) (42)
3(5(2(5(3(4(4(4(2(2(0(x1))))))))))) 2(3(2(3(0(0(2(0(4(3(x1)))))))))) (43)
4(1(0(0(5(5(4(3(1(5(2(x1))))))))))) 1(5(3(5(2(5(5(2(2(3(x1)))))))))) (44)
4(1(2(5(0(4(4(0(4(1(3(x1))))))))))) 3(1(0(1(2(0(0(0(2(5(x1)))))))))) (45)
4(1(3(3(3(4(1(2(1(1(1(x1))))))))))) 4(4(2(5(0(1(5(5(0(1(x1)))))))))) (46)
5(2(1(5(2(1(2(3(1(5(0(x1))))))))))) 2(2(0(1(5(2(1(5(1(5(x1)))))))))) (47)
5(2(5(2(2(1(4(1(3(3(4(x1))))))))))) 3(4(1(2(2(4(1(1(1(4(x1)))))))))) (48)
5(2(5(3(1(5(0(3(2(2(1(x1))))))))))) 4(0(5(4(3(5(4(5(3(4(x1)))))))))) (49)
5(3(2(0(5(2(5(2(0(4(3(x1))))))))))) 4(0(4(0(1(4(2(5(3(1(x1)))))))))) (50)
5(4(4(4(3(4(1(2(5(0(2(x1))))))))))) 2(4(3(3(4(3(2(2(4(0(x1)))))))))) (51)
0(4(5(1(0(4(0(4(3(2(3(1(x1)))))))))))) 2(0(3(2(1(4(2(0(0(1(x1)))))))))) (52)
0(5(3(4(3(4(3(5(3(3(0(0(x1)))))))))))) 1(4(4(2(3(4(5(2(0(2(x1)))))))))) (53)
1(0(5(3(0(3(0(5(5(4(0(1(x1)))))))))))) 3(2(5(2(5(2(1(1(4(1(x1)))))))))) (54)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 228 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,5}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 6):

[5(x1)] = 6x1 + 0
[4(x1)] = 6x1 + 1
[3(x1)] = 6x1 + 2
[2(x1)] = 6x1 + 3
[1(x1)] = 6x1 + 4
[0(x1)] = 6x1 + 5

We obtain the labeled TRS

There are 1368 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[51(x1)] = x1 +
1
[52(x1)] = x1 +
1
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
1
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
14
[44(x1)] = x1 +
4
[45(x1)] = x1 +
0
[30(x1)] = x1 +
4
[31(x1)] = x1 +
0
[32(x1)] = x1 +
4
[33(x1)] = x1 +
0
[34(x1)] = x1 +
1
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
1
[23(x1)] = x1 +
4
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
1
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[13(x1)] = x1 +
4
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
4
[02(x1)] = x1 +
14
[03(x1)] = x1 +
1
[04(x1)] = x1 +
4
[05(x1)] = x1 +
0
all of the following rules can be deleted.

There are 1332 ruless (increase limit for explicit display).

1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
51#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 51#(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (1685)
51#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1686)
51#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 51#(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (1687)
51#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1688)
51#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 51#(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (1689)
51#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1690)
51#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 51#(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (1691)
51#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1692)
51#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 51#(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (1693)
51#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1694)
51#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 51#(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (1695)
51#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1696)
41#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 41#(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (1697)
41#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1698)
41#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 41#(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (1699)
41#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1700)
41#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 41#(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (1701)
41#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1702)
41#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 41#(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (1703)
41#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1704)
41#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 41#(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (1705)
41#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1706)
41#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 41#(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (1707)
41#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1708)
31#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (1709)
31#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1710)
31#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (1711)
31#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1712)
31#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (1713)
31#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1714)
31#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (1715)
31#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1716)
31#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (1717)
31#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1718)
31#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (1719)
31#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1720)
21#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1721)
21#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 21#(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (1722)
21#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1723)
21#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 21#(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (1724)
21#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1725)
21#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 21#(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (1726)
21#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1727)
21#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 21#(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (1728)
21#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1729)
21#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 21#(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (1730)
21#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1731)
21#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 21#(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (1732)
11#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1733)
11#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 11#(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (1734)
11#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1735)
11#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 11#(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (1736)
11#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1737)
11#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 11#(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (1738)
11#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1739)
11#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 11#(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (1740)
11#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1741)
11#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 11#(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (1742)
11#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1743)
11#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 11#(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (1744)
01#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1745)
01#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 01#(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (1746)
01#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1747)
01#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 01#(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (1748)
01#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1749)
01#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 01#(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (1750)
01#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1751)
01#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 01#(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (1752)
01#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1753)
01#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 01#(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (1754)
01#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1755)
01#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 01#(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (1756)

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 +
0
[41(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
1
[45(x1)] = x1 +
0
[31(x1)] = x1 +
1
[35(x1)] = x1 +
0
[21(x1)] = x1 +
0
[25(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
[51#(x1)] = x1 +
1
[41#(x1)] = x1 +
1
[31#(x1)] = x1 +
0
[21#(x1)] = x1 +
1
[11#(x1)] = x1 +
1
[01#(x1)] = x1 +
1
together with the usable rules
01(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 01(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (533)
01(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 01(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (534)
01(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 01(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (535)
01(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 01(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (536)
01(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 01(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (537)
01(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 01(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (538)
11(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 11(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (539)
11(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 11(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (540)
11(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 11(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (541)
11(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 11(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (542)
11(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 11(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (543)
11(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 11(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (544)
21(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 21(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (545)
21(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 21(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (546)
21(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 21(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (547)
21(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 21(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (548)
21(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 21(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (549)
21(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 21(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (550)
31(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (551)
31(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (552)
31(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (553)
31(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (554)
31(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (555)
31(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (556)
41(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 41(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (557)
41(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 41(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (558)
41(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 41(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (559)
41(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 41(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (560)
41(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 41(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (561)
41(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 41(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (562)
51(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 51(44(12(31(45(05(02(35(04(11(43(25(05(x1))))))))))))) (563)
51(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 51(44(12(31(45(05(02(35(04(11(43(25(04(x1))))))))))))) (564)
51(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 51(44(12(31(45(05(02(35(04(11(43(25(03(x1))))))))))))) (565)
51(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 51(44(12(31(45(05(02(35(04(11(43(25(02(x1))))))))))))) (566)
51(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 51(44(12(31(45(05(02(35(04(11(43(25(01(x1))))))))))))) (567)
51(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 51(44(12(31(45(05(02(35(04(11(43(25(00(x1))))))))))))) (568)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
51#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1686)
51#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1688)
51#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1690)
51#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1692)
51#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1694)
51#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1696)
41#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1698)
41#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1700)
41#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1702)
41#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1704)
41#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1706)
41#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1708)
31#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1710)
31#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1712)
31#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1714)
31#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1716)
31#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1718)
31#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1720)
21#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1721)
21#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1723)
21#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1725)
21#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1727)
21#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1729)
21#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1731)
11#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1733)
11#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1735)
11#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1737)
11#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1739)
11#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1741)
11#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1743)
01#(44(12(31(45(02(35(05(04(11(43(25(00(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(00(x1)))))))))) (1745)
01#(44(12(31(45(02(35(05(04(11(43(25(01(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(01(x1)))))))))) (1747)
01#(44(12(31(45(02(35(05(04(11(43(25(02(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(02(x1)))))))))) (1749)
01#(44(12(31(45(02(35(05(04(11(43(25(03(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(03(x1)))))))))) (1751)
01#(44(12(31(45(02(35(05(04(11(43(25(04(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(04(x1)))))))))) (1753)
01#(44(12(31(45(02(35(05(04(11(43(25(05(x1))))))))))))) 31#(45(05(02(35(04(11(43(25(05(x1)))))))))) (1755)
and no rules could be deleted.

1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.