Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26965)

The rewrite relation of the following TRS is considered.

0(0(1(2(1(0(3(2(x1)))))))) 0(2(0(1(1(0(3(2(x1)))))))) (1)
1(0(4(1(2(5(2(4(x1)))))))) 1(0(4(1(5(2(2(4(x1)))))))) (2)
1(4(4(0(4(1(5(2(5(x1))))))))) 1(4(4(1(4(5(0(2(5(x1))))))))) (3)
4(4(1(3(0(5(5(5(3(x1))))))))) 4(1(4(3(5(0(5(5(3(x1))))))))) (4)
1(1(3(1(2(1(1(1(0(0(x1)))))))))) 2(0(3(3(2(0(3(5(0(1(x1)))))))))) (5)
1(3(0(5(5(1(1(1(2(2(x1)))))))))) 1(3(5(5(1(0(1(1(2(2(x1)))))))))) (6)
3(0(1(4(4(2(0(2(2(4(x1)))))))))) 1(1(1(4(4(0(5(3(5(3(x1)))))))))) (7)
0(0(5(4(0(4(2(3(5(2(2(x1))))))))))) 1(5(0(2(4(4(4(0(4(2(x1)))))))))) (8)
0(1(0(1(0(3(2(3(5(5(1(x1))))))))))) 3(2(2(3(4(4(3(1(3(4(x1)))))))))) (9)
0(1(0(2(4(2(1(2(5(1(5(x1))))))))))) 1(5(3(1(3(1(1(5(2(1(x1)))))))))) (10)
0(2(0(4(4(2(4(1(0(3(3(x1))))))))))) 4(5(2(3(1(4(1(3(5(2(x1)))))))))) (11)
0(2(2(4(1(5(3(0(0(0(1(x1))))))))))) 4(1(1(3(1(0(5(1(2(0(x1)))))))))) (12)
0(3(1(0(3(2(4(2(2(1(2(x1))))))))))) 1(3(3(1(3(4(0(1(0(3(x1)))))))))) (13)
0(5(2(5(2(5(1(4(4(4(2(x1))))))))))) 2(2(1(5(4(4(4(5(5(0(2(x1))))))))))) (14)
1(0(0(3(4(2(5(4(2(1(1(x1))))))))))) 2(4(5(4(4(3(3(4(2(2(x1)))))))))) (15)
1(2(2(0(2(0(4(4(1(1(5(x1))))))))))) 5(2(5(2(1(2(1(0(0(0(x1)))))))))) (16)
1(3(1(3(2(4(5(0(2(2(1(x1))))))))))) 2(5(1(1(2(2(3(1(4(2(x1)))))))))) (17)
1(3(1(4(1(2(2(1(1(1(5(x1))))))))))) 3(1(3(0(1(1(5(2(5(0(x1)))))))))) (18)
1(3(5(1(2(3(5(0(1(5(3(x1))))))))))) 2(0(5(1(1(3(2(3(5(3(x1)))))))))) (19)
1(4(2(5(0(0(4(2(3(5(3(x1))))))))))) 1(2(5(5(2(0(2(1(1(2(x1)))))))))) (20)
1(5(2(0(4(1(0(2(1(3(2(x1))))))))))) 5(0(2(1(2(1(5(2(0(1(x1)))))))))) (21)
1(5(3(2(1(3(0(2(1(0(3(x1))))))))))) 5(0(5(3(4(0(4(4(1(2(x1)))))))))) (22)
2(1(0(1(4(2(3(5(2(4(4(x1))))))))))) 1(0(1(5(4(4(2(1(1(3(x1)))))))))) (23)
2(3(5(0(0(4(5(0(3(0(5(x1))))))))))) 2(5(0(3(5(2(3(4(1(4(x1)))))))))) (24)
2(4(3(5(2(1(5(4(1(2(4(x1))))))))))) 1(3(1(4(3(1(3(0(5(3(x1)))))))))) (25)
2(5(1(3(2(3(2(4(1(1(4(x1))))))))))) 1(0(4(1(5(5(3(5(3(3(x1)))))))))) (26)
2(5(3(2(5(1(2(1(1(5(4(x1))))))))))) 5(5(1(2(2(1(2(5(4(3(x1)))))))))) (27)
2(5(4(0(3(1(4(1(1(1(0(x1))))))))))) 2(5(4(0(1(3(4(1(1(1(0(x1))))))))))) (28)
2(5(4(1(5(1(5(2(3(2(4(x1))))))))))) 2(1(2(0(5(1(4(4(0(5(x1)))))))))) (29)
3(3(0(0(1(1(5(0(2(4(3(x1))))))))))) 5(3(3(0(3(0(3(4(5(4(x1)))))))))) (30)
3(5(2(3(3(2(2(1(4(2(1(x1))))))))))) 3(5(4(3(2(5(3(3(2(4(x1)))))))))) (31)
4(1(4(4(0(3(0(0(4(2(5(x1))))))))))) 3(4(2(5(0(2(5(1(1(0(x1)))))))))) (32)
4(2(5(3(2(4(1(2(3(0(1(x1))))))))))) 3(0(4(1(3(0(4(0(1(2(x1)))))))))) (33)
4(4(0(0(2(1(4(3(5(0(5(x1))))))))))) 3(4(2(3(2(1(0(4(1(1(x1)))))))))) (34)
4(4(4(3(3(5(4(4(4(5(1(x1))))))))))) 0(3(0(3(2(1(2(2(3(1(x1)))))))))) (35)
4(5(1(2(0(1(0(5(4(2(2(x1))))))))))) 1(0(5(4(2(1(0(5(5(4(x1)))))))))) (36)
4(5(1(2(2(0(1(4(1(3(1(x1))))))))))) 2(3(3(4(1(0(0(1(5(2(x1)))))))))) (37)
4(5(4(5(5(0(4(3(3(2(4(x1))))))))))) 3(1(2(3(0(2(1(4(3(5(x1)))))))))) (38)
5(1(2(0(1(0(5(3(2(0(3(x1))))))))))) 5(1(3(1(0(2(2(1(4(2(x1)))))))))) (39)
5(2(1(1(0(1(4(4(1(1(1(x1))))))))))) 4(0(3(1(2(3(1(3(0(1(x1)))))))))) (40)
5(2(4(3(5(4(4(0(2(2(1(x1))))))))))) 5(3(4(5(0(1(4(5(0(3(x1)))))))))) (41)
0(0(2(5(1(2(4(1(4(4(4(5(x1)))))))))))) 4(1(0(4(0(3(2(4(3(0(x1)))))))))) (42)
0(2(5(3(3(2(3(5(0(0(3(2(x1)))))))))))) 5(0(2(0(1(3(1(2(5(1(x1)))))))))) (43)
1(0(2(5(2(1(2(0(1(0(2(2(x1)))))))))))) 1(0(2(5(1(2(2(0(1(0(2(2(x1)))))))))))) (44)
1(4(4(1(5(5(5(4(3(5(5(3(x1)))))))))))) 4(5(5(1(1(4(1(2(4(4(x1)))))))))) (45)
2(0(5(2(2(3(0(1(0(5(4(3(x1)))))))))))) 5(3(4(0(1(3(2(1(5(2(x1)))))))))) (46)
2(1(1(1(5(4(1(5(0(1(4(2(x1)))))))))))) 4(4(0(5(0(4(3(1(2(5(x1)))))))))) (47)
2(2(2(1(5(5(5(0(5(4(5(3(x1)))))))))))) 4(0(3(5(0(5(2(4(2(5(x1)))))))))) (48)
2(5(3(0(0(5(1(2(5(5(2(1(x1)))))))))))) 0(0(0(2(0(2(3(2(1(4(x1)))))))))) (49)
2(5(3(4(2(3(1(2(5(3(2(0(x1)))))))))))) 0(1(2(5(4(1(0(0(0(4(x1)))))))))) (50)
3(3(3(4(2(0(4(1(5(0(1(5(x1)))))))))))) 4(0(0(3(1(3(3(4(3(0(x1)))))))))) (51)
5(0(1(2(1(4(4(0(5(0(5(4(x1)))))))))))) 5(0(1(2(1(4(0(4(5(0(5(4(x1)))))))))))) (52)
5(1(3(3(4(1(2(2(5(1(5(0(x1)))))))))))) 4(2(0(3(0(1(4(0(4(4(x1)))))))))) (53)
5(2(2(3(5(4(3(3(3(0(0(3(x1)))))))))))) 4(0(5(3(5(0(0(4(0(4(x1)))))))))) (54)
5(2(3(0(3(5(4(3(0(1(0(3(x1)))))))))))) 5(0(4(5(5(2(2(0(1(4(x1)))))))))) (55)
5(3(3(2(2(3(0(2(0(0(1(2(x1)))))))))))) 4(4(2(4(0(3(2(1(1(3(x1)))))))))) (56)
5(3(5(0(4(2(0(0(0(4(3(2(x1)))))))))))) 0(3(4(5(4(2(3(2(5(0(x1)))))))))) (57)
5(5(5(1(0(0(3(5(5(3(4(1(x1)))))))))))) 1(3(2(0(2(2(2(5(2(2(x1)))))))))) (58)
2(5(0(5(4(4(5(5(1(3(1(0(1(x1))))))))))))) 2(5(0(4(5(5(4(5(1(3(1(0(1(x1))))))))))))) (59)
2(5(1(0(5(3(3(5(2(2(1(2(3(x1))))))))))))) 2(5(1(0(5(3(5(3(2(2(1(2(3(x1))))))))))))) (60)
4(0(1(4(1(4(4(3(1(3(1(4(4(x1))))))))))))) 4(0(1(4(1(4(3(4(1(3(1(4(4(x1))))))))))))) (61)
4(2(2(2(2(2(3(2(5(3(1(2(4(x1))))))))))))) 4(2(3(2(2(2(2(3(2(5(1(2(4(x1))))))))))))) (62)
4(3(5(2(2(3(5(3(3(3(3(5(0(x1))))))))))))) 3(4(4(2(2(2(0(0(1(0(x1)))))))))) (63)
5(2(3(5(2(4(2(1(0(4(2(0(5(x1))))))))))))) 5(2(2(3(2(1(0(5(4(4(2(0(5(x1))))))))))))) (64)
1(5(0(2(1(0(3(5(5(2(0(3(0(5(x1)))))))))))))) 1(5(0(2(1(0(5(3(5(2(0(3(0(5(x1)))))))))))))) (65)
3(5(3(4(2(2(2(5(4(4(3(4(0(4(x1)))))))))))))) 3(5(3(4(2(2(2(4(5(4(3(4(0(4(x1)))))))))))))) (66)
4(0(2(4(1(4(4(5(1(0(0(4(0(5(x1)))))))))))))) 4(0(2(4(1(4(5(4(1(0(0(4(0(5(x1)))))))))))))) (67)
1(1(0(3(0(3(4(4(4(4(4(0(0(1(1(x1))))))))))))))) 1(1(0(3(0(4(3(4(4(4(4(0(0(1(1(x1))))))))))))))) (68)
1(2(4(4(2(3(0(0(4(3(3(0(5(5(3(x1))))))))))))))) 1(2(4(4(3(2(0(3(5(0(0(5(3(4(3(x1))))))))))))))) (69)
1(3(2(5(3(1(5(3(3(5(3(2(0(4(4(x1))))))))))))))) 1(3(2(5(3(5(1(3(3(5(3(2(0(4(4(x1))))))))))))))) (70)
5(5(3(3(0(3(4(2(1(2(3(1(1(4(1(x1))))))))))))))) 5(5(0(3(3(3(4(2(2(1(3(1(1(4(1(x1))))))))))))))) (71)
0(5(3(4(3(5(2(2(2(0(2(1(0(1(4(2(x1)))))))))))))))) 0(5(3(4(3(5(2(2(2(0(1(2(0(1(4(2(x1)))))))))))))))) (72)
0(0(0(3(5(0(0(5(4(3(5(4(5(4(3(2(4(x1))))))))))))))))) 0(0(0(3(5(0(5(0(4(3(5(4(5(4(3(2(4(x1))))))))))))))))) (73)
5(4(0(2(4(4(5(2(1(3(3(0(4(1(2(1(0(x1))))))))))))))))) 5(4(0(2(4(4(5(2(1(3(3(0(1(4(2(1(0(x1))))))))))))))))) (74)
3(1(4(4(3(3(1(3(0(2(0(2(5(3(5(0(3(1(x1)))))))))))))))))) 3(1(4(4(3(1(3(3(0(2(2(0(5(3(5(3(0(1(x1)))))))))))))))))) (75)
5(5(5(0(2(1(1(5(4(4(0(4(4(3(1(4(4(3(x1)))))))))))))))))) 5(5(5(0(2(1(1(5(4(4(0(4(4(3(4(1(4(3(x1)))))))))))))))))) (76)
3(1(2(2(1(5(2(1(2(5(3(1(1(5(1(2(5(3(4(x1))))))))))))))))))) 3(5(1(1(3(4(1(2(2(2(1(5(1(2(2(1(5(3(5(x1))))))))))))))))))) (77)
3(5(2(4(0(2(1(0(0(5(3(0(4(1(4(2(0(0(3(x1))))))))))))))))))) 3(1(0(5(1(4(2(2(3(0(4(0(2(0(4(5(0(0(3(x1))))))))))))))))))) (78)
0(2(5(1(4(2(5(3(1(4(1(0(3(2(3(4(3(0(1(1(3(x1))))))))))))))))))))) 0(2(5(1(4(2(5(1(3(4(1(0(3(2(3(4(3(0(1(1(3(x1))))))))))))))))))))) (79)
1(0(5(2(4(3(5(0(0(5(2(5(5(4(5(4(0(0(5(5(4(x1))))))))))))))))))))) 1(0(5(2(4(3(5(0(0(5(2(5(5(4(4(5(0(0(5(5(4(x1))))))))))))))))))))) (80)
1(2(1(4(2(1(3(4(2(5(1(4(5(1(3(0(4(1(0(4(4(x1))))))))))))))))))))) 1(2(1(4(2(1(3(2(4(5(1(4(5(1(3(0(4(1(0(4(4(x1))))))))))))))))))))) (81)
3(4(0(0(2(0(4(1(5(5(0(0(4(3(5(2(1(0(2(4(4(x1))))))))))))))))))))) 3(4(0(0(2(0(4(1(5(0(5(0(4(3(5(2(1(0(2(4(4(x1))))))))))))))))))))) (82)
5(1(4(3(3(3(4(1(1(4(0(0(0(3(2(3(1(3(5(5(1(0(x1)))))))))))))))))))))) 5(1(4(3(3(3(4(1(1(4(0(0(0(3(2(3(3(1(5(5(1(0(x1)))))))))))))))))))))) (83)
2(0(3(3(0(5(3(1(4(3(0(1(1(4(0(5(5(3(1(2(1(2(4(2(5(x1))))))))))))))))))))))))) 2(0(3(3(0(5(1(3(4(3(0(1(1(4(0(5(5(3(1(2(1(2(4(2(5(x1))))))))))))))))))))))))) (84)
2(1(1(1(4(4(1(4(4(4(5(3(2(2(1(4(4(4(4(1(2(2(3(1(1(x1))))))))))))))))))))))))) 2(1(1(4(1(4(1(4(4(4(5(3(2(2(1(4(4(4(4(1(2(2(3(1(1(x1))))))))))))))))))))))))) (85)
2(1(2(1(1(4(1(3(2(0(2(2(1(5(3(2(3(5(0(2(0(0(5(0(2(x1))))))))))))))))))))))))) 2(1(2(1(1(4(1(3(2(0(2(2(1(5(3(3(2(5(0(2(0(0(5(0(2(x1))))))))))))))))))))))))) (86)
0(4(0(2(5(4(5(1(3(5(2(0(1(1(0(4(1(3(0(4(2(3(4(5(5(1(4(x1))))))))))))))))))))))))))) 0(4(0(2(5(4(5(1(3(5(0(2(1(1(0(4(1(3(0(4(2(3(4(5(5(1(4(x1))))))))))))))))))))))))))) (87)
4(5(3(1(0(2(2(2(4(5(3(5(5(5(0(2(1(2(4(0(4(4(1(3(0(0(2(x1))))))))))))))))))))))))))) 4(5(3(1(0(2(2(2(4(5(3(5(5(5(0(2(1(2(4(4(0(4(1(3(0(0(2(x1))))))))))))))))))))))))))) (88)
5(1(2(3(2(3(4(2(4(2(1(0(4(4(0(3(0(3(2(5(3(1(5(2(3(1(0(x1))))))))))))))))))))))))))) 5(1(2(3(2(3(4(2(4(2(1(0(4(4(0(3(0(3(2(5(3(1(5(3(2(1(0(x1))))))))))))))))))))))))))) (89)
2(0(4(5(3(3(2(4(3(4(4(4(1(5(1(5(5(0(2(4(4(1(0(5(0(5(3(3(x1)))))))))))))))))))))))))))) 2(0(4(5(3(3(2(4(3(4(4(1(4(5(1(5(5(0(2(4(4(1(0(5(0(5(3(3(x1)))))))))))))))))))))))))))) (90)
2(0(0(0(0(0(5(4(5(1(2(3(2(3(4(3(5(5(5(0(1(3(3(1(4(1(4(0(2(x1))))))))))))))))))))))))))))) 2(0(0(0(0(0(5(4(5(1(2(3(2(3(3(4(5(5(5(0(1(3(3(1(4(1(4(0(2(x1))))))))))))))))))))))))))))) (91)
2(0(3(0(4(2(1(1(4(5(0(1(2(1(4(3(1(3(0(1(1(0(5(4(4(2(3(3(3(x1))))))))))))))))))))))))))))) 2(0(3(0(4(2(1(1(4(5(0(1(2(1(4(3(1(3(0(1(1(0(4(5(4(2(3(3(3(x1))))))))))))))))))))))))))))) (92)
2(2(5(3(2(2(0(4(4(4(4(0(5(0(5(3(4(4(4(0(0(5(0(5(0(2(0(1(3(x1))))))))))))))))))))))))))))) 2(2(5(3(2(2(0(4(4(4(4(0(5(0(5(3(4(4(4(0(5(0(0(5(0(2(0(1(3(x1))))))))))))))))))))))))))))) (93)
4(5(5(0(5(5(5(2(1(2(3(0(3(2(1(1(2(1(3(0(1(1(5(1(1(5(0(0(4(4(x1)))))))))))))))))))))))))))))) 4(5(5(5(0(5(5(2(1(2(3(0(3(1(1(2(2(1(0(1(3(1(5(1(5(1(0(0(4(4(x1)))))))))))))))))))))))))))))) (94)
5(5(0(5(0(0(3(4(4(0(0(0(0(4(0(4(5(3(1(1(1(3(1(1(2(1(0(1(2(4(x1)))))))))))))))))))))))))))))) 5(5(0(5(0(0(4(3(4(0(0(0(0(4(0(4(5(3(1(1(1(3(1(1(2(1(0(1(2(4(x1)))))))))))))))))))))))))))))) (95)

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 +
11
[4(x1)] = x1 +
14
[3(x1)] = x1 +
11
[2(x1)] = x1 +
11
[1(x1)] = x1 +
12
[0(x1)] = x1 +
11
all of the following rules can be deleted.
1(1(3(1(2(1(1(1(0(0(x1)))))))))) 2(0(3(3(2(0(3(5(0(1(x1)))))))))) (5)
3(0(1(4(4(2(0(2(2(4(x1)))))))))) 1(1(1(4(4(0(5(3(5(3(x1)))))))))) (7)
0(0(5(4(0(4(2(3(5(2(2(x1))))))))))) 1(5(0(2(4(4(4(0(4(2(x1)))))))))) (8)
0(1(0(1(0(3(2(3(5(5(1(x1))))))))))) 3(2(2(3(4(4(3(1(3(4(x1)))))))))) (9)
0(1(0(2(4(2(1(2(5(1(5(x1))))))))))) 1(5(3(1(3(1(1(5(2(1(x1)))))))))) (10)
0(2(0(4(4(2(4(1(0(3(3(x1))))))))))) 4(5(2(3(1(4(1(3(5(2(x1)))))))))) (11)
0(2(2(4(1(5(3(0(0(0(1(x1))))))))))) 4(1(1(3(1(0(5(1(2(0(x1)))))))))) (12)
0(3(1(0(3(2(4(2(2(1(2(x1))))))))))) 1(3(3(1(3(4(0(1(0(3(x1)))))))))) (13)
1(0(0(3(4(2(5(4(2(1(1(x1))))))))))) 2(4(5(4(4(3(3(4(2(2(x1)))))))))) (15)
1(2(2(0(2(0(4(4(1(1(5(x1))))))))))) 5(2(5(2(1(2(1(0(0(0(x1)))))))))) (16)
1(3(1(3(2(4(5(0(2(2(1(x1))))))))))) 2(5(1(1(2(2(3(1(4(2(x1)))))))))) (17)
1(3(1(4(1(2(2(1(1(1(5(x1))))))))))) 3(1(3(0(1(1(5(2(5(0(x1)))))))))) (18)
1(3(5(1(2(3(5(0(1(5(3(x1))))))))))) 2(0(5(1(1(3(2(3(5(3(x1)))))))))) (19)
1(4(2(5(0(0(4(2(3(5(3(x1))))))))))) 1(2(5(5(2(0(2(1(1(2(x1)))))))))) (20)
1(5(2(0(4(1(0(2(1(3(2(x1))))))))))) 5(0(2(1(2(1(5(2(0(1(x1)))))))))) (21)
1(5(3(2(1(3(0(2(1(0(3(x1))))))))))) 5(0(5(3(4(0(4(4(1(2(x1)))))))))) (22)
2(1(0(1(4(2(3(5(2(4(4(x1))))))))))) 1(0(1(5(4(4(2(1(1(3(x1)))))))))) (23)
2(3(5(0(0(4(5(0(3(0(5(x1))))))))))) 2(5(0(3(5(2(3(4(1(4(x1)))))))))) (24)
2(4(3(5(2(1(5(4(1(2(4(x1))))))))))) 1(3(1(4(3(1(3(0(5(3(x1)))))))))) (25)
2(5(1(3(2(3(2(4(1(1(4(x1))))))))))) 1(0(4(1(5(5(3(5(3(3(x1)))))))))) (26)
2(5(3(2(5(1(2(1(1(5(4(x1))))))))))) 5(5(1(2(2(1(2(5(4(3(x1)))))))))) (27)
2(5(4(1(5(1(5(2(3(2(4(x1))))))))))) 2(1(2(0(5(1(4(4(0(5(x1)))))))))) (29)
3(3(0(0(1(1(5(0(2(4(3(x1))))))))))) 5(3(3(0(3(0(3(4(5(4(x1)))))))))) (30)
3(5(2(3(3(2(2(1(4(2(1(x1))))))))))) 3(5(4(3(2(5(3(3(2(4(x1)))))))))) (31)
4(1(4(4(0(3(0(0(4(2(5(x1))))))))))) 3(4(2(5(0(2(5(1(1(0(x1)))))))))) (32)
4(2(5(3(2(4(1(2(3(0(1(x1))))))))))) 3(0(4(1(3(0(4(0(1(2(x1)))))))))) (33)
4(4(0(0(2(1(4(3(5(0(5(x1))))))))))) 3(4(2(3(2(1(0(4(1(1(x1)))))))))) (34)
4(4(4(3(3(5(4(4(4(5(1(x1))))))))))) 0(3(0(3(2(1(2(2(3(1(x1)))))))))) (35)
4(5(1(2(0(1(0(5(4(2(2(x1))))))))))) 1(0(5(4(2(1(0(5(5(4(x1)))))))))) (36)
4(5(1(2(2(0(1(4(1(3(1(x1))))))))))) 2(3(3(4(1(0(0(1(5(2(x1)))))))))) (37)
4(5(4(5(5(0(4(3(3(2(4(x1))))))))))) 3(1(2(3(0(2(1(4(3(5(x1)))))))))) (38)
5(1(2(0(1(0(5(3(2(0(3(x1))))))))))) 5(1(3(1(0(2(2(1(4(2(x1)))))))))) (39)
5(2(1(1(0(1(4(4(1(1(1(x1))))))))))) 4(0(3(1(2(3(1(3(0(1(x1)))))))))) (40)
5(2(4(3(5(4(4(0(2(2(1(x1))))))))))) 5(3(4(5(0(1(4(5(0(3(x1)))))))))) (41)
0(0(2(5(1(2(4(1(4(4(4(5(x1)))))))))))) 4(1(0(4(0(3(2(4(3(0(x1)))))))))) (42)
0(2(5(3(3(2(3(5(0(0(3(2(x1)))))))))))) 5(0(2(0(1(3(1(2(5(1(x1)))))))))) (43)
1(4(4(1(5(5(5(4(3(5(5(3(x1)))))))))))) 4(5(5(1(1(4(1(2(4(4(x1)))))))))) (45)
2(0(5(2(2(3(0(1(0(5(4(3(x1)))))))))))) 5(3(4(0(1(3(2(1(5(2(x1)))))))))) (46)
2(1(1(1(5(4(1(5(0(1(4(2(x1)))))))))))) 4(4(0(5(0(4(3(1(2(5(x1)))))))))) (47)
2(2(2(1(5(5(5(0(5(4(5(3(x1)))))))))))) 4(0(3(5(0(5(2(4(2(5(x1)))))))))) (48)
2(5(3(0(0(5(1(2(5(5(2(1(x1)))))))))))) 0(0(0(2(0(2(3(2(1(4(x1)))))))))) (49)
2(5(3(4(2(3(1(2(5(3(2(0(x1)))))))))))) 0(1(2(5(4(1(0(0(0(4(x1)))))))))) (50)
3(3(3(4(2(0(4(1(5(0(1(5(x1)))))))))))) 4(0(0(3(1(3(3(4(3(0(x1)))))))))) (51)
5(1(3(3(4(1(2(2(5(1(5(0(x1)))))))))))) 4(2(0(3(0(1(4(0(4(4(x1)))))))))) (53)
5(2(2(3(5(4(3(3(3(0(0(3(x1)))))))))))) 4(0(5(3(5(0(0(4(0(4(x1)))))))))) (54)
5(2(3(0(3(5(4(3(0(1(0(3(x1)))))))))))) 5(0(4(5(5(2(2(0(1(4(x1)))))))))) (55)
5(3(3(2(2(3(0(2(0(0(1(2(x1)))))))))))) 4(4(2(4(0(3(2(1(1(3(x1)))))))))) (56)
5(3(5(0(4(2(0(0(0(4(3(2(x1)))))))))))) 0(3(4(5(4(2(3(2(5(0(x1)))))))))) (57)
5(5(5(1(0(0(3(5(5(3(4(1(x1)))))))))))) 1(3(2(0(2(2(2(5(2(2(x1)))))))))) (58)
4(3(5(2(2(3(5(3(3(3(3(5(0(x1))))))))))))) 3(4(4(2(2(2(0(0(1(0(x1)))))))))) (63)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 270 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 1620 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 +
4
[51(x1)] = x1 +
0
[52(x1)] = x1 +
3
[53(x1)] = x1 +
16
[54(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[41(x1)] = x1 +
4
[42(x1)] = x1 +
3
[43(x1)] = x1 +
1
[44(x1)] = x1 +
0
[45(x1)] = x1 +
16
[30(x1)] = x1 +
1
[31(x1)] = x1 +
1
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
3
[35(x1)] = x1 +
3
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
1
[23(x1)] = x1 +
0
[24(x1)] = x1 +
4
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
3
[14(x1)] = x1 +
4
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
3
[02(x1)] = x1 +
3
[03(x1)] = x1 +
4
[04(x1)] = x1 +
0
[05(x1)] = x1 +
16
all of the following rules can be deleted.

There are 1548 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(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1986)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1987)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1988)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1989)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1990)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1991)
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1992)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1993)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1994)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1995)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1996)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1997)
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (1998)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (1999)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (2000)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (2001)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (2002)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (2003)
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) (2004)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) (2005)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) (2006)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) (2007)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) (2008)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) (2009)
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) (2010)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) (2011)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) (2012)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) (2013)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) (2014)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) (2015)
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) (2016)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) (2017)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) (2018)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) (2019)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) (2020)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) (2021)
35(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 35(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) (2022)
34(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 34(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) (2023)
33(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 33(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) (2024)
32(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 32(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) (2025)
31(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 31(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) (2026)
30(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 30(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) (2027)
35(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 35(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) (2028)
34(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 34(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) (2029)
33(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 33(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) (2030)
32(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 32(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) (2031)
31(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 31(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) (2032)
30(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 30(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) (2033)
35(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 35(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) (2034)
34(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 34(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) (2035)
33(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 33(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) (2036)
32(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 32(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) (2037)
31(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 31(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) (2038)
30(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 30(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) (2039)
35(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 35(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) (2040)
34(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 34(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) (2041)
33(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 33(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) (2042)
32(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 32(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) (2043)
31(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 31(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) (2044)
30(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 30(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) (2045)
35(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 35(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) (2046)
34(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 34(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) (2047)
33(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 33(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) (2048)
32(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 32(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) (2049)
31(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 31(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) (2050)
30(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 30(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) (2051)
35(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 35(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) (2052)
34(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 34(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) (2053)
33(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 33(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) (2054)
32(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 32(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) (2055)
31(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 31(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) (2056)
30(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 30(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) (2057)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 144 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
[52(x1)] = x1 +
0
[53(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[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 +
1
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[03(x1)] = x1 +
1
[04(x1)] = x1 +
1
[05(x1)] = x1 +
1
[30#(x1)] = x1 +
1
[31#(x1)] = x1 +
1
[32#(x1)] = x1 +
1
[33#(x1)] = x1 +
1
[34#(x1)] = x1 +
1
[35#(x1)] = x1 +
0
[20#(x1)] = x1 +
1
[21#(x1)] = x1 +
1
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
1
[24#(x1)] = x1 +
1
[25#(x1)] = x1 +
0
together with the usable rules
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1986)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1987)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1988)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1989)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1990)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) (1991)
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1992)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1993)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1994)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1995)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1996)
20(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 20(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) (1997)
25(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 25(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (1998)
24(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 24(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (1999)
23(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 23(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (2000)
22(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 22(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (2001)
21(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 21(03(05(35(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) (2002)
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30(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 30(12(04(25(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) (2057)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
30#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1))))))))))))))))))))))))))) (2059)
30#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1))))))))))))))))))))))))))) (2061)
30#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1))))))))))))))))))))))))))) (2063)
30#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1))))))))))))))))))))))))))) (2065)
30#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1))))))))))))))))))))))))))) (2067)
30#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1))))))))))))))))))))))))))) (2069)
31#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1))))))))))))))))))))))))))) (2071)
31#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1))))))))))))))))))))))))))) (2073)
31#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1))))))))))))))))))))))))))) (2075)
31#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1))))))))))))))))))))))))))) (2077)
31#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1))))))))))))))))))))))))))) (2079)
31#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1))))))))))))))))))))))))))) (2081)
32#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1))))))))))))))))))))))))))) (2083)
32#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1))))))))))))))))))))))))))) (2085)
32#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1))))))))))))))))))))))))))) (2087)
32#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1))))))))))))))))))))))))))) (2089)
32#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1))))))))))))))))))))))))))) (2091)
32#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1))))))))))))))))))))))))))) (2093)
33#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1))))))))))))))))))))))))))) (2095)
33#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1))))))))))))))))))))))))))) (2097)
33#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1))))))))))))))))))))))))))) (2099)
33#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1))))))))))))))))))))))))))) (2101)
33#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1))))))))))))))))))))))))))) (2103)
33#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1))))))))))))))))))))))))))) (2105)
34#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1))))))))))))))))))))))))))) (2107)
34#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1))))))))))))))))))))))))))) (2109)
34#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1))))))))))))))))))))))))))) (2111)
34#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1))))))))))))))))))))))))))) (2113)
34#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1))))))))))))))))))))))))))) (2115)
34#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1))))))))))))))))))))))))))) (2117)
35#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(53(x1))))))))))))))))))))))))))) (2119)
35#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(43(x1))))))))))))))))))))))))))) (2121)
35#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(33(x1))))))))))))))))))))))))))) (2123)
35#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(23(x1))))))))))))))))))))))))))) (2125)
35#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(13(x1))))))))))))))))))))))))))) (2127)
35#(12(04(25(03(55(00(55(00(05(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1)))))))))))))))))))))))))))))) 25#(03(55(00(05(55(00(45(41(41(31(52(00(55(00(45(41(41(41(01(25(23(33(52(20(23(03(x1))))))))))))))))))))))))))) (2129)
20#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1))))))))))))))))))))))))) (2130)
20#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1))))))))))))))))))))))))) (2132)
20#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1))))))))))))))))))))))))) (2134)
20#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1))))))))))))))))))))))))) (2136)
20#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1))))))))))))))))))))))))) (2138)
20#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1))))))))))))))))))))))))) (2140)
21#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1))))))))))))))))))))))))) (2142)
21#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1))))))))))))))))))))))))) (2144)
21#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1))))))))))))))))))))))))) (2146)
21#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1))))))))))))))))))))))))) (2148)
21#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1))))))))))))))))))))))))) (2150)
21#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1))))))))))))))))))))))))) (2152)
22#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1))))))))))))))))))))))))) (2154)
22#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1))))))))))))))))))))))))) (2156)
22#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1))))))))))))))))))))))))) (2158)
22#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1))))))))))))))))))))))))) (2160)
22#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1))))))))))))))))))))))))) (2162)
22#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1))))))))))))))))))))))))) (2164)
23#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1))))))))))))))))))))))))) (2166)
23#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1))))))))))))))))))))))))) (2168)
23#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1))))))))))))))))))))))))) (2170)
23#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1))))))))))))))))))))))))) (2172)
23#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1))))))))))))))))))))))))) (2174)
23#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1))))))))))))))))))))))))) (2176)
24#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1))))))))))))))))))))))))) (2178)
24#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1))))))))))))))))))))))))) (2180)
24#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1))))))))))))))))))))))))) (2182)
24#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1))))))))))))))))))))))))) (2184)
24#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1))))))))))))))))))))))))) (2186)
24#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1))))))))))))))))))))))))) (2188)
25#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(51(x1))))))))))))))))))))))))) (2190)
25#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(41(x1))))))))))))))))))))))))) (2192)
25#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(31(x1))))))))))))))))))))))))) (2194)
25#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(21(x1))))))))))))))))))))))))) (2196)
25#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(11(x1))))))))))))))))))))))))) (2198)
25#(03(05(35(12(44(41(01(45(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1)))))))))))))))))))))))))))) 35#(12(44(01(45(41(21(13(24(03(55(50(50(30(52(40(21(23(23(03(15(34(52(40(01(x1))))))))))))))))))))))))) (2200)
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.