Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26976)

The rewrite relation of the following TRS is considered.

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

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 +
5
[0(x1)] = x1 +
4
all of the following rules can be deleted.
1(0(0(2(2(2(5(2(3(3(x1)))))))))) 0(1(2(3(0(0(5(5(4(3(x1)))))))))) (8)
1(2(2(5(1(1(2(4(2(0(x1)))))))))) 2(4(1(5(4(3(4(1(3(0(x1)))))))))) (9)
4(2(2(2(2(4(4(4(1(3(x1)))))))))) 4(5(5(0(3(5(0(2(5(1(x1)))))))))) (11)
0(0(0(4(5(5(2(4(5(1(3(x1))))))))))) 3(1(3(5(4(2(5(1(1(1(x1)))))))))) (13)
0(0(5(1(0(0(5(4(3(4(1(x1))))))))))) 2(1(4(0(1(5(4(3(4(2(x1)))))))))) (14)
0(1(5(2(0(5(3(3(0(2(2(x1))))))))))) 4(1(5(3(0(3(0(2(0(4(x1)))))))))) (15)
0(3(1(3(4(4(4(1(2(5(2(x1))))))))))) 1(4(3(2(2(1(1(1(3(4(x1)))))))))) (16)
0(3(1(4(0(1(2(0(3(5(0(x1))))))))))) 1(5(4(0(2(5(3(4(3(4(x1)))))))))) (17)
0(4(5(2(5(5(4(3(5(1(0(x1))))))))))) 5(3(4(5(5(3(3(5(4(4(x1)))))))))) (18)
1(0(0(2(2(3(5(0(2(0(4(x1))))))))))) 2(1(1(3(5(2(2(5(4(4(x1)))))))))) (19)
1(0(2(3(2(3(3(0(3(2(0(x1))))))))))) 3(2(2(3(5(5(1(4(0(1(x1)))))))))) (20)
1(1(2(5(1(4(2(5(5(2(4(x1))))))))))) 0(2(2(2(5(3(1(1(0(4(x1)))))))))) (21)
1(2(4(5(5(3(2(4(1(1(5(x1))))))))))) 3(4(1(5(3(1(1(4(0(3(x1)))))))))) (22)
1(3(0(1(5(5(3(3(5(3(3(x1))))))))))) 5(2(1(3(0(2(5(5(2(0(x1)))))))))) (23)
1(3(0(2(0(5(0(0(1(1(4(x1))))))))))) 5(2(4(0(0(5(3(0(3(0(x1)))))))))) (24)
1(3(4(2(0(5(2(0(4(4(4(x1))))))))))) 3(0(1(3(0(1(0(2(3(5(x1)))))))))) (25)
1(3(4(5(0(3(3(2(1(4(3(x1))))))))))) 4(5(1(0(3(3(4(2(3(4(x1)))))))))) (26)
1(4(2(0(1(5(4(5(4(3(1(x1))))))))))) 2(3(2(5(5(5(5(0(0(4(x1)))))))))) (27)
1(4(2(4(5(2(3(1(0(1(4(x1))))))))))) 4(0(1(0(3(4(4(1(1(0(x1)))))))))) (28)
1(4(4(1(0(4(2(5(0(3(2(x1))))))))))) 3(3(5(3(2(3(0(3(1(2(x1)))))))))) (29)
1(4(4(4(2(4(1(3(5(0(2(x1))))))))))) 3(0(5(2(4(1(2(0(2(5(x1)))))))))) (30)
1(5(2(4(2(0(0(1(0(5(0(x1))))))))))) 1(1(2(3(4(0(1(5(4(1(x1)))))))))) (31)
2(1(4(3(3(1(0(5(2(5(1(x1))))))))))) 1(3(4(5(5(4(0(0(2(1(x1)))))))))) (32)
2(5(3(5(3(4(5(0(0(0(2(x1))))))))))) 0(5(1(3(1(0(1(1(4(2(x1)))))))))) (33)
3(0(1(2(0(0(2(0(5(2(5(x1))))))))))) 0(4(1(3(4(5(3(1(0(4(x1)))))))))) (34)
3(1(0(4(1(1(3(3(2(3(4(x1))))))))))) 1(1(5(3(5(2(1(2(3(5(x1)))))))))) (35)
3(1(3(5(4(4(0(5(1(0(0(x1))))))))))) 4(3(5(1(2(2(0(1(2(5(x1)))))))))) (36)
3(1(5(1(5(0(5(1(3(4(2(x1))))))))))) 5(4(3(4(0(3(4(0(0(3(x1)))))))))) (37)
3(2(0(5(4(2(5(0(4(2(1(x1))))))))))) 3(2(3(5(2(5(5(5(1(4(x1)))))))))) (38)
3(2(2(3(2(0(3(0(2(1(4(x1))))))))))) 5(4(2(2(4(3(5(3(0(5(x1)))))))))) (39)
3(3(1(2(3(1(2(1(0(1(2(x1))))))))))) 0(3(0(4(0(2(5(1(3(5(x1)))))))))) (40)
3(4(0(3(3(5(5(1(4(5(3(x1))))))))))) 1(5(0(3(2(0(4(4(1(3(x1)))))))))) (41)
4(1(0(3(5(4(4(3(3(4(5(x1))))))))))) 5(3(0(0(1(4(5(5(2(0(x1)))))))))) (42)
4(1(4(0(0(4(4(5(3(0(0(x1))))))))))) 1(4(5(5(5(4(5(3(3(0(x1)))))))))) (43)
4(2(2(1(0(4(4(5(0(4(5(x1))))))))))) 3(5(5(2(0(4(5(2(5(5(x1)))))))))) (44)
4(3(5(5(0(1(0(1(1(0(1(x1))))))))))) 2(0(5(2(0(1(1(5(5(1(x1)))))))))) (45)
4(4(1(2(3(2(2(0(4(2(5(x1))))))))))) 0(4(1(4(2(2(4(5(3(5(x1)))))))))) (46)
4(4(2(0(1(5(5(2(0(0(5(x1))))))))))) 3(3(2(0(3(4(5(1(5(4(x1)))))))))) (47)
4(5(5(2(3(4(5(1(1(0(5(x1))))))))))) 0(3(0(1(2(3(3(4(2(3(x1)))))))))) (48)
5(0(0(5(1(3(4(3(5(1(3(x1))))))))))) 3(1(3(5(2(2(4(3(3(0(x1)))))))))) (49)
5(1(0(0(5(3(3(0(4(3(4(x1))))))))))) 3(0(5(2(0(0(1(1(1(5(x1)))))))))) (50)
5(1(4(0(5(5(2(3(5(0(0(x1))))))))))) 5(3(3(1(4(3(0(2(3(4(x1)))))))))) (51)
5(2(4(0(5(1(4(0(5(1(5(x1))))))))))) 4(3(3(4(4(4(4(5(0(1(x1)))))))))) (52)
5(3(0(0(0(0(3(2(5(2(1(x1))))))))))) 2(4(1(5(5(2(4(3(1(0(x1)))))))))) (53)
5(4(4(0(2(4(3(1(3(0(5(x1))))))))))) 4(2(5(3(3(5(3(0(4(0(x1)))))))))) (54)
0(0(1(5(3(5(2(4(0(5(3(4(x1)))))))))))) 1(2(5(0(1(2(1(3(4(4(x1)))))))))) (55)
1(0(0(3(4(1(0(4(1(2(0(4(x1)))))))))))) 3(0(0(0(2(2(2(2(3(0(x1)))))))))) (56)
5(2(0(4(5(0(5(5(1(0(1(0(x1)))))))))))) 1(1(4(4(3(1(2(2(4(2(x1)))))))))) (58)
5(3(0(5(0(4(1(0(4(4(1(1(x1)))))))))))) 2(1(5(0(2(0(3(2(3(3(x1)))))))))) (59)
5(3(1(2(5(0(5(3(3(4(5(3(x1)))))))))))) 2(4(4(2(2(4(2(0(3(2(x1)))))))))) (60)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 240 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 1440 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 +
3
[51(x1)] = x1 +
4
[52(x1)] = x1 +
3
[53(x1)] = x1 +
0
[54(x1)] = x1 +
4
[55(x1)] = x1 +
3
[40(x1)] = x1 +
3
[41(x1)] = x1 +
3
[42(x1)] = x1 +
0
[43(x1)] = x1 +
1
[44(x1)] = x1 +
5
[45(x1)] = x1 +
0
[30(x1)] = x1 +
4
[31(x1)] = x1 +
3
[32(x1)] = x1 +
4
[33(x1)] = x1 +
0
[34(x1)] = x1 +
3
[35(x1)] = x1 +
0
[20(x1)] = x1 +
1
[21(x1)] = x1 +
0
[22(x1)] = x1 +
3
[23(x1)] = x1 +
1
[24(x1)] = x1 +
0
[25(x1)] = x1 +
4
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
3
[13(x1)] = x1 +
3
[14(x1)] = x1 +
0
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
4
[03(x1)] = x1 +
3
[04(x1)] = x1 +
4
[05(x1)] = x1 +
3
all of the following rules can be deleted.

There are 1368 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
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1771)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1772)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1773)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1774)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1775)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1776)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1777)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1778)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1779)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1780)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1781)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1782)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1783)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1784)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1785)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1786)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1787)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1788)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1789)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1790)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1791)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1792)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1793)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1794)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) (1795)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) (1796)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) (1797)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) (1798)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) (1799)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(45(x1)))))))))))))))))))))))))))) (1800)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) (1801)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) (1802)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) (1803)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) (1804)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) (1805)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(55(x1)))))))))))))))))))))))))))) (1806)
35(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) 35(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) (1807)
34(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) 34(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) (1808)
33(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) 33(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) (1809)
32(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) 32(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) (1810)
31(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) 31(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) (1811)
30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(00(x1)))))))))))))))))))))))))))) (1812)
35(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) 35(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) (1813)
34(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) 34(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) (1814)
33(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) 33(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) (1815)
32(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) 32(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) (1816)
31(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) 31(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) (1817)
30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) (1818)
35(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) 35(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) (1819)
34(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) 34(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) (1820)
33(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) 33(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) (1821)
32(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) 32(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) (1822)
31(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) 31(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) (1823)
30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(20(x1)))))))))))))))))))))))))))) (1824)
35(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) 35(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) (1825)
34(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) 34(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) (1826)
33(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) 33(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) (1827)
32(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) 32(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) (1828)
31(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) 31(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) (1829)
30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(30(x1)))))))))))))))))))))))))))) (1830)
35(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) 35(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) (1831)
34(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) 34(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) (1832)
33(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) 33(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) (1833)
32(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) 32(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) (1834)
31(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) 31(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) (1835)
30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) (1836)
35(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 35(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1837)
34(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 34(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1838)
33(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 33(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1839)
32(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 32(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1840)
31(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 31(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1841)
30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1842)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 396 ruless (increase limit for explicit display).

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[51(x1)] = x1 +
0
[52(x1)] = x1 +
1
[53(x1)] = x1 +
1
[55(x1)] = x1 +
1
[40(x1)] = x1 +
1
[41(x1)] = x1 +
0
[42(x1)] = x1 +
1
[43(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
1
[31(x1)] = x1 +
1
[32(x1)] = x1 +
1
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
1
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
1
[23(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[05(x1)] = x1 +
1
[30#(x1)] = x1 +
0
[31#(x1)] = x1 +
0
[32#(x1)] = x1 +
0
[33#(x1)] = x1 +
1
[34#(x1)] = x1 +
1
[35#(x1)] = x1 +
0
[00#(x1)] = x1 +
1
[01#(x1)] = x1 +
0
[02#(x1)] = x1 +
1
[03#(x1)] = x1 +
1
[04#(x1)] = x1 +
1
[05#(x1)] = x1 +
0
together with the usable rules
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1771)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1772)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1773)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1774)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1775)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(05(x1)))))))))))))))))))))))))))) (1776)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1777)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1778)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1779)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1780)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1781)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(15(x1)))))))))))))))))))))))))))) (1782)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1783)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1784)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1785)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1786)
01(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 01(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1787)
00(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) 00(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(25(x1)))))))))))))))))))))))))))) (1788)
05(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 05(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1789)
04(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 04(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1790)
03(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 03(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1791)
02(35(52(40(01(35(22(43(21(23(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) 02(35(52(40(01(35(22(23(43(21(23(53(50(00(45(21(23(53(40(51(40(51(00(05(05(15(04(35(x1)))))))))))))))))))))))))))) (1792)
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30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(10(x1)))))))))))))))))))))))))))) (1818)
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30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(40(x1)))))))))))))))))))))))))))) (1836)
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31(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 31(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1841)
30(32(42(01(05(55(30(42(31(22(53(50(30(52(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) 30(32(42(01(05(55(30(42(31(22(53(30(52(50(00(45(41(11(34(52(00(35(12(04(05(25(53(50(x1)))))))))))))))))))))))))))) (1842)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 324 ruless (increase limit for explicit display).

and no rules could be deleted.

1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.