Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26919)

The rewrite relation of the following TRS is considered.

0(1(2(3(4(0(x1)))))) 0(1(3(2(4(0(x1)))))) (1)
0(4(5(3(1(2(2(1(x1)))))))) 0(4(3(5(1(2(2(1(x1)))))))) (2)
1(0(5(4(2(4(1(0(x1)))))))) 1(0(5(2(4(4(1(0(x1)))))))) (3)
2(0(4(2(4(1(2(1(x1)))))))) 2(4(0(2(4(1(2(1(x1)))))))) (4)
2(5(5(5(3(2(5(3(x1)))))))) 2(5(2(5(5(3(5(3(x1)))))))) (5)
5(4(5(1(3(0(3(0(x1)))))))) 5(4(0(3(5(3(1(0(x1)))))))) (6)
0(0(4(3(2(2(3(5(1(x1))))))))) 4(0(3(0(2(2(3(5(1(x1))))))))) (7)
3(1(2(0(5(1(2(2(1(x1))))))))) 3(1(2(0(1(5(2(2(1(x1))))))))) (8)
3(5(0(5(5(1(5(4(2(5(x1)))))))))) 3(5(0(5(5(1(4(5(2(5(x1)))))))))) (9)
0(0(1(2(5(3(5(2(3(0(5(x1))))))))))) 0(0(2(1(5(3(5(2(3(0(5(x1))))))))))) (10)
0(1(1(5(0(2(4(3(5(3(1(x1))))))))))) 5(5(1(5(4(5(3(0(2(2(x1)))))))))) (11)
0(1(3(1(3(5(1(1(1(3(2(x1))))))))))) 1(0(1(5(4(1(5(2(4(0(x1)))))))))) (12)
0(1(4(1(2(1(2(4(4(1(2(x1))))))))))) 2(3(4(5(3(4(0(1(3(1(x1)))))))))) (13)
0(2(0(4(5(2(1(5(5(4(2(x1))))))))))) 1(3(0(5(5(5(2(0(3(1(x1)))))))))) (14)
0(2(4(2(3(2(4(2(2(1(5(x1))))))))))) 0(5(2(3(0(2(0(3(2(1(x1)))))))))) (15)
0(5(3(0(1(2(2(0(3(1(2(x1))))))))))) 0(2(3(1(4(0(0(5(5(3(x1)))))))))) (16)
1(0(0(5(5(2(1(3(4(4(3(x1))))))))))) 5(2(5(2(1(3(0(3(0(1(x1)))))))))) (17)
1(0(2(4(0(5(0(5(0(2(3(x1))))))))))) 4(3(3(0(4(1(2(4(5(1(x1)))))))))) (18)
1(0(3(4(5(5(3(5(0(2(0(x1))))))))))) 2(1(0(4(0(2(1(3(4(3(x1)))))))))) (19)
1(2(3(3(5(4(3(5(3(3(0(x1))))))))))) 5(1(2(2(1(2(3(5(0(5(x1)))))))))) (20)
1(2(4(5(1(5(0(3(1(2(2(x1))))))))))) 2(1(1(4(3(5(4(0(3(3(x1)))))))))) (21)
1(4(2(1(3(0(5(2(2(3(1(x1))))))))))) 5(1(5(1(1(0(4(4(1(3(x1)))))))))) (22)
1(4(2(5(3(0(4(3(3(3(0(x1))))))))))) 4(1(2(4(1(4(0(0(2(5(x1)))))))))) (23)
2(0(2(1(5(3(5(1(3(1(3(x1))))))))))) 1(2(0(3(3(2(0(5(0(4(x1)))))))))) (24)
2(0(5(0(5(4(1(1(2(3(3(x1))))))))))) 4(3(4(3(5(4(0(4(5(2(x1)))))))))) (25)
2(1(0(3(4(4(3(4(3(4(3(x1))))))))))) 2(5(3(0(4(2(2(5(1(3(x1)))))))))) (26)
2(1(2(5(1(1(0(3(1(1(2(x1))))))))))) 3(4(4(5(2(1(3(4(1(0(x1)))))))))) (27)
2(1(2(5(2(4(0(3(0(1(0(x1))))))))))) 0(2(4(4(0(2(1(4(4(0(x1)))))))))) (28)
2(1(5(0(5(0(0(1(4(4(5(x1))))))))))) 5(4(0(3(2(2(5(3(4(5(x1)))))))))) (29)
2(2(4(3(0(1(2(4(3(4(2(x1))))))))))) 3(5(2(2(2(4(0(1(3(1(x1)))))))))) (30)
2(2(4(5(3(1(3(0(5(1(0(x1))))))))))) 2(4(5(2(1(3(3(0(5(1(0(x1))))))))))) (31)
2(3(5(5(3(3(0(0(2(5(3(x1))))))))))) 3(5(4(1(1(1(5(5(2(5(x1)))))))))) (32)
3(0(1(0(2(4(1(3(4(3(3(x1))))))))))) 3(5(1(2(0(0(2(0(2(2(x1)))))))))) (33)
3(0(2(0(2(4(2(3(2(0(2(x1))))))))))) 3(1(3(3(4(1(2(2(3(2(x1)))))))))) (34)
3(0(3(0(2(3(1(2(3(1(5(x1))))))))))) 3(5(5(3(5(5(5(2(2(1(x1)))))))))) (35)
3(0(5(2(3(5(2(3(3(5(3(x1))))))))))) 5(4(1(0(0(0(2(3(2(3(x1)))))))))) (36)
3(1(1(0(1(5(2(5(3(1(1(x1))))))))))) 0(1(5(1(0(0(3(2(1(3(x1)))))))))) (37)
3(3(1(1(3(4(2(5(1(1(0(x1))))))))))) 4(3(4(0(1(4(2(4(4(5(x1)))))))))) (38)
3(3(4(1(5(3(5(4(2(4(0(x1))))))))))) 0(0(5(4(0(3(3(4(0(2(x1)))))))))) (39)
3(4(1(3(4(0(5(4(0(3(0(x1))))))))))) 1(4(2(5(3(1(2(3(0(3(x1)))))))))) (40)
3(5(1(5(5(1(3(3(2(1(4(x1))))))))))) 0(0(1(3(4(3(4(5(4(2(x1)))))))))) (41)
3(5(4(0(5(5(2(4(4(3(3(x1))))))))))) 3(5(4(0(5(2(5(4(4(3(3(x1))))))))))) (42)
4(1(0(3(4(5(3(0(0(5(0(x1))))))))))) 4(1(5(0(0(5(0(5(5(2(x1)))))))))) (43)
4(1(3(5(0(2(3(3(5(0(2(x1))))))))))) 0(5(3(4(0(5(3(5(1(3(x1)))))))))) (44)
4(1(5(2(4(4(1(5(4(2(4(x1))))))))))) 3(0(4(3(2(2(0(4(0(4(x1)))))))))) (45)
4(3(3(4(4(2(4(4(4(4(0(x1))))))))))) 0(5(0(1(5(4(3(4(3(0(x1)))))))))) (46)
4(5(1(1(3(1(2(0(0(5(2(x1))))))))))) 0(1(3(0(2(1(1(3(4(1(x1)))))))))) (47)
4(5(4(4(5(1(1(2(2(5(5(x1))))))))))) 0(3(5(0(0(5(2(1(5(5(x1)))))))))) (48)
5(0(0(4(3(1(3(5(1(5(1(x1))))))))))) 3(4(1(3(3(4(1(5(4(4(x1)))))))))) (49)
5(0(5(0(2(5(5(0(5(0(2(x1))))))))))) 1(5(4(5(1(2(5(4(0(4(x1)))))))))) (50)
5(3(3(2(4(5(2(0(1(3(2(x1))))))))))) 1(1(1(3(0(0(2(1(0(5(x1)))))))))) (51)
5(4(1(5(1(3(1(0(4(0(2(x1))))))))))) 5(5(1(2(1(4(4(0(2(4(x1)))))))))) (52)
5(4(4(3(2(4(5(4(0(5(3(x1))))))))))) 2(4(5(5(2(0(3(4(1(5(x1)))))))))) (53)
5(5(4(5(2(4(3(3(5(2(2(x1))))))))))) 0(5(3(5(3(4(4(0(0(2(x1)))))))))) (54)
2(1(5(1(3(2(1(0(1(3(3(4(x1)))))))))))) 0(1(3(3(0(1(0(0(2(5(x1)))))))))) (55)
3(1(0(5(0(0(1(2(5(5(4(2(x1)))))))))))) 3(5(0(2(0(1(5(1(5(0(4(2(x1)))))))))))) (56)
3(2(1(0(1(5(0(3(2(5(0(0(x1)))))))))))) 4(1(0(4(4(5(3(0(0(2(x1)))))))))) (57)
4(1(3(5(3(2(2(2(5(1(0(5(x1)))))))))))) 0(0(1(5(4(0(0(1(5(1(x1)))))))))) (58)
4(2(1(2(5(5(1(3(3(5(4(3(x1)))))))))))) 4(1(5(2(5(2(3(1(5(3(4(3(x1)))))))))))) (59)
4(2(1(4(4(2(5(1(5(2(5(4(x1)))))))))))) 4(2(0(1(1(4(3(2(4(1(x1)))))))))) (60)
5(0(3(4(4(3(4(5(2(2(3(5(x1)))))))))))) 2(5(0(4(0(3(1(1(5(2(x1)))))))))) (61)
5(0(5(3(2(2(5(4(3(3(0(4(x1)))))))))))) 0(3(2(5(2(0(5(3(0(5(x1)))))))))) (62)
5(4(0(0(1(5(0(3(1(0(1(3(x1)))))))))))) 1(3(1(4(3(3(0(3(0(5(x1)))))))))) (63)
1(2(5(4(0(0(5(3(1(0(1(2(4(x1))))))))))))) 1(2(5(4(0(5(0(3(1(0(1(2(4(x1))))))))))))) (64)
2(4(5(3(3(2(3(2(3(3(5(5(4(x1))))))))))))) 4(2(3(3(1(0(1(0(4(0(x1)))))))))) (65)
3(2(0(5(1(0(0(3(5(0(3(4(4(x1))))))))))))) 3(2(0(1(5(0(0(3(5(0(3(4(4(x1))))))))))))) (66)
3(3(2(2(5(1(4(3(4(2(1(5(1(x1))))))))))))) 3(3(2(2(5(4(1(3(4(2(5(1(1(x1))))))))))))) (67)
3(3(4(1(2(2(2(4(1(1(2(0(3(x1))))))))))))) 3(2(1(2(4(4(1(3(0(2(1(3(2(x1))))))))))))) (68)
2(5(0(3(2(1(0(1(2(0(0(1(5(4(3(1(x1)))))))))))))))) 2(5(0(0(3(2(1(2(0(5(1(4(0(1(3(1(x1)))))))))))))))) (69)
3(2(1(1(5(0(5(1(0(1(2(0(3(5(4(2(x1)))))))))))))))) 3(2(1(5(1(1(0(5(0(2(1(3(0(4(5(2(x1)))))))))))))))) (70)
1(2(1(4(4(2(0(0(4(1(5(4(3(5(4(3(5(0(x1)))))))))))))))))) 1(2(1(4(4(2(1(0(0(5(4(4(4(5(3(3(5(0(x1)))))))))))))))))) (71)
2(5(2(2(0(2(2(2(5(0(3(0(5(5(0(5(3(3(x1)))))))))))))))))) 2(5(2(2(0(2(2(2(5(0(3(0(5(0(5(5(3(3(x1)))))))))))))))))) (72)
4(2(2(0(2(0(5(0(4(3(4(0(2(1(3(2(3(1(3(x1))))))))))))))))))) 4(2(2(0(2(0(5(0(4(3(4(0(2(1(3(3(2(1(3(x1))))))))))))))))))) (73)
4(3(5(3(4(0(5(1(3(5(1(2(5(5(2(4(3(0(1(x1))))))))))))))))))) 4(3(5(3(4(0(5(1(3(5(2(1(5(5(2(4(3(0(1(x1))))))))))))))))))) (74)
2(0(0(4(4(5(3(5(4(1(1(0(3(4(2(1(3(4(2(0(x1)))))))))))))))))))) 2(0(0(4(4(5(3(5(4(1(0(1(3(4(2(1(3(4(2(0(x1)))))))))))))))))))) (75)
2(0(5(3(4(4(4(3(1(0(4(1(2(4(0(0(4(0(5(3(1(x1))))))))))))))))))))) 2(0(5(3(4(4(4(1(3(0(4(1(2(4(0(0(4(0(5(3(1(x1))))))))))))))))))))) (76)
2(5(5(2(2(0(1(5(1(0(5(2(4(1(1(2(2(2(4(3(4(x1))))))))))))))))))))) 2(5(5(2(2(0(1(5(0(1(5(2(4(1(1(2(2(2(4(3(4(x1))))))))))))))))))))) (77)
1(2(1(4(1(2(3(5(4(0(2(2(1(1(1(1(1(1(1(5(2(4(x1)))))))))))))))))))))) 1(2(1(4(2(1(3(5(4(0(2(2(1(1(1(1(1(1(1(5(2(4(x1)))))))))))))))))))))) (78)
4(1(1(2(4(2(1(1(1(1(1(3(0(1(5(2(2(3(0(5(0(2(x1)))))))))))))))))))))) 4(1(1(4(2(2(1(1(1(1(1(3(0(1(5(2(2(3(0(5(0(2(x1)))))))))))))))))))))) (79)
1(0(0(4(3(5(3(1(0(4(2(4(3(4(5(3(1(0(0(5(4(0(2(3(x1)))))))))))))))))))))))) 1(0(0(4(3(5(3(1(0(4(2(4(3(5(4(3(1(0(0(5(4(0(2(3(x1)))))))))))))))))))))))) (80)
3(5(4(3(2(4(0(4(0(2(1(2(1(4(4(2(0(4(1(1(3(4(2(3(x1)))))))))))))))))))))))) 3(5(4(3(2(4(4(0(0(2(2(1(1(4(4(4(2(1(1(0(4(2(3(3(x1)))))))))))))))))))))))) (81)
3(5(5(2(1(2(0(0(5(2(0(1(1(2(0(0(5(3(4(4(5(4(3(5(x1)))))))))))))))))))))))) 3(5(5(2(1(2(0(0(5(2(0(1(1(2(0(5(0(3(4(4(5(4(3(5(x1)))))))))))))))))))))))) (82)
5(2(5(4(5(1(4(0(5(0(2(2(5(4(2(1(4(3(1(0(3(3(5(1(x1)))))))))))))))))))))))) 5(2(5(4(5(1(4(0(5(0(2(2(5(4(2(1(4(3(1(3(0(3(5(1(x1)))))))))))))))))))))))) (83)
3(2(4(5(3(2(4(2(5(5(4(4(2(2(3(5(0(5(0(4(2(2(0(5(3(x1))))))))))))))))))))))))) 3(2(4(5(3(2(2(4(5(5(4(4(2(2(3(5(0(5(0(4(2(2(0(5(3(x1))))))))))))))))))))))))) (84)
1(3(4(2(2(3(1(3(3(5(1(5(3(0(3(3(1(4(1(3(5(1(0(1(1(3(x1)))))))))))))))))))))))))) 1(2(5(3(2(3(3(1(4(1(4(1(1(5(3(3(0(1(1(3(1(3(3(5(0(3(x1)))))))))))))))))))))))))) (85)
5(0(0(4(5(4(2(3(5(0(0(0(3(1(3(0(5(2(5(3(3(3(3(1(5(3(x1)))))))))))))))))))))))))) 5(0(0(4(5(4(2(3(5(0(0(0(3(1(3(0(2(5(5(3(3(3(3(1(5(3(x1)))))))))))))))))))))))))) (86)
0(2(4(1(1(1(2(5(4(2(3(4(1(1(1(3(3(5(1(0(4(1(0(3(4(1(2(x1))))))))))))))))))))))))))) 0(2(4(1(1(1(2(5(4(3(2(4(1(1(1(3(3(5(1(0(4(1(0(3(4(1(2(x1))))))))))))))))))))))))))) (87)
1(5(5(0(0(2(2(2(1(2(1(4(1(3(3(1(0(3(2(1(5(1(3(1(2(4(0(1(x1)))))))))))))))))))))))))))) 1(5(5(0(0(2(2(2(1(2(1(4(1(3(3(1(0(3(2(1(5(1(3(2(1(4(0(1(x1)))))))))))))))))))))))))))) (88)
4(0(2(1(4(2(3(2(5(5(4(2(0(5(5(3(4(1(3(1(1(1(4(3(1(5(3(5(x1)))))))))))))))))))))))))))) 4(0(2(1(4(2(3(2(5(5(4(2(0(5(5(3(4(1(3(1(1(1(3(4(1(5(3(5(x1)))))))))))))))))))))))))))) (89)
4(3(3(5(1(2(2(4(4(1(4(5(5(0(0(2(1(5(4(4(2(0(4(4(2(3(5(2(x1)))))))))))))))))))))))))))) 4(3(3(5(1(2(2(4(4(4(1(5(5(0(0(2(1(5(4(4(2(0(4(4(2(3(5(2(x1)))))))))))))))))))))))))))) (90)
3(3(1(4(3(1(5(1(4(2(0(5(5(5(3(3(4(0(0(0(2(2(3(4(3(1(2(3(3(x1))))))))))))))))))))))))))))) 3(3(1(4(3(1(5(1(4(0(2(5(5(5(3(3(4(0(0(0(2(2(3(4(3(1(2(3(3(x1))))))))))))))))))))))))))))) (91)
0(2(3(2(0(0(3(3(4(0(3(0(5(0(4(1(5(2(3(5(3(5(3(3(0(1(2(2(4(2(x1)))))))))))))))))))))))))))))) 0(2(3(2(0(0(3(3(4(0(3(0(5(0(4(1(5(2(3(5(3(3(5(3(0(1(2(2(4(2(x1)))))))))))))))))))))))))))))) (92)
0(5(4(0(2(3(0(5(3(2(1(5(5(4(4(1(0(1(2(1(5(4(3(0(1(2(2(0(3(3(x1)))))))))))))))))))))))))))))) 0(5(4(0(2(3(0(5(3(2(1(5(5(4(4(1(0(1(2(1(5(4(3(1(0(2(2(0(3(3(x1)))))))))))))))))))))))))))))) (93)
1(0(0(0(4(3(1(4(4(3(3(1(0(5(4(4(1(2(3(4(3(3(4(0(0(5(4(2(1(4(x1)))))))))))))))))))))))))))))) 1(0(0(0(4(3(1(4(4(3(3(1(0(5(4(4(1(2(3(4(3(3(4(0(5(0(4(2(1(4(x1)))))))))))))))))))))))))))))) (94)
3(1(1(5(0(5(0(5(0(5(2(5(1(2(1(2(0(5(2(4(5(5(1(2(4(4(2(2(2(5(x1)))))))))))))))))))))))))))))) 3(1(1(5(0(5(0(5(0(5(2(5(1(2(1(0(2(5(2(4(5(5(1(2(4(4(2(2(2(5(x1)))))))))))))))))))))))))))))) (95)
3(5(2(5(4(2(2(2(5(0(4(5(0(1(0(4(2(2(2(3(5(0(0(2(0(1(1(0(5(3(x1)))))))))))))))))))))))))))))) 3(5(2(5(4(2(2(2(5(0(5(4(0(1(0(4(2(2(2(3(5(0(0(2(0(1(1(0(5(3(x1)))))))))))))))))))))))))))))) (96)
4(4(1(3(3(2(1(1(4(5(0(2(2(1(5(4(5(5(0(4(3(4(0(1(2(4(0(1(0(5(x1)))))))))))))))))))))))))))))) 4(4(1(3(3(2(1(1(5(4(0(2(2(1(5(4(5(5(0(4(3(4(0(1(2(4(0(1(0(5(x1)))))))))))))))))))))))))))))) (97)

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 +
19
[4(x1)] = x1 +
18
[3(x1)] = x1 +
18
[2(x1)] = x1 +
19
[1(x1)] = x1 +
18
[0(x1)] = x1 +
13
all of the following rules can be deleted.
0(1(1(5(0(2(4(3(5(3(1(x1))))))))))) 5(5(1(5(4(5(3(0(2(2(x1)))))))))) (11)
0(1(3(1(3(5(1(1(1(3(2(x1))))))))))) 1(0(1(5(4(1(5(2(4(0(x1)))))))))) (12)
0(1(4(1(2(1(2(4(4(1(2(x1))))))))))) 2(3(4(5(3(4(0(1(3(1(x1)))))))))) (13)
0(2(0(4(5(2(1(5(5(4(2(x1))))))))))) 1(3(0(5(5(5(2(0(3(1(x1)))))))))) (14)
0(2(4(2(3(2(4(2(2(1(5(x1))))))))))) 0(5(2(3(0(2(0(3(2(1(x1)))))))))) (15)
0(5(3(0(1(2(2(0(3(1(2(x1))))))))))) 0(2(3(1(4(0(0(5(5(3(x1)))))))))) (16)
1(0(0(5(5(2(1(3(4(4(3(x1))))))))))) 5(2(5(2(1(3(0(3(0(1(x1)))))))))) (17)
1(0(2(4(0(5(0(5(0(2(3(x1))))))))))) 4(3(3(0(4(1(2(4(5(1(x1)))))))))) (18)
1(0(3(4(5(5(3(5(0(2(0(x1))))))))))) 2(1(0(4(0(2(1(3(4(3(x1)))))))))) (19)
1(2(3(3(5(4(3(5(3(3(0(x1))))))))))) 5(1(2(2(1(2(3(5(0(5(x1)))))))))) (20)
1(2(4(5(1(5(0(3(1(2(2(x1))))))))))) 2(1(1(4(3(5(4(0(3(3(x1)))))))))) (21)
1(4(2(1(3(0(5(2(2(3(1(x1))))))))))) 5(1(5(1(1(0(4(4(1(3(x1)))))))))) (22)
1(4(2(5(3(0(4(3(3(3(0(x1))))))))))) 4(1(2(4(1(4(0(0(2(5(x1)))))))))) (23)
2(0(2(1(5(3(5(1(3(1(3(x1))))))))))) 1(2(0(3(3(2(0(5(0(4(x1)))))))))) (24)
2(0(5(0(5(4(1(1(2(3(3(x1))))))))))) 4(3(4(3(5(4(0(4(5(2(x1)))))))))) (25)
2(1(0(3(4(4(3(4(3(4(3(x1))))))))))) 2(5(3(0(4(2(2(5(1(3(x1)))))))))) (26)
2(1(2(5(1(1(0(3(1(1(2(x1))))))))))) 3(4(4(5(2(1(3(4(1(0(x1)))))))))) (27)
2(1(2(5(2(4(0(3(0(1(0(x1))))))))))) 0(2(4(4(0(2(1(4(4(0(x1)))))))))) (28)
2(1(5(0(5(0(0(1(4(4(5(x1))))))))))) 5(4(0(3(2(2(5(3(4(5(x1)))))))))) (29)
2(2(4(3(0(1(2(4(3(4(2(x1))))))))))) 3(5(2(2(2(4(0(1(3(1(x1)))))))))) (30)
2(3(5(5(3(3(0(0(2(5(3(x1))))))))))) 3(5(4(1(1(1(5(5(2(5(x1)))))))))) (32)
3(0(1(0(2(4(1(3(4(3(3(x1))))))))))) 3(5(1(2(0(0(2(0(2(2(x1)))))))))) (33)
3(0(2(0(2(4(2(3(2(0(2(x1))))))))))) 3(1(3(3(4(1(2(2(3(2(x1)))))))))) (34)
3(0(3(0(2(3(1(2(3(1(5(x1))))))))))) 3(5(5(3(5(5(5(2(2(1(x1)))))))))) (35)
3(0(5(2(3(5(2(3(3(5(3(x1))))))))))) 5(4(1(0(0(0(2(3(2(3(x1)))))))))) (36)
3(1(1(0(1(5(2(5(3(1(1(x1))))))))))) 0(1(5(1(0(0(3(2(1(3(x1)))))))))) (37)
3(3(1(1(3(4(2(5(1(1(0(x1))))))))))) 4(3(4(0(1(4(2(4(4(5(x1)))))))))) (38)
3(3(4(1(5(3(5(4(2(4(0(x1))))))))))) 0(0(5(4(0(3(3(4(0(2(x1)))))))))) (39)
3(4(1(3(4(0(5(4(0(3(0(x1))))))))))) 1(4(2(5(3(1(2(3(0(3(x1)))))))))) (40)
3(5(1(5(5(1(3(3(2(1(4(x1))))))))))) 0(0(1(3(4(3(4(5(4(2(x1)))))))))) (41)
4(1(0(3(4(5(3(0(0(5(0(x1))))))))))) 4(1(5(0(0(5(0(5(5(2(x1)))))))))) (43)
4(1(3(5(0(2(3(3(5(0(2(x1))))))))))) 0(5(3(4(0(5(3(5(1(3(x1)))))))))) (44)
4(1(5(2(4(4(1(5(4(2(4(x1))))))))))) 3(0(4(3(2(2(0(4(0(4(x1)))))))))) (45)
4(3(3(4(4(2(4(4(4(4(0(x1))))))))))) 0(5(0(1(5(4(3(4(3(0(x1)))))))))) (46)
4(5(1(1(3(1(2(0(0(5(2(x1))))))))))) 0(1(3(0(2(1(1(3(4(1(x1)))))))))) (47)
4(5(4(4(5(1(1(2(2(5(5(x1))))))))))) 0(3(5(0(0(5(2(1(5(5(x1)))))))))) (48)
5(0(0(4(3(1(3(5(1(5(1(x1))))))))))) 3(4(1(3(3(4(1(5(4(4(x1)))))))))) (49)
5(0(5(0(2(5(5(0(5(0(2(x1))))))))))) 1(5(4(5(1(2(5(4(0(4(x1)))))))))) (50)
5(3(3(2(4(5(2(0(1(3(2(x1))))))))))) 1(1(1(3(0(0(2(1(0(5(x1)))))))))) (51)
5(4(1(5(1(3(1(0(4(0(2(x1))))))))))) 5(5(1(2(1(4(4(0(2(4(x1)))))))))) (52)
5(4(4(3(2(4(5(4(0(5(3(x1))))))))))) 2(4(5(5(2(0(3(4(1(5(x1)))))))))) (53)
5(5(4(5(2(4(3(3(5(2(2(x1))))))))))) 0(5(3(5(3(4(4(0(0(2(x1)))))))))) (54)
2(1(5(1(3(2(1(0(1(3(3(4(x1)))))))))))) 0(1(3(3(0(1(0(0(2(5(x1)))))))))) (55)
3(2(1(0(1(5(0(3(2(5(0(0(x1)))))))))))) 4(1(0(4(4(5(3(0(0(2(x1)))))))))) (57)
4(1(3(5(3(2(2(2(5(1(0(5(x1)))))))))))) 0(0(1(5(4(0(0(1(5(1(x1)))))))))) (58)
4(2(1(4(4(2(5(1(5(2(5(4(x1)))))))))))) 4(2(0(1(1(4(3(2(4(1(x1)))))))))) (60)
5(0(3(4(4(3(4(5(2(2(3(5(x1)))))))))))) 2(5(0(4(0(3(1(1(5(2(x1)))))))))) (61)
5(0(5(3(2(2(5(4(3(3(0(4(x1)))))))))))) 0(3(2(5(2(0(5(3(0(5(x1)))))))))) (62)
5(4(0(0(1(5(0(3(1(0(1(3(x1)))))))))))) 1(3(1(4(3(3(0(3(0(5(x1)))))))))) (63)
2(4(5(3(3(2(3(2(3(3(5(5(4(x1))))))))))))) 4(2(3(3(1(0(1(0(4(0(x1)))))))))) (65)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 282 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 1692 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 +
14
[51(x1)] = x1 +
0
[52(x1)] = x1 +
8
[53(x1)] = x1 +
2
[54(x1)] = x1 +
14
[55(x1)] = x1 +
0
[40(x1)] = x1 +
8
[41(x1)] = x1 +
0
[42(x1)] = x1 +
14
[43(x1)] = x1 +
16
[44(x1)] = x1 +
14
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
14
[32(x1)] = x1 +
14
[33(x1)] = x1 +
0
[34(x1)] = x1 +
15
[35(x1)] = x1 +
2
[20(x1)] = x1 +
7
[21(x1)] = x1 +
2
[22(x1)] = x1 +
14
[23(x1)] = x1 +
14
[24(x1)] = x1 +
2
[25(x1)] = x1 +
14
[10(x1)] = x1 +
2
[11(x1)] = x1 +
1
[12(x1)] = x1 +
0
[13(x1)] = x1 +
16
[14(x1)] = x1 +
7
[15(x1)] = x1 +
0
[00(x1)] = x1 +
14
[01(x1)] = x1 +
14
[02(x1)] = x1 +
14
[03(x1)] = x1 +
0
[04(x1)] = x1 +
16
[05(x1)] = x1 +
16
all of the following rules can be deleted.

There are 1620 ruless (increase limit for explicit display).

1.1.1.1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2072)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2073)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2074)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2075)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2076)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2077)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2078)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2079)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2080)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2081)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2082)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2083)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2084)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2085)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2086)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2087)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2088)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2089)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2090)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2091)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2092)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2093)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2094)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2095)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2096)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2097)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2098)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2099)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2100)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2101)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2102)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2103)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2104)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2105)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2106)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2107)
25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) (2108)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) (2109)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) (2110)
22(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) 22(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) (2111)
21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) (2112)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) (2113)
25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2114)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2115)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2116)
22(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 22(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2117)
21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2118)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2119)
25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2120)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2121)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2122)
22(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 22(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2123)
21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2124)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2125)
25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2126)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2127)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2128)
22(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 22(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2129)
21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2130)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2131)
25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2132)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2133)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2134)
22(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 22(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2135)
21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2136)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2137)
25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2138)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2139)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2140)
22(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 22(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2141)
21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2142)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2143)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

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

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[52(x1)] = x1 +
1
[53(x1)] = x1 +
0
[55(x1)] = x1 +
0
[43(x1)] = x1 +
1
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
1
[31(x1)] = x1 +
0
[32(x1)] = x1 +
1
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
1
[20(x1)] = x1 +
0
[21(x1)] = x1 +
1
[22(x1)] = x1 +
0
[23(x1)] = x1 +
1
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[13(x1)] = x1 +
1
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
1
[05(x1)] = x1 +
0
[30#(x1)] = x1 +
0
[31#(x1)] = x1 +
1
[32#(x1)] = x1 +
0
[33#(x1)] = x1 +
1
[34#(x1)] = x1 +
1
[35#(x1)] = x1 +
0
[20#(x1)] = x1 +
1
[21#(x1)] = x1 +
0
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
0
[24#(x1)] = x1 +
1
[25#(x1)] = x1 +
1
together with the usable rules
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2072)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2073)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2074)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2075)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2076)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(03(x1))))))))))))))))))) (2077)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2078)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2079)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2080)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2081)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2082)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(13(x1))))))))))))))))))) (2083)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2084)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2085)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2086)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2087)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2088)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(23(x1))))))))))))))))))) (2089)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2090)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2091)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2092)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2093)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2094)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(33(x1))))))))))))))))))) (2095)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2096)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2097)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2098)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2099)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2100)
30(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) 30(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(43(x1))))))))))))))))))) (2101)
35(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 35(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2102)
34(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 34(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2103)
33(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 33(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2104)
32(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 32(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2105)
31(32(52(00(55(50(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) 31(32(52(50(00(55(00(35(02(55(20(23(23(03(25(23(53(20(53(x1))))))))))))))))))) (2106)
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21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(05(x1))))))))))))))))))))))))))))))) (2112)
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25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2114)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2115)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2116)
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20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(15(x1))))))))))))))))))))))))))))))) (2119)
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24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2121)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2122)
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21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(25(x1))))))))))))))))))))))))))))))) (2124)
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24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2127)
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21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2130)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(35(x1))))))))))))))))))))))))))))))) (2131)
25(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 25(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2132)
24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(45(x1))))))))))))))))))))))))))))))) (2133)
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24(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 24(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2139)
23(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 23(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2140)
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21(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 21(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2142)
20(43(21(23(13(04(35(32(52(30(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) 20(43(21(23(13(04(35(52(30(32(52(30(22(53(10(44(01(55(00(35(02(45(31(32(02(05(25(33(22(03(55(x1))))))))))))))))))))))))))))))) (2143)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

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

and no rules could be deleted.

1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.