Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26910)

The rewrite relation of the following TRS is considered.

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

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 +
26
[51(x1)] = x1 +
21
[52(x1)] = x1 +
5
[53(x1)] = x1 +
0
[54(x1)] = x1 +
26
[55(x1)] = x1 +
21
[40(x1)] = x1 +
26
[41(x1)] = x1 +
5
[42(x1)] = x1 +
21
[43(x1)] = x1 +
0
[44(x1)] = x1 +
21
[45(x1)] = x1 +
22
[30(x1)] = x1 +
1
[31(x1)] = x1 +
1
[32(x1)] = x1 +
3
[33(x1)] = x1 +
21
[34(x1)] = x1 +
0
[35(x1)] = x1 +
5
[20(x1)] = x1 +
21
[21(x1)] = x1 +
0
[22(x1)] = x1 +
1
[23(x1)] = x1 +
5
[24(x1)] = x1 +
5
[25(x1)] = x1 +
26
[10(x1)] = x1 +
0
[11(x1)] = x1 +
26
[12(x1)] = x1 +
0
[13(x1)] = x1 +
22
[14(x1)] = x1 +
21
[15(x1)] = x1 +
21
[00(x1)] = x1 +
21
[01(x1)] = x1 +
0
[02(x1)] = x1 +
21
[03(x1)] = x1 +
0
[04(x1)] = x1 +
1
[05(x1)] = x1 +
0
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
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1986)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1987)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1988)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1989)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1990)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1991)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1992)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1993)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1994)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1995)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1996)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1997)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (1998)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (1999)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2000)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2001)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2002)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2003)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2004)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2005)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2006)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2007)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2008)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2009)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2010)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2011)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2012)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2013)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2014)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2015)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2016)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2017)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2018)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2019)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2020)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2021)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2022)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2023)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2024)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2025)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2026)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2027)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2028)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2029)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2030)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2031)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2032)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2033)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2034)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2035)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2036)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2037)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2038)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2039)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2040)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2041)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2042)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2043)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2044)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2045)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2046)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2047)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2048)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2049)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2050)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2051)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2052)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2053)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2054)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2055)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2056)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2057)

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
[54(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[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 +
1
[35(x1)] = x1 +
1
[20(x1)] = x1 +
0
[23(x1)] = x1 +
0
[24(x1)] = x1 +
0
[10(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
0
[14(x1)] = x1 +
1
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
1
[04(x1)] = x1 +
1
[40#(x1)] = x1 +
1
[41#(x1)] = x1 +
1
[42#(x1)] = x1 +
1
[43#(x1)] = x1 +
1
[44#(x1)] = x1 +
1
[45#(x1)] = x1 +
1
[30#(x1)] = x1 +
0
[31#(x1)] = x1 +
1
[32#(x1)] = x1 +
0
[33#(x1)] = x1 +
1
[34#(x1)] = x1 +
0
[35#(x1)] = x1 +
0
together with the usable rules
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1986)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1987)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1988)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1989)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1990)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(00(x1)))))))))))))))))) (1991)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1992)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1993)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1994)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1995)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1996)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(10(x1)))))))))))))))))) (1997)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (1998)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (1999)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2000)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2001)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2002)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(20(x1)))))))))))))))))) (2003)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2004)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2005)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2006)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2007)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2008)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(30(x1)))))))))))))))))) (2009)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2010)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2011)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2012)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2013)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2014)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(40(x1)))))))))))))))))) (2015)
45(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 45(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2016)
44(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 44(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2017)
43(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 43(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2018)
42(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 42(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2019)
41(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 41(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2020)
40(01(15(34(12(04(15(14(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) 40(01(15(34(12(14(04(15(24(53(10(04(55(10(04(15(54(50(x1)))))))))))))))))) (2021)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2022)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2023)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2024)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2025)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2026)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(04(x1)))))))))))))))))))))))) (2027)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2028)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2029)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2030)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2031)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2032)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(14(x1)))))))))))))))))))))))) (2033)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2034)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2035)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2036)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2037)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2038)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(24(x1)))))))))))))))))))))))) (2039)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2040)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2041)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2042)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2043)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2044)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(34(x1)))))))))))))))))))))))) (2045)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2046)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2047)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2048)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2049)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2050)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(44(x1)))))))))))))))))))))))) (2051)
35(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 35(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2052)
34(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 34(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2053)
33(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 33(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2054)
32(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 32(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2055)
31(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 31(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2056)
30(52(30(12(14(04(15(34(32(02(35(32(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) 30(52(30(12(14(04(15(34(32(32(02(35(02(35(02(15(34(52(50(10(24(23(13(54(x1)))))))))))))))))))))))) (2057)
(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.