Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/27034)

The rewrite relation of the following TRS is considered.

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

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 +
30
[3(x1)] = x1 +
30
[2(x1)] = x1 +
30
[1(x1)] = x1 +
25
[0(x1)] = x1 +
30
all of the following rules can be deleted.
0(0(5(4(3(4(0(4(0(2(4(x1))))))))))) 2(2(5(4(5(2(2(4(2(2(x1)))))))))) (8)
0(0(5(5(3(3(5(1(1(3(4(x1))))))))))) 1(1(2(2(5(0(4(2(4(4(x1)))))))))) (9)
0(1(4(1(0(3(3(1(3(1(1(x1))))))))))) 1(4(4(2(3(5(0(4(0(0(x1)))))))))) (10)
0(1(5(5(5(2(3(0(1(4(5(x1))))))))))) 1(3(0(5(0(5(0(4(2(4(x1)))))))))) (11)
0(2(3(2(3(1(0(0(4(2(2(x1))))))))))) 5(3(3(1(0(4(4(4(2(3(x1)))))))))) (12)
0(3(0(0(1(0(2(5(1(5(5(x1))))))))))) 0(0(5(2(0(1(3(4(0(2(x1)))))))))) (13)
0(3(3(3(1(4(3(4(3(0(4(x1))))))))))) 5(5(1(2(1(2(4(1(2(3(x1)))))))))) (14)
0(3(4(0(3(3(1(5(3(0(3(x1))))))))))) 0(5(3(0(5(3(1(4(2(3(x1)))))))))) (15)
0(3(5(3(5(4(3(5(4(1(3(x1))))))))))) 2(4(5(1(0(4(4(3(0(2(x1)))))))))) (16)
0(4(5(1(2(4(0(4(3(3(3(x1))))))))))) 0(4(1(4(3(2(4(5(4(3(x1)))))))))) (17)
0(5(0(5(3(3(5(5(4(3(2(x1))))))))))) 1(1(3(3(3(0(5(4(2(3(x1)))))))))) (18)
0(5(2(3(4(2(5(4(5(3(0(x1))))))))))) 4(3(2(1(2(5(4(1(4(2(x1)))))))))) (19)
0(5(3(3(2(5(1(4(1(1(0(x1))))))))))) 4(5(2(4(3(0(0(2(1(5(x1)))))))))) (20)
1(0(2(0(5(3(1(4(4(0(1(x1))))))))))) 0(3(2(5(1(5(5(3(3(4(x1)))))))))) (21)
1(3(3(1(0(0(3(0(5(4(4(x1))))))))))) 4(3(3(2(0(5(4(1(0(0(x1)))))))))) (22)
1(4(5(3(1(3(4(1(3(4(0(x1))))))))))) 2(5(4(4(1(1(3(0(2(0(x1)))))))))) (24)
1(5(5(4(2(5(1(2(0(0(3(x1))))))))))) 3(1(5(3(0(5(4(4(4(2(x1)))))))))) (25)
2(1(3(1(0(4(5(5(1(4(1(x1))))))))))) 3(0(4(5(4(2(2(1(4(0(x1)))))))))) (26)
2(2(4(2(5(2(2(3(3(0(3(x1))))))))))) 5(2(1(4(1(1(2(0(5(5(x1)))))))))) (27)
2(3(1(1(2(4(5(2(1(4(4(x1))))))))))) 3(0(1(2(1(5(4(5(5(2(x1)))))))))) (28)
2(4(0(0(5(4(2(3(5(0(5(x1))))))))))) 4(1(5(1(2(1(4(0(0(3(x1)))))))))) (29)
3(0(0(4(2(0(2(2(3(3(1(x1))))))))))) 0(0(1(0(3(4(5(0(2(5(x1)))))))))) (30)
3(0(2(5(5(3(2(5(1(4(1(x1))))))))))) 4(2(2(0(1(3(1(4(0(5(x1)))))))))) (31)
3(0(5(3(5(0(2(5(0(3(3(x1))))))))))) 4(2(1(5(0(4(0(0(5(0(x1)))))))))) (32)
3(1(4(3(2(1(3(4(4(4(3(x1))))))))))) 0(3(0(1(2(4(1(0(0(3(x1)))))))))) (33)
3(4(1(1(5(1(0(5(3(4(3(x1))))))))))) 1(5(4(3(5(5(0(3(1(1(x1)))))))))) (34)
3(5(0(4(3(2(0(0(2(3(4(x1))))))))))) 3(2(0(2(5(4(4(5(4(4(x1)))))))))) (35)
4(0(5(4(4(0(0(2(0(4(0(x1))))))))))) 2(2(0(5(5(3(3(1(2(5(x1)))))))))) (36)
4(1(5(4(5(2(0(1(5(0(0(x1))))))))))) 3(0(2(4(1(1(5(4(3(2(x1)))))))))) (37)
4(2(2(4(5(2(3(0(4(3(5(x1))))))))))) 1(4(2(1(5(3(0(0(4(5(x1)))))))))) (38)
4(3(0(3(4(1(5(3(0(3(5(x1))))))))))) 3(5(5(4(4(2(4(3(0(1(x1)))))))))) (39)
4(3(2(0(2(2(3(3(2(5(2(x1))))))))))) 0(3(0(2(2(3(5(5(0(1(x1)))))))))) (40)
4(5(3(3(1(3(1(5(4(1(2(x1))))))))))) 1(4(3(3(0(4(4(3(4(1(x1)))))))))) (42)
4(5(5(1(2(3(1(1(0(1(4(x1))))))))))) 2(5(4(0(3(0(4(1(3(2(x1)))))))))) (43)
5(0(3(0(4(1(2(3(3(3(5(x1))))))))))) 0(1(5(4(5(2(2(2(5(4(x1)))))))))) (44)
5(4(3(3(1(0(5(4(4(3(0(x1))))))))))) 4(1(2(4(1(3(4(3(5(4(x1)))))))))) (45)
0(2(2(4(3(0(4(3(1(2(3(4(x1)))))))))))) 4(4(5(5(0(3(1(5(2(1(x1)))))))))) (46)
0(5(2(2(3(3(4(4(4(2(2(1(x1)))))))))))) 3(1(1(5(4(5(0(5(4(5(x1)))))))))) (47)
1(2(4(1(2(5(3(0(4(4(2(2(x1)))))))))))) 5(5(3(0(5(4(2(2(1(4(x1)))))))))) (49)
1(4(5(3(0(2(5(1(0(3(4(0(x1)))))))))))) 1(2(1(0(4(1(1(1(2(5(x1)))))))))) (50)
2(1(4(3(2(5(0(2(3(5(3(2(x1)))))))))))) 5(1(5(1(0(3(3(1(3(5(x1)))))))))) (51)
2(3(0(1(4(3(3(4(5(2(0(0(x1)))))))))))) 2(5(5(0(5(3(0(2(2(1(x1)))))))))) (52)
3(1(4(1(5(1(4(3(3(2(0(2(x1)))))))))))) 4(4(4(2(3(1(4(3(5(0(x1)))))))))) (53)
3(3(2(3(0(5(2(5(1(3(2(1(x1)))))))))))) 1(0(5(3(1(3(4(1(1(5(x1)))))))))) (54)
3(4(0(4(1(3(0(4(0(2(2(2(x1)))))))))))) 2(2(3(1(1(5(2(5(4(0(x1)))))))))) (55)
3(4(2(4(4(0(5(0(4(2(0(0(x1)))))))))))) 0(3(3(5(1(4(5(4(5(5(x1)))))))))) (56)
4(1(4(4(4(1(0(2(3(4(4(4(x1)))))))))))) 0(5(0(5(2(3(4(0(4(1(x1)))))))))) (57)
4(5(5(0(1(3(2(1(4(0(2(3(x1)))))))))))) 4(1(5(0(5(0(0(1(0(1(x1)))))))))) (58)
5(0(5(0(4(4(2(4(0(4(1(4(x1)))))))))))) 1(2(0(0(5(2(1(2(5(0(x1)))))))))) (59)
5(4(4(5(2(3(4(2(2(5(5(2(x1)))))))))))) 2(3(1(1(3(5(2(0(2(4(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 252 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 1512 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[51(x1)] = x1 +
1
[52(x1)] = x1 +
0
[53(x1)] = x1 +
3
[54(x1)] = x1 +
3
[55(x1)] = x1 +
0
[40(x1)] = x1 +
3
[41(x1)] = x1 +
3
[42(x1)] = x1 +
3
[43(x1)] = x1 +
0
[44(x1)] = x1 +
25
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
9
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
9
[35(x1)] = x1 +
3
[20(x1)] = x1 +
9
[21(x1)] = x1 +
3
[22(x1)] = x1 +
9
[23(x1)] = x1 +
25
[24(x1)] = x1 +
51
[25(x1)] = x1 +
0
[10(x1)] = x1 +
1
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
46
[15(x1)] = x1 +
65
[00(x1)] = x1 +
3
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
all of the following rules can be deleted.

There are 1440 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
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1857)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1858)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1859)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1860)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1861)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1862)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1863)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1864)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1865)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1866)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1867)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1868)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1869)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1870)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1871)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1872)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1873)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1874)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1875)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1876)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1877)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1878)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1879)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1880)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1881)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1882)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1883)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1884)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1885)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1886)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1887)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1888)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1889)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1890)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1891)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1892)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1893)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1894)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1895)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1896)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1897)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1898)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1899)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1900)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1901)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1902)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1903)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1904)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1905)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1906)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1907)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1908)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1909)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1910)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1911)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1912)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1913)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1914)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1915)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1916)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1917)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1918)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1919)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1920)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1921)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1922)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1923)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1924)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1925)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1926)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1927)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1928)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 468 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 +
1
[51(x1)] = x1 +
0
[52(x1)] = x1 +
1
[53(x1)] = x1 +
1
[54(x1)] = x1 +
0
[55(x1)] = x1 +
1
[40(x1)] = x1 +
1
[41(x1)] = x1 +
1
[42(x1)] = x1 +
0
[43(x1)] = x1 +
1
[45(x1)] = x1 +
1
[30(x1)] = x1 +
1
[31(x1)] = x1 +
1
[32(x1)] = x1 +
1
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
1
[24(x1)] = x1 +
1
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
1
[12(x1)] = x1 +
0
[14(x1)] = x1 +
1
[00(x1)] = x1 +
1
[01(x1)] = x1 +
1
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[50#(x1)] = x1 +
0
[51#(x1)] = x1 +
1
[52#(x1)] = x1 +
0
[53#(x1)] = x1 +
0
[54#(x1)] = x1 +
1
[55#(x1)] = x1 +
0
[30#(x1)] = x1 +
0
[31#(x1)] = x1 +
0
[32#(x1)] = x1 +
0
[33#(x1)] = x1 +
1
[34#(x1)] = x1 +
1
[35#(x1)] = x1 +
1
together with the usable rules
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1857)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1858)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1859)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1860)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1861)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(00(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(00(x1))))))))))))))))) (1862)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1863)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1864)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1865)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1866)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1867)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(10(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(10(x1))))))))))))))))) (1868)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1869)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1870)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1871)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1872)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1873)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(20(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(20(x1))))))))))))))))) (1874)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1875)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1876)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1877)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1878)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1879)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(30(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(30(x1))))))))))))))))) (1880)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1881)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1882)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1883)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1884)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1885)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(40(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(40(x1))))))))))))))))) (1886)
55(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 55(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1887)
54(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 54(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1888)
53(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 53(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1889)
52(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 52(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1890)
51(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 51(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1891)
50(00(45(31(22(53(30(52(50(10(14(54(20(03(25(53(50(x1))))))))))))))))) 50(00(45(31(22(53(50(30(52(10(14(54(20(03(25(53(50(x1))))))))))))))))) (1892)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1893)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1894)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1895)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1896)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1897)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(02(x1))))))))))))))))))))))))) (1898)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1899)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1900)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1901)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1902)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1903)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(12(x1))))))))))))))))))))))))) (1904)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1905)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1906)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1907)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1908)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1909)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(22(x1))))))))))))))))))))))))) (1910)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1911)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1912)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1913)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1914)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1915)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(32(x1))))))))))))))))))))))))) (1916)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1917)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1918)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1919)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1920)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1921)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(42(x1))))))))))))))))))))))))) (1922)
35(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 35(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1923)
34(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 34(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1924)
33(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 33(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1925)
32(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 32(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1926)
31(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 31(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1927)
30(52(40(41(11(14(14(24(43(01(55(30(52(30(32(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) 30(52(40(41(11(14(14(24(43(01(55(30(32(52(30(52(50(50(40(41(21(43(01(35(52(x1))))))))))))))))))))))))) (1928)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 396 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.