Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26949)

The rewrite relation of the following TRS is considered.

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

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 +
2
[52(x1)] = x1 +
11
[53(x1)] = x1 +
11
[54(x1)] = x1 +
5
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[41(x1)] = x1 +
1
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
2
[45(x1)] = x1 +
0
[30(x1)] = x1 +
21
[31(x1)] = x1 +
0
[32(x1)] = x1 +
1
[33(x1)] = x1 +
5
[34(x1)] = x1 +
11
[35(x1)] = x1 +
2
[20(x1)] = x1 +
5
[21(x1)] = x1 +
11
[22(x1)] = x1 +
21
[23(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
5
[12(x1)] = x1 +
5
[13(x1)] = x1 +
2
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
5
[01(x1)] = x1 +
0
[02(x1)] = x1 +
5
[03(x1)] = x1 +
0
[04(x1)] = x1 +
11
[05(x1)] = x1 +
5
all of the following rules can be deleted.

There are 1476 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(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1857)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1858)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1859)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1860)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1861)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1862)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1863)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1864)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1865)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1866)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1867)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1868)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1869)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1870)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1871)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1872)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1873)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1874)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1875)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1876)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1877)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1878)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1879)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1880)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1881)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1882)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1883)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1884)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1885)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1886)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1887)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1888)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1889)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1890)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1891)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1892)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 50#(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1893)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1894)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 50#(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1895)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1896)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 50#(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1897)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1898)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 50#(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1899)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1900)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 50#(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1901)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1902)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 50#(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1903)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1904)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 51#(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1905)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1906)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 51#(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1907)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1908)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 51#(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1909)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1910)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 51#(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1911)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1912)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 51#(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1913)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1914)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 51#(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1915)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1916)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1917)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1918)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1919)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1920)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1921)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1922)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1923)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1924)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1925)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1926)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1927)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1928)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1929)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 53#(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1930)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1931)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 53#(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1932)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1933)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 53#(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1934)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1935)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 53#(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1936)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1937)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 53#(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1938)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1939)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 53#(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1940)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1941)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 54#(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1942)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1943)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 54#(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1944)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1945)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 54#(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1946)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1947)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 54#(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1948)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1949)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 54#(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1950)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1951)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 54#(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1952)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1953)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 55#(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1954)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1955)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 55#(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1956)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1957)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 55#(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1958)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1959)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 55#(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1960)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1961)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 55#(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1962)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1963)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 55#(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1964)

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[51(x1)] = x1 +
0
[52(x1)] = x1 +
1
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
1
[32(x1)] = x1 +
1
[34(x1)] = x1 +
0
[20(x1)] = x1 +
0
[10(x1)] = x1 +
0
[12(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[02(x1)] = x1 +
0
[04(x1)] = x1 +
0
[50#(x1)] = x1 +
1
[51#(x1)] = x1 +
1
[52#(x1)] = x1 +
0
[53#(x1)] = x1 +
1
[54#(x1)] = x1 +
1
[55#(x1)] = x1 +
1
together with the usable rules
55(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1857)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1858)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1859)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1860)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1861)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(00(x1))))))))))))))) (1862)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1863)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1864)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1865)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1866)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1867)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(10(x1))))))))))))))) (1868)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1869)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1870)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1871)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1872)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1873)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(20(x1))))))))))))))) (1874)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1875)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1876)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1877)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1878)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1879)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(30(x1))))))))))))))) (1880)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1881)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1882)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1883)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1884)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1885)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(40(x1))))))))))))))) (1886)
55(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 55(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1887)
54(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 54(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1888)
53(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 53(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1889)
52(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1890)
51(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 51(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1891)
50(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 50(30(32(52(30(12(04(15(14(34(02(45(51(50(50(x1))))))))))))))) (1892)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1894)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1896)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1898)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1900)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1902)
50#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1904)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1906)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1908)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1910)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1912)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1914)
51#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1916)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1918)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1920)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1922)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1924)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1926)
52#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1928)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1929)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1931)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1933)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1935)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1937)
53#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1939)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1941)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1943)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1945)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1947)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1949)
54#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1951)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(50(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(50(x1)))))))))))) (1953)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(40(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(40(x1)))))))))))) (1955)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(30(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(30(x1)))))))))))) (1957)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(20(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(20(x1)))))))))))) (1959)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(10(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(10(x1)))))))))))) (1961)
55#(30(32(52(30(12(14(04(15(34(02(45(51(50(00(x1))))))))))))))) 52#(30(12(04(15(14(34(02(45(51(50(00(x1)))))))))))) (1963)
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.