Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26978)

The rewrite relation of the following TRS is considered.

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

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 +
5
[4(x1)] = x1 +
6
[3(x1)] = x1 +
5
[2(x1)] = x1 +
5
[1(x1)] = x1 +
5
[0(x1)] = x1 +
6
all of the following rules can be deleted.
0(3(0(0(1(0(4(4(0(2(x1)))))))))) 1(4(3(5(4(2(0(1(0(2(x1)))))))))) (4)
1(2(0(3(4(0(0(2(5(4(x1)))))))))) 1(2(1(5(4(5(5(1(1(1(x1)))))))))) (5)
2(5(4(0(4(5(0(0(0(2(x1)))))))))) 3(5(3(0(1(4(1(1(3(1(x1)))))))))) (7)
3(4(0(0(5(3(1(3(4(3(x1)))))))))) 3(4(3(1(0(4(3(5(1(3(x1)))))))))) (8)
0(0(3(2(0(5(5(3(1(3(3(x1))))))))))) 0(2(3(3(1(2(1(2(3(4(x1)))))))))) (9)
0(1(1(2(4(0(2(2(2(3(5(x1))))))))))) 0(4(5(5(1(5(2(4(5(1(x1)))))))))) (10)
0(1(3(1(0(4(0(1(2(0(4(x1))))))))))) 4(5(4(3(5(5(3(2(4(2(x1)))))))))) (11)
0(1(4(1(4(1(4(4(1(0(0(x1))))))))))) 3(0(3(5(2(4(5(1(0(0(x1)))))))))) (12)
0(1(5(2(4(4(1(3(2(1(1(x1))))))))))) 4(3(3(2(3(3(3(4(0(4(x1)))))))))) (13)
0(3(1(2(4(5(3(5(2(4(2(x1))))))))))) 0(4(3(0(2(4(2(1(4(3(x1)))))))))) (14)
0(3(3(2(3(4(5(3(1(1(4(x1))))))))))) 3(3(5(5(3(5(0(0(4(0(x1)))))))))) (15)
0(4(1(4(5(0(3(5(1(3(4(x1))))))))))) 1(2(1(4(2(1(4(0(3(4(x1)))))))))) (16)
0(4(4(1(1(0(2(4(1(3(5(x1))))))))))) 0(3(2(2(0(0(1(1(0(2(x1)))))))))) (17)
0(4(5(3(0(4(3(1(2(1(4(x1))))))))))) 3(0(4(5(2(5(2(4(3(5(x1)))))))))) (18)
0(4(5(3(3(5(4(4(2(2(4(x1))))))))))) 1(4(0(1(2(2(2(5(0(3(x1)))))))))) (19)
1(1(2(2(0(4(3(0(1(4(2(x1))))))))))) 0(2(5(2(3(0(5(2(5(3(x1)))))))))) (20)
1(2(2(4(5(2(3(0(2(2(2(x1))))))))))) 5(1(3(0(1(2(4(0(2(5(x1)))))))))) (21)
1(5(0(1(4(3(0(3(4(3(1(x1))))))))))) 4(3(5(0(5(0(3(4(0(4(x1)))))))))) (22)
2(1(1(5(5(5(3(4(3(3(0(x1))))))))))) 4(5(5(3(3(4(4(0(0(4(x1)))))))))) (23)
2(1(2(2(1(4(5(5(4(5(1(x1))))))))))) 0(4(0(4(4(5(3(1(4(5(x1)))))))))) (24)
2(2(1(5(4(4(2(0(2(2(0(x1))))))))))) 1(5(3(4(3(4(1(1(3(0(x1)))))))))) (25)
2(2(3(1(1(5(3(0(2(0(2(x1))))))))))) 5(5(4(4(3(4(2(0(5(0(x1)))))))))) (26)
2(2(4(0(5(2(1(3(3(2(5(x1))))))))))) 0(5(3(2(5(2(5(1(1(4(x1)))))))))) (27)
2(5(2(2(5(0(4(1(5(1(1(x1))))))))))) 1(1(2(3(2(1(4(3(4(2(x1)))))))))) (28)
2(5(2(3(0(4(5(2(1(4(3(x1))))))))))) 4(4(1(3(2(2(0(4(1(3(x1)))))))))) (29)
2(5(4(1(5(2(2(1(2(4(2(x1))))))))))) 0(2(2(5(4(5(1(3(4(2(x1)))))))))) (30)
2(5(5(1(5(2(2(2(4(4(3(x1))))))))))) 1(0(5(4(5(1(4(1(1(0(x1)))))))))) (31)
3(1(2(2(1(1(3(5(4(5(1(x1))))))))))) 1(4(1(0(3(5(4(2(2(4(x1)))))))))) (32)
3(3(3(3(2(1(4(0(3(3(1(x1))))))))))) 3(5(3(1(3(4(4(3(0(0(x1)))))))))) (33)
3(4(4(1(5(5(2(3(0(4(4(x1))))))))))) 1(5(5(1(4(3(4(1(3(1(x1)))))))))) (34)
3(5(5(1(1(3(2(4(2(1(2(x1))))))))))) 4(5(1(4(5(1(3(5(3(0(x1)))))))))) (35)
4(0(2(0(1(5(4(0(5(5(0(x1))))))))))) 0(4(2(4(0(0(2(0(4(4(x1)))))))))) (36)
4(0(4(3(3(2(0(1(0(5(2(x1))))))))))) 1(3(0(1(1(4(5(1(0(5(x1)))))))))) (37)
4(2(0(3(1(1(5(4(0(5(2(x1))))))))))) 2(1(3(5(0(4(0(2(5(5(x1)))))))))) (38)
4(2(2(5(2(0(4(3(5(1(4(x1))))))))))) 2(4(0(4(1(0(0(5(4(5(x1)))))))))) (39)
4(3(0(2(0(5(2(0(4(3(2(x1))))))))))) 5(2(1(1(1(4(5(5(5(0(x1)))))))))) (40)
4(4(1(3(1(1(3(4(1(1(2(x1))))))))))) 4(1(5(2(4(3(0(2(3(5(x1)))))))))) (41)
5(0(2(5(1(3(3(5(0(2(0(x1))))))))))) 4(0(4(5(1(1(4(0(1(4(x1)))))))))) (42)
5(1(5(3(3(4(1(0(0(3(5(x1))))))))))) 5(3(4(3(1(3(2(2(0(0(x1)))))))))) (43)
5(1(5(5(4(1(3(2(3(5(5(x1))))))))))) 1(1(0(5(1(0(0(2(5(0(x1)))))))))) (44)
5(2(3(3(0(2(0(2(2(5(0(x1))))))))))) 3(4(1(4(3(2(3(5(5(3(x1)))))))))) (45)
5(4(0(5(5(2(3(1(4(0(1(x1))))))))))) 5(1(3(2(3(3(0(1(0(0(x1)))))))))) (46)
5(4(3(0(0(2(5(0(1(2(3(x1))))))))))) 2(5(0(3(2(5(4(2(1(0(x1)))))))))) (47)
5(4(3(4(3(5(3(1(0(5(1(x1))))))))))) 3(4(4(2(4(0(3(0(4(2(x1)))))))))) (48)
5(5(0(2(2(0(3(3(5(3(5(x1))))))))))) 0(0(3(5(5(5(4(2(4(1(x1)))))))))) (49)
5(5(4(0(4(0(3(1(0(4(5(x1))))))))))) 1(2(1(4(1(1(0(0(3(2(x1)))))))))) (50)
0(3(3(5(0(5(2(4(4(3(1(2(x1)))))))))))) 1(3(2(5(2(0(0(0(1(0(x1)))))))))) (51)
0(3(4(2(3(1(4(2(2(2(4(2(x1)))))))))))) 2(2(2(0(1(4(5(2(1(3(x1)))))))))) (52)
2(3(3(2(0(4(1(1(2(3(4(1(x1)))))))))))) 5(2(5(1(5(2(0(5(4(5(x1)))))))))) (55)
3(3(5(1(0(1(1(2(1(4(1(3(x1)))))))))))) 5(3(0(5(1(0(2(5(2(4(x1)))))))))) (56)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 222 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 1332 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

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

There are 1296 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
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1642)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1643)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1644)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1645)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1646)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1647)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1648)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1649)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1650)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1651)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1652)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1653)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1654)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1655)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1656)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1657)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1658)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1659)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1660)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1661)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1662)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1663)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1664)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1665)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1666)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1667)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1668)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1669)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1670)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1671)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1672)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1673)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1674)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1675)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1676)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1677)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 20#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1678)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1679)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 20#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1680)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1681)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 20#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1682)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1683)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 20#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1684)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1685)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 20#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1686)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1687)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 20#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1688)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1689)
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21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1691)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 21#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1692)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1693)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 21#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1694)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1695)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 21#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1696)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1697)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 21#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1698)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1699)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 21#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1700)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1701)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 22#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1702)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1703)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 22#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1704)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1705)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 22#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1706)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1707)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 22#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1708)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1709)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 22#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1710)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1711)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 22#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1712)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1713)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 23#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1714)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1715)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 23#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1716)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1717)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 23#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1718)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1719)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 23#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1720)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1721)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 23#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1722)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1723)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 23#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1724)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1725)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 24#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1726)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1727)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 24#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1728)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1729)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 24#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1730)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1731)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 24#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1732)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1733)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 24#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1734)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1735)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 24#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1736)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1737)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1738)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1739)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1740)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1741)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1742)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1743)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1744)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1745)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1746)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1747)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1748)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1749)

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
[54(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[31(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
1
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
1
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
[20#(x1)] = x1 +
1
[21#(x1)] = x1 +
1
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
1
[24#(x1)] = x1 +
1
[25#(x1)] = x1 +
0
together with the usable rules
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1642)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1643)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1644)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1645)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1646)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) (1647)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1648)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1649)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1650)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1651)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1652)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) (1653)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1654)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1655)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1656)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1657)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1658)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) (1659)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1660)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1661)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1662)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1663)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1664)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) (1665)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1666)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1667)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1668)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1669)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1670)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) (1671)
25(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1672)
24(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 24(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1673)
23(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 23(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1674)
22(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 22(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1675)
21(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 21(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1676)
20(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 20(03(25(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) (1677)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1679)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1681)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1683)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1685)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1687)
20#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1689)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1691)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1693)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1695)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1697)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1699)
21#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1701)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1703)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1705)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1707)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1709)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1711)
22#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1713)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1715)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1717)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1719)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1721)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1723)
23#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1725)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1727)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1729)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1731)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1733)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1735)
24#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1737)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(51(x1)))))))))))))))))))))))) (1738)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(41(x1)))))))))))))))))))))))) (1740)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(31(x1)))))))))))))))))))))))) (1742)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(21(x1)))))))))))))))))))))))) (1744)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(11(x1)))))))))))))))))))))))) (1746)
25#(03(25(03(55(50(10(54(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))))) 25#(03(55(10(54(50(40(11(14(54(00(05(35(02(15(44(11(04(35(22(43(21(43(01(x1)))))))))))))))))))))))) (1748)
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.