Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/27026)

The rewrite relation of the following TRS is considered.

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

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 +
17
[4(x1)] = x1 +
18
[3(x1)] = x1 +
18
[2(x1)] = x1 +
17
[1(x1)] = x1 +
22
[0(x1)] = x1 +
22
all of the following rules can be deleted.
0(3(1(1(1(0(3(4(1(3(x1)))))))))) 2(2(2(2(5(2(4(4(0(2(x1)))))))))) (3)
1(0(2(5(1(4(2(5(1(0(x1)))))))))) 2(4(2(1(0(3(2(2(5(4(x1)))))))))) (5)
1(1(4(5(1(0(0(5(2(1(x1)))))))))) 2(4(3(4(0(2(4(1(5(3(x1)))))))))) (6)
1(2(2(3(3(0(1(5(4(1(x1)))))))))) 1(0(2(4(3(1(2(4(2(3(x1)))))))))) (7)
1(2(4(5(1(1(0(1(0(2(x1)))))))))) 2(2(4(1(0(1(2(1(5(2(x1)))))))))) (9)
1(5(4(4(4(3(4(3(0(5(x1)))))))))) 2(5(1(2(4(2(4(0(2(5(x1)))))))))) (11)
4(0(0(4(5(1(1(5(1(5(x1)))))))))) 4(2(5(0(2(4(3(4(4(4(x1)))))))))) (13)
0(0(0(5(4(2(3(3(3(1(0(x1))))))))))) 5(2(5(0(0(3(3(2(3(5(x1)))))))))) (14)
0(0(1(0(0(3(2(0(4(1(5(x1))))))))))) 3(5(2(3(3(4(3(5(5(1(x1)))))))))) (15)
0(1(0(5(3(5(1(2(1(2(1(x1))))))))))) 1(3(5(0(5(1(5(5(2(0(x1)))))))))) (16)
0(1(3(4(5(2(1(3(5(0(4(x1))))))))))) 1(4(4(5(1(0(3(5(3(5(x1)))))))))) (17)
0(1(4(1(2(1(4(5(0(2(1(x1))))))))))) 2(4(3(4(1(0(5(3(3(4(x1)))))))))) (18)
0(2(2(2(0(2(3(1(5(1(1(x1))))))))))) 1(5(0(3(4(4(4(3(1(3(x1)))))))))) (19)
0(2(3(3(0(4(2(4(3(0(1(x1))))))))))) 3(4(5(0(2(0(4(0(1(5(x1)))))))))) (20)
0(5(1(2(1(1(2(1(2(1(0(x1))))))))))) 1(2(1(2(1(3(0(4(4(3(x1)))))))))) (21)
1(0(0(4(1(1(5(5(4(4(0(x1))))))))))) 4(0(4(0(2(5(1(0(3(5(x1)))))))))) (22)
1(2(5(5(1(4(5(5(1(0(1(x1))))))))))) 0(3(5(5(2(3(0(4(2(5(x1)))))))))) (25)
1(3(2(2(0(3(3(5(5(3(1(x1))))))))))) 2(3(5(3(1(2(5(1(5(4(x1)))))))))) (26)
1(4(3(5(5(1(0(4(3(2(0(x1))))))))))) 3(2(4(3(2(4(0(3(5(4(x1)))))))))) (27)
1(4(5(5(2(2(5(3(5(4(5(x1))))))))))) 5(0(2(0(5(2(2(2(0(0(x1)))))))))) (28)
2(1(5(2(1(0(3(5(0(1(5(x1))))))))))) 3(0(4(3(0(2(5(2(3(3(x1)))))))))) (29)
2(2(1(0(5(0(0(3(0(5(2(x1))))))))))) 1(0(2(2(2(4(5(3(4(4(x1)))))))))) (30)
2(3(4(1(3(2(4(1(4(0(0(x1))))))))))) 5(2(2(2(2(1(4(4(2(0(x1)))))))))) (31)
2(5(2(4(3(5(2(4(2(3(1(x1))))))))))) 1(5(4(2(1(1(0(5(4(2(x1)))))))))) (32)
3(0(2(1(4(5(3(2(4(5(0(x1))))))))))) 4(0(5(1(1(5(1(2(2(3(x1)))))))))) (33)
3(1(2(1(0(2(3(3(4(3(0(x1))))))))))) 3(0(0(2(4(5(4(4(5(3(x1)))))))))) (34)
3(1(4(5(2(3(5(5(4(2(2(x1))))))))))) 3(4(5(0(0(0(3(2(3(0(x1)))))))))) (35)
3(2(1(3(2(4(4(0(5(3(4(x1))))))))))) 0(3(5(5(4(4(4(4(0(1(x1)))))))))) (36)
3(3(3(0(5(3(2(4(5(3(2(x1))))))))))) 0(3(4(2(4(1(3(4(0(3(x1)))))))))) (37)
3(4(3(1(2(3(2(5(2(2(0(x1))))))))))) 1(1(4(0(1(5(5(5(1(4(x1)))))))))) (38)
3(5(1(2(1(5(1(0(0(5(2(x1))))))))))) 0(5(3(0(3(2(0(0(2(0(x1)))))))))) (39)
4(0(4(1(2(5(0(2(3(3(2(x1))))))))))) 3(1(4(5(2(1(5(3(0(1(x1)))))))))) (40)
4(1(4(2(3(2(1(4(3(4(0(x1))))))))))) 1(1(2(5(5(1(4(0(5(3(x1)))))))))) (41)
4(4(1(3(3(1(1(2(4(5(3(x1))))))))))) 1(2(0(5(4(0(1(4(1(1(x1)))))))))) (42)
4(5(0(3(4(4(3(2(0(4(3(x1))))))))))) 1(0(1(1(5(2(3(5(3(2(x1)))))))))) (43)
4(5(4(0(0(5(5(0(2(5(2(x1))))))))))) 3(4(5(0(2(1(5(0(1(4(x1)))))))))) (44)
4(5(4(0(2(0(2(1(0(1(3(x1))))))))))) 5(3(2(1(0(1(4(4(0(0(x1)))))))))) (45)
5(2(5(5(3(0(5(5(5(2(4(x1))))))))))) 0(4(3(3(2(3(1(1(5(2(x1)))))))))) (46)
5(3(2(1(2(5(1(5(2(5(1(x1))))))))))) 1(0(3(1(5(4(1(5(2(5(x1)))))))))) (47)
5(4(2(3(2(1(5(0(4(0(1(x1))))))))))) 1(4(0(2(1(3(0(0(2(5(x1)))))))))) (48)
5(4(4(5(5(0(2(5(0(1(4(x1))))))))))) 0(5(1(5(5(4(0(2(3(2(x1)))))))))) (49)
5(4(5(4(3(4(5(5(5(1(1(x1))))))))))) 0(2(0(3(1(3(0(4(5(4(x1)))))))))) (50)
0(0(2(4(5(5(2(3(4(1(0(2(x1)))))))))))) 5(1(5(0(3(2(5(1(4(3(x1)))))))))) (51)
0(5(2(1(0(5(0(4(4(0(3(4(x1)))))))))))) 1(1(0(5(1(1(3(3(2(3(x1)))))))))) (52)
0(5(4(2(4(5(2(1(4(3(4(4(x1)))))))))))) 3(4(2(0(1(3(5(3(2(3(x1)))))))))) (53)
1(4(5(5(0(4(5(1(5(5(2(1(x1)))))))))))) 3(1(3(0(3(4(4(1(0(1(x1)))))))))) (54)
2(4(5(4(3(2(1(4(0(2(4(0(x1)))))))))))) 3(3(5(0(1(0(4(3(0(3(x1)))))))))) (55)
3(1(0(0(2(0(5(5(4(0(3(4(x1)))))))))))) 1(5(4(4(3(0(0(3(3(5(x1)))))))))) (56)
4(2(3(2(3(2(2(0(5(3(3(4(x1)))))))))))) 5(2(0(0(0(3(1(5(3(0(x1)))))))))) (57)
4(4(4(1(1(1(4(1(5(4(4(4(4(x1))))))))))))) 3(0(3(5(4(0(4(1(5(0(x1)))))))))) (61)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 258 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 1548 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 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
0
[54(x1)] = x1 +
2
[55(x1)] = x1 +
2
[40(x1)] = x1 +
4
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
4
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
2
[31(x1)] = x1 +
0
[32(x1)] = x1 +
1
[33(x1)] = x1 +
7
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
7
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
4
[24(x1)] = x1 +
4
[25(x1)] = x1 +
4
[10(x1)] = x1 +
2
[11(x1)] = x1 +
1
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
1
[00(x1)] = x1 +
2
[01(x1)] = x1 +
0
[02(x1)] = x1 +
4
[03(x1)] = x1 +
2
[04(x1)] = x1 +
0
[05(x1)] = x1 +
4
all of the following rules can be deleted.

There are 1512 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
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1900)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1901)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1902)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1903)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1904)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1905)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1906)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1907)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1908)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1909)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1910)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1911)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1912)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1913)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1914)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1915)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1916)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1917)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1918)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1919)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1920)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1921)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1922)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1923)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1924)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1925)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1926)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1927)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1928)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1929)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1930)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1931)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1932)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1933)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1934)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1935)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 10#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1936)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1937)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 10#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1938)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1939)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 10#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1940)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1941)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 10#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1942)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1943)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 10#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1944)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1945)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 10#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1946)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1947)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 11#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1948)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1949)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 11#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1950)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1951)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 11#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1952)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1953)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 11#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1954)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1955)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 11#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1956)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1957)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 11#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1958)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1959)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1960)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1961)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1962)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1963)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1964)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1965)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1966)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1967)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1968)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1969)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1970)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1971)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1972)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 13#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1973)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1974)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 13#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1975)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1976)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 13#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1977)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1978)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 13#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1979)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1980)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 13#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1981)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1982)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 13#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1983)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1984)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 14#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1985)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1986)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 14#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1987)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1988)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 14#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1989)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1990)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 14#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1991)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1992)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 14#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1993)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1994)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 14#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1995)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1996)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 15#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1997)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1998)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 15#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1999)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (2000)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 15#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (2001)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (2002)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 15#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (2003)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (2004)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 15#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (2005)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (2006)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 15#(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (2007)

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
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[33(x1)] = x1 +
1
[34(x1)] = x1 +
0
[20(x1)] = x1 +
0
[23(x1)] = x1 +
0
[24(x1)] = x1 +
1
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[04(x1)] = x1 +
0
[10#(x1)] = x1 +
1
[11#(x1)] = x1 +
1
[12#(x1)] = x1 +
0
[13#(x1)] = x1 +
1
[14#(x1)] = x1 +
1
[15#(x1)] = x1 +
1
together with the usable rules
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1900)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1901)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1902)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1903)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1904)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) (1905)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1906)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1907)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1908)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1909)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1910)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) (1911)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1912)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1913)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1914)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1915)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1916)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) (1917)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1918)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1919)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1920)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1921)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1922)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) (1923)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1924)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1925)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1926)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1927)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1928)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) (1929)
15(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 15(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1930)
14(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 14(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1931)
13(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 13(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1932)
12(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1933)
11(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 11(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1934)
10(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 10(24(33(12(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) (1935)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1937)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1939)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1941)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1943)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1945)
10#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1947)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1949)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1951)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1953)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1955)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1957)
11#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1959)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1960)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1962)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1964)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1966)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1968)
12#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1970)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1972)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1974)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1976)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1978)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1980)
13#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1982)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1984)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1986)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (1988)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (1990)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (1992)
14#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (1994)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(54(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(54(x1))))))))))))))))))) (1996)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(44(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(44(x1))))))))))))))))))) (1998)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(34(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(34(x1))))))))))))))))))) (2000)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(24(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(24(x1))))))))))))))))))) (2002)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(14(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(14(x1))))))))))))))))))) (2004)
15#(24(33(12(44(01(55(20(23(53(00(55(50(50(10(04(45(01(55(10(14(04(x1)))))))))))))))))))))) 12#(44(01(55(20(23(53(50(00(55(50(10(04(45(01(55(10(14(04(x1))))))))))))))))))) (2006)
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.