Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/25808)

The rewrite relation of the following TRS is considered.

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

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 +
37
[51(x1)] = x1 +
46
[52(x1)] = x1 +
0
[53(x1)] = x1 +
4
[54(x1)] = x1 +
37
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[41(x1)] = x1 +
41
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
37
[45(x1)] = x1 +
1
[30(x1)] = x1 +
38
[31(x1)] = x1 +
0
[32(x1)] = x1 +
9
[33(x1)] = x1 +
37
[34(x1)] = x1 +
4
[35(x1)] = x1 +
37
[20(x1)] = x1 +
37
[21(x1)] = x1 +
0
[22(x1)] = x1 +
41
[23(x1)] = x1 +
9
[24(x1)] = x1 +
9
[25(x1)] = x1 +
37
[10(x1)] = x1 +
41
[11(x1)] = x1 +
37
[12(x1)] = x1 +
9
[13(x1)] = x1 +
37
[14(x1)] = x1 +
37
[15(x1)] = x1 +
9
[00(x1)] = x1 +
0
[01(x1)] = x1 +
37
[02(x1)] = x1 +
37
[03(x1)] = x1 +
9
[04(x1)] = x1 +
37
[05(x1)] = x1 +
0
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
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1900)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1901)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1902)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1903)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1904)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1905)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1906)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1907)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1908)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1909)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1910)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1911)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1912)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1913)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1914)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1915)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1916)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1917)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1918)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1919)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1920)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1921)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1922)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1923)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1924)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1925)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1926)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1927)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1928)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1929)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1930)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1931)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1932)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1933)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1934)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1935)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1936)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1937)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1938)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1939)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1940)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1941)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1942)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1943)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1944)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1945)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1946)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1947)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1948)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 41#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1949)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1950)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 41#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1951)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1952)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 41#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1953)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1954)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 41#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1955)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1956)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 41#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1957)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1958)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 41#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1959)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1960)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 42#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1961)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1962)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 42#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1963)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1964)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 42#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1965)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1966)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 42#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1967)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1968)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 42#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1969)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1970)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 42#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1971)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1972)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 43#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1973)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1974)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 43#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1975)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1976)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 43#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1977)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1978)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 43#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1979)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1980)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 43#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1981)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1982)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 43#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1983)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1984)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 44#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1985)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1986)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 44#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1987)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1988)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 44#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1989)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1990)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 44#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1991)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1992)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 44#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1993)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1994)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 44#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1995)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1996)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 45#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1997)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1998)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 45#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1999)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (2000)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 45#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (2001)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (2002)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 45#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (2003)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (2004)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 45#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (2005)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (2006)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 45#(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(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
[51(x1)] = x1 +
1
[52(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
1
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[32(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[22(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[02(x1)] = x1 +
0
[04(x1)] = x1 +
0
[40#(x1)] = x1 +
0
[41#(x1)] = x1 +
1
[42#(x1)] = x1 +
1
[43#(x1)] = x1 +
1
[44#(x1)] = x1 +
1
[45#(x1)] = x1 +
1
together with the usable rules
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1900)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1901)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1902)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1903)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1904)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) (1905)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1906)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1907)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1908)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1909)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1910)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) (1911)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1912)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1913)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1914)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1915)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1916)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) (1917)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1918)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1919)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1920)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1921)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1922)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) (1923)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1924)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1925)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1926)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1927)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1928)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) (1929)
45(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 45(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1930)
44(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 44(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1931)
43(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 43(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1932)
42(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 42(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1933)
41(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 41(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1934)
40(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40(51(40(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) (1935)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1937)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1939)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1941)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1943)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1945)
40#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1947)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1948)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1950)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1952)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1954)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1956)
41#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1958)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1960)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1962)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1964)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1966)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1968)
42#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1970)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1972)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1974)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1976)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1978)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1980)
43#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1982)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1984)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1986)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (1988)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (1990)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (1992)
44#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))) (1994)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(52(x1))))))))))))))))))) (1996)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(42(x1))))))))))))))))))) (1998)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(32(x1))))))))))))))))))) (2000)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(22(x1))))))))))))))))))) (2002)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(12(x1))))))))))))))))))) (2004)
45#(51(40(11(14(04(15(14(34(42(41(51(30(52(00(55(50(10(04(35(02(x1))))))))))))))))))))) 40#(11(14(14(04(15(34(42(41(51(30(52(00(55(50(10(04(35(02(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.