Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/25726)

The rewrite relation of the following TRS is considered.

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

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 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 +
1
[51(x1)] = x1 +
3
[52(x1)] = x1 +
0
[53(x1)] = x1 +
5
[54(x1)] = x1 +
0
[55(x1)] = x1 +
4
[40(x1)] = x1 +
0
[41(x1)] = x1 +
5
[42(x1)] = x1 +
4
[43(x1)] = x1 +
3
[44(x1)] = x1 +
3
[45(x1)] = x1 +
3
[30(x1)] = x1 +
4
[31(x1)] = x1 +
4
[32(x1)] = x1 +
1
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
0
[20(x1)] = x1 +
4
[21(x1)] = x1 +
1
[22(x1)] = x1 +
0
[23(x1)] = x1 +
3
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
3
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
4
[14(x1)] = x1 +
4
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
3
[02(x1)] = x1 +
3
[03(x1)] = x1 +
0
[04(x1)] = x1 +
3
[05(x1)] = x1 +
1
all of the following rules can be deleted.

There are 1476 ruless (increase limit for explicit display).

1.1.1.1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1900)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1901)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1902)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1903)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1904)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1905)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1906)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1907)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1908)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1909)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1910)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1911)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1912)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1913)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1914)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1915)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1916)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1917)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1918)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1919)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1920)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1921)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1922)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1923)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1924)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1925)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1926)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1927)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1928)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1929)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1930)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1931)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1932)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1933)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1934)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1935)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1936)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1937)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1938)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1939)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1940)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1941)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1942)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1943)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1944)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1945)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1946)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1947)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1948)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1949)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1950)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1951)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1952)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1953)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1954)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1955)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1956)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1957)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1958)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1959)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1960)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1961)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1962)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1963)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1964)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1965)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1966)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1967)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1968)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1969)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1970)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1971)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 144 ruless (increase limit for explicit display).

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
1
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
1
[22(x1)] = x1 +
0
[23(x1)] = x1 +
0
[25(x1)] = x1 +
0
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
1
[03(x1)] = x1 +
0
[04(x1)] = x1 +
0
[05(x1)] = x1 +
1
[40#(x1)] = x1 +
1
[41#(x1)] = x1 +
1
[42#(x1)] = x1 +
1
[43#(x1)] = x1 +
1
[44#(x1)] = x1 +
1
[45#(x1)] = x1 +
1
[00#(x1)] = x1 +
1
[01#(x1)] = x1 +
1
[02#(x1)] = x1 +
0
[03#(x1)] = x1 +
1
[04#(x1)] = x1 +
1
[05#(x1)] = x1 +
0
together with the usable rules
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1900)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1901)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1902)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1903)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1904)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) (1905)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1906)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1907)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1908)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1909)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1910)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) (1911)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1912)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1913)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1914)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1915)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1916)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) (1917)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1918)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1919)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1920)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1921)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1922)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) (1923)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1924)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1925)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1926)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1927)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1928)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) (1929)
05(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1930)
04(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 04(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1931)
03(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 03(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1932)
02(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 02(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1933)
01(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 01(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1934)
00(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 00(05(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) (1935)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1936)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1937)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1938)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1939)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1940)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) (1941)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1942)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1943)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1944)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1945)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1946)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) (1947)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1948)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1949)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1950)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1951)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1952)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) (1953)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1954)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1955)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1956)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1957)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1958)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) (1959)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1960)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1961)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1962)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1963)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1964)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) (1965)
45(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 45(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1966)
44(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 44(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1967)
43(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 43(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1968)
42(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 42(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1969)
41(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 41(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1970)
40(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 40(21(33(02(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) (1971)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
40#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1))))))))))))))))) (1973)
40#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1))))))))))))))))) (1975)
40#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1))))))))))))))))) (1977)
40#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1))))))))))))))))) (1979)
40#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1))))))))))))))))) (1981)
40#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1))))))))))))))))) (1983)
41#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1))))))))))))))))) (1985)
41#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1))))))))))))))))) (1987)
41#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1))))))))))))))))) (1989)
41#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1))))))))))))))))) (1991)
41#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1))))))))))))))))) (1993)
41#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1))))))))))))))))) (1995)
42#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1))))))))))))))))) (1997)
42#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1))))))))))))))))) (1999)
42#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1))))))))))))))))) (2001)
42#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1))))))))))))))))) (2003)
42#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1))))))))))))))))) (2005)
42#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1))))))))))))))))) (2007)
43#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1))))))))))))))))) (2009)
43#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1))))))))))))))))) (2011)
43#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1))))))))))))))))) (2013)
43#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1))))))))))))))))) (2015)
43#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1))))))))))))))))) (2017)
43#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1))))))))))))))))) (2019)
44#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1))))))))))))))))) (2021)
44#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1))))))))))))))))) (2023)
44#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1))))))))))))))))) (2025)
44#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1))))))))))))))))) (2027)
44#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1))))))))))))))))) (2029)
44#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1))))))))))))))))) (2031)
45#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(52(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(52(x1))))))))))))))))) (2033)
45#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(42(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(42(x1))))))))))))))))) (2035)
45#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(32(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(32(x1))))))))))))))))) (2037)
45#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(22(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(22(x1))))))))))))))))) (2039)
45#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(12(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(12(x1))))))))))))))))) (2041)
45#(21(33(02(55(20(33(22(33(32(52(20(23(03(55(50(50(30(32(02(x1)))))))))))))))))))) 02#(55(20(33(32(22(33(52(20(23(03(55(50(50(30(32(02(x1))))))))))))))))) (2043)
00#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1))))))))))))))))) (2045)
00#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1))))))))))))))))) (2047)
00#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1))))))))))))))))) (2049)
00#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1))))))))))))))))) (2051)
00#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1))))))))))))))))) (2053)
00#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1))))))))))))))))) (2055)
01#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1))))))))))))))))) (2057)
01#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1))))))))))))))))) (2059)
01#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1))))))))))))))))) (2061)
01#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1))))))))))))))))) (2063)
01#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1))))))))))))))))) (2065)
01#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1))))))))))))))))) (2067)
02#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1))))))))))))))))) (2069)
02#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1))))))))))))))))) (2071)
02#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1))))))))))))))))) (2073)
02#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1))))))))))))))))) (2075)
02#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1))))))))))))))))) (2077)
02#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1))))))))))))))))) (2079)
03#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1))))))))))))))))) (2081)
03#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1))))))))))))))))) (2083)
03#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1))))))))))))))))) (2085)
03#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1))))))))))))))))) (2087)
03#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1))))))))))))))))) (2089)
03#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1))))))))))))))))) (2091)
04#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1))))))))))))))))) (2093)
04#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1))))))))))))))))) (2095)
04#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1))))))))))))))))) (2097)
04#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1))))))))))))))))) (2099)
04#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1))))))))))))))))) (2101)
04#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1))))))))))))))))) (2103)
05#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(53(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(53(x1))))))))))))))))) (2104)
05#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(43(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(43(x1))))))))))))))))) (2106)
05#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(33(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(33(x1))))))))))))))))) (2108)
05#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(23(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(23(x1))))))))))))))))) (2110)
05#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(13(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(13(x1))))))))))))))))) (2112)
05#(05(25(23(33(22(13(04(35(42(31(52(30(02(35(02(25(03(x1)))))))))))))))))) 05#(25(33(22(23(13(04(35(42(31(52(30(02(35(02(25(03(x1))))))))))))))))) (2114)
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.