Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/27036)

The rewrite relation of the following TRS is considered.

0(1(1(0(2(3(x1)))))) 0(1(1(2(0(3(x1)))))) (1)
2(4(3(2(5(3(4(x1))))))) 2(4(3(5(2(3(4(x1))))))) (2)
1(4(5(0(4(2(1(5(x1)))))))) 1(0(5(4(4(2(1(5(x1)))))))) (3)
1(4(5(3(2(3(4(2(x1)))))))) 1(4(3(5(2(3(4(2(x1)))))))) (4)
4(0(3(1(5(3(2(1(x1)))))))) 4(0(3(5(1(3(2(1(x1)))))))) (5)
2(4(4(4(3(2(5(0(4(x1))))))))) 2(4(4(3(4(2(5(0(4(x1))))))))) (6)
3(2(4(5(5(0(0(5(3(x1))))))))) 3(2(4(5(0(5(0(5(3(x1))))))))) (7)
5(4(2(0(2(4(5(2(2(x1))))))))) 5(4(2(2(0(4(5(2(2(x1))))))))) (8)
0(1(3(1(1(3(2(3(3(2(x1)))))))))) 2(5(4(2(5(1(2(0(5(4(x1)))))))))) (9)
0(2(1(4(0(2(5(3(3(4(x1)))))))))) 2(4(5(4(4(5(4(5(4(2(x1)))))))))) (10)
1(0(3(5(2(3(4(2(1(0(x1)))))))))) 5(2(4(2(3(2(5(2(2(5(x1)))))))))) (11)
1(2(4(4(1(5(3(1(4(1(x1)))))))))) 5(2(1(4(0(2(2(5(5(1(x1)))))))))) (12)
1(3(0(3(0(3(0(1(2(2(x1)))))))))) 4(3(5(4(2(5(4(3(3(5(x1)))))))))) (13)
2(0(0(2(3(0(4(5(3(3(x1)))))))))) 2(0(2(0(3(0(4(5(3(3(x1)))))))))) (14)
2(1(1(3(1(5(2(3(4(0(x1)))))))))) 0(2(4(2(5(4(4(4(5(3(x1)))))))))) (15)
2(2(4(3(2(2(5(3(3(2(x1)))))))))) 1(4(5(2(4(1(2(0(4(2(x1)))))))))) (16)
2(3(1(0(3(5(1(5(2(4(x1)))))))))) 3(4(0(1(3(4(2(2(2(4(x1)))))))))) (17)
3(1(5(1(3(0(3(1(3(2(x1)))))))))) 4(0(5(1(1(4(0(1(5(3(x1)))))))))) (18)
3(3(3(1(4(0(1(4(3(1(x1)))))))))) 5(4(1(3(4(0(1(1(5(1(x1)))))))))) (19)
5(3(1(4(3(0(1(0(5(1(x1)))))))))) 5(2(0(1(3(5(4(2(2(5(x1)))))))))) (20)
0(1(1(4(2(0(4(5(5(1(4(x1))))))))))) 3(3(4(4(4(4(0(3(1(4(x1)))))))))) (21)
0(1(5(4(3(3(4(0(2(0(3(x1))))))))))) 3(2(3(5(0(4(1(5(1(0(x1)))))))))) (22)
0(2(1(0(5(1(3(5(2(2(1(x1))))))))))) 2(1(5(3(3(4(2(0(0(0(x1)))))))))) (23)
0(3(2(0(3(5(4(3(0(0(2(x1))))))))))) 1(0(3(4(3(2(5(5(4(1(x1)))))))))) (24)
0(4(0(4(5(1(3(3(2(2(1(x1))))))))))) 2(2(4(5(1(5(3(3(4(5(x1)))))))))) (25)
0(4(3(3(5(1(0(3(1(1(3(x1))))))))))) 3(0(2(0(2(3(1(0(2(4(x1)))))))))) (26)
1(1(1(0(3(5(2(2(1(0(5(x1))))))))))) 1(0(3(5(4(4(1(3(1(5(x1)))))))))) (27)
1(1(1(2(0(5(0(2(3(3(5(x1))))))))))) 2(3(5(0(4(3(2(0(1(5(x1)))))))))) (28)
1(1(3(4(3(2(4(4(4(5(5(x1))))))))))) 0(5(1(2(2(4(1(5(5(5(x1)))))))))) (29)
1(1(5(5(5(4(1(2(1(0(1(x1))))))))))) 4(1(5(2(0(2(3(0(2(1(x1)))))))))) (30)
1(2(1(4(5(4(4(0(1(0(0(x1))))))))))) 5(2(4(4(3(2(3(5(1(1(x1)))))))))) (31)
1(3(0(0(5(1(3(0(4(3(5(x1))))))))))) 0(2(4(1(5(5(4(3(1(4(x1)))))))))) (32)
1(3(2(5(5(0(4(1(5(1(4(x1))))))))))) 1(3(2(5(0(5(4(1(5(1(4(x1))))))))))) (33)
1(4(1(3(5(0(2(5(2(3(2(x1))))))))))) 5(1(1(1(0(2(3(1(3(2(x1)))))))))) (34)
1(4(2(4(1(4(3(5(1(4(1(x1))))))))))) 3(5(2(1(1(4(3(1(5(5(x1)))))))))) (35)
2(0(5(4(2(1(1(1(3(2(3(x1))))))))))) 2(0(5(4(2(1(1(3(1(2(3(x1))))))))))) (36)
2(3(2(0(5(0(4(5(4(3(1(x1))))))))))) 5(3(3(3(5(2(5(3(3(1(x1)))))))))) (37)
2(3(2(2(5(0(0(4(2(5(1(x1))))))))))) 2(1(1(5(1(1(5(1(2(5(x1)))))))))) (38)
2(4(0(3(5(2(0(4(2(5(5(x1))))))))))) 5(1(3(3(1(1(4(2(2(0(x1)))))))))) (39)
2(5(3(4(3(1(4(2(2(5(4(x1))))))))))) 2(5(3(4(3(4(1(2(2(5(4(x1))))))))))) (40)
3(1(4(0(5(0(3(3(2(2(0(x1))))))))))) 1(5(0(4(2(5(3(3(4(3(x1)))))))))) (41)
3(3(1(1(4(3(5(3(0(1(5(x1))))))))))) 2(3(4(3(1(3(2(3(2(0(x1)))))))))) (42)
3(3(4(0(3(2(4(4(3(5(4(x1))))))))))) 4(5(3(0(4(3(4(1(0(0(x1)))))))))) (43)
3(4(3(0(3(2(0(0(4(4(1(x1))))))))))) 3(2(3(1(1(1(5(5(2(2(x1)))))))))) (44)
4(3(4(1(0(2(3(1(0(3(5(x1))))))))))) 2(5(2(0(1(4(2(3(4(0(x1)))))))))) (45)
4(4(2(3(4(1(0(3(4(1(5(x1))))))))))) 4(0(1(4(0(3(4(0(0(1(x1)))))))))) (46)
4(4(2(4(3(3(3(5(2(2(0(x1))))))))))) 5(0(5(1(0(1(1(4(2(4(x1)))))))))) (47)
5(0(1(3(5(5(3(3(5(2(4(x1))))))))))) 2(2(4(1(4(0(1(1(4(1(x1)))))))))) (48)
5(0(3(0(5(4(3(4(0(3(1(x1))))))))))) 0(4(2(1(0(3(0(5(4(5(x1)))))))))) (49)
5(0(3(1(1(1(1(0(4(1(5(x1))))))))))) 3(3(5(4(1(1(2(0(0(0(x1)))))))))) (50)
5(2(3(1(4(3(4(1(4(2(2(x1))))))))))) 2(2(5(4(5(4(5(1(3(1(x1)))))))))) (51)
5(4(1(0(1(0(1(4(2(3(3(x1))))))))))) 3(4(1(0(1(0(4(5(4(4(x1)))))))))) (52)
5(5(1(1(0(1(0(5(1(5(3(x1))))))))))) 4(5(5(2(2(3(2(2(3(2(x1)))))))))) (53)
0(0(3(3(0(3(3(2(1(3(2(1(x1)))))))))))) 0(0(3(0(3(3(3(1(2(3(2(1(x1)))))))))))) (54)
0(4(4(4(5(5(5(0(4(1(3(0(x1)))))))))))) 1(2(1(3(0(3(3(2(1(3(x1)))))))))) (55)
0(4(5(4(2(5(5(0(5(0(5(1(x1)))))))))))) 5(3(4(5(3(0(5(0(5(4(x1)))))))))) (56)
1(0(4(2(2(5(5(0(0(4(2(4(x1)))))))))))) 5(2(3(5(0(0(3(1(3(5(x1)))))))))) (57)
2(1(0(0(1(4(4(4(4(4(2(2(x1)))))))))))) 0(0(3(0(1(5(5(3(0(3(x1)))))))))) (58)
3(2(4(5(0(1(4(0(4(0(5(2(x1)))))))))))) 2(0(3(3(3(3(3(0(3(0(x1)))))))))) (59)
3(4(4(0(4(0(0(1(5(4(3(2(x1)))))))))))) 0(3(1(0(0(5(2(1(5(5(x1)))))))))) (60)
3(5(5(0(4(3(1(0(1(3(4(2(x1)))))))))))) 0(5(0(2(2(1(3(5(1(0(x1)))))))))) (61)
4(0(4(2(4(0(4(0(5(4(2(3(x1)))))))))))) 1(5(2(0(4(0(0(2(3(0(x1)))))))))) (62)
4(2(3(4(4(0(4(3(2(4(1(4(x1)))))))))))) 4(2(0(4(0(1(3(0(5(0(x1)))))))))) (63)
1(5(1(1(2(3(1(4(2(5(0(0(2(x1))))))))))))) 5(2(1(1(1(1(3(2(0(4(0(5(2(x1))))))))))))) (64)
2(2(0(1(1(5(4(3(0(2(1(1(2(x1))))))))))))) 2(2(0(1(1(5(4(3(2(0(1(1(2(x1))))))))))))) (65)
0(1(1(0(2(1(0(5(0(3(1(1(4(0(0(x1))))))))))))))) 0(1(1(2(0(1(0(5(0(3(1(1(4(0(0(x1))))))))))))))) (66)
0(2(4(0(1(0(2(4(2(3(0(1(2(1(5(x1))))))))))))))) 4(0(2(0(1(0(4(2(2(0(3(1(2(1(5(x1))))))))))))))) (67)
5(3(5(0(1(2(2(0(3(3(1(2(4(2(5(4(3(x1))))))))))))))))) 5(3(5(0(1(2(2(3(0(3(1(2(4(2(5(4(3(x1))))))))))))))))) (68)
2(1(0(3(3(4(1(5(3(0(3(5(1(0(4(3(1(2(x1)))))))))))))))))) 2(1(0(3(3(4(1(3(5(0(3(5(1(0(4(3(1(2(x1)))))))))))))))))) (69)
2(2(3(3(1(1(1(4(4(2(5(3(4(4(3(0(2(4(x1)))))))))))))))))) 2(2(3(3(1(1(1(4(4(2(5(4(3(4(3(0(2(4(x1)))))))))))))))))) (70)
4(4(0(5(0(2(0(1(1(5(3(2(5(5(4(4(5(2(x1)))))))))))))))))) 4(4(0(0(2(5(0(1(5(2(1(3(5(4(5(4(5(2(x1)))))))))))))))))) (71)
1(0(0(5(3(0(4(1(1(5(0(1(3(1(0(2(5(4(4(x1))))))))))))))))))) 1(0(0(5(3(0(4(1(1(5(0(1(3(1(2(0(5(4(4(x1))))))))))))))))))) (72)
0(4(4(0(4(5(2(5(0(1(5(2(3(3(0(2(4(1(4(2(x1)))))))))))))))))))) 0(4(4(0(4(5(2(5(0(1(2(5(3(3(0(2(4(1(4(2(x1)))))))))))))))))))) (73)
3(2(5(5(3(5(4(3(5(1(4(0(3(3(4(4(0(3(2(2(x1)))))))))))))))))))) 3(2(5(5(3(5(4(3(5(1(0(4(3(3(4(4(0(3(2(2(x1)))))))))))))))))))) (74)
4(0(0(2(3(5(2(3(5(1(4(4(5(0(0(1(1(3(5(3(x1)))))))))))))))))))) 4(0(2(0(3(5(2(3(5(1(4(4(5(0(0(1(1(3(5(3(x1)))))))))))))))))))) (75)
0(4(4(0(2(4(5(4(4(4(3(5(2(5(5(1(5(5(2(1(0(x1))))))))))))))))))))) 0(4(4(2(0(5(4(4(4(4(5(2(3(5(5(5(1(5(2(1(0(x1))))))))))))))))))))) (76)
1(0(3(0(1(2(0(5(1(2(4(1(0(0(0(2(2(3(3(0(5(x1))))))))))))))))))))) 1(0(3(0(1(2(0(5(1(4(2(1(0(0(0(2(2(3(3(0(5(x1))))))))))))))))))))) (77)
3(4(1(1(0(2(5(3(3(0(5(0(3(0(3(5(4(3(4(0(2(x1))))))))))))))))))))) 3(4(0(1(1(5(2(3(3(0(5(0(0(3(3(5(4(3(4(0(2(x1))))))))))))))))))))) (78)
4(5(3(2(4(3(4(4(1(3(0(2(2(5(5(5(5(5(1(3(4(x1))))))))))))))))))))) 4(5(2(3(4(3(4(4(1(3(0(2(2(5(5(5(5(5(1(3(4(x1))))))))))))))))))))) (79)
1(2(4(3(0(2(0(0(0(1(3(5(0(1(0(1(5(3(2(0(3(0(x1)))))))))))))))))))))) 1(2(4(3(0(2(0(0(0(1(3(5(0(1(0(5(1(3(2(0(3(0(x1)))))))))))))))))))))) (80)
1(3(4(1(1(4(4(2(4(4(5(3(3(0(4(3(2(4(1(3(4(3(x1)))))))))))))))))))))) 1(3(4(1(1(4(4(2(4(4(5(3(3(0(4(3(2(1(4(3(4(3(x1)))))))))))))))))))))) (81)
2(0(4(0(3(5(2(1(0(0(0(1(1(5(0(4(4(4(3(4(3(1(1(x1))))))))))))))))))))))) 2(0(4(0(3(5(2(1(0(0(0(1(1(5(0(4(4(4(3(3(4(1(1(x1))))))))))))))))))))))) (82)
2(2(2(2(3(5(3(2(5(2(4(1(1(2(4(3(3(0(4(1(3(2(1(x1))))))))))))))))))))))) 2(2(2(2(3(5(3(2(5(2(4(1(1(4(2(3(3(0(4(1(3(2(1(x1))))))))))))))))))))))) (83)
0(4(3(4(4(1(2(4(1(3(4(5(0(0(0(1(4(3(0(3(2(2(0(2(2(x1))))))))))))))))))))))))) 0(4(3(4(4(2(1(4(1(3(4(5(0(0(0(1(4(3(0(3(2(2(0(2(2(x1))))))))))))))))))))))))) (84)
3(4(5(0(3(4(2(3(1(3(0(2(4(5(0(0(4(5(3(0(5(1(5(3(1(x1))))))))))))))))))))))))) 3(4(0(5(3(4(2(3(1(3(0(2(4(5(0(0(4(5(3(0(5(1(5(3(1(x1))))))))))))))))))))))))) (85)
0(3(2(2(5(0(0(0(2(4(2(1(4(1(1(5(1(2(5(0(0(0(2(4(5(0(x1)))))))))))))))))))))))))) 0(3(2(0(5(2(0(2(0(4(2(4(1(1(1(5(5(1(2(0(2(0(4(0(5(0(x1)))))))))))))))))))))))))) (86)
4(3(2(4(1(4(5(4(2(1(2(4(0(3(2(0(3(5(0(0(5(0(5(1(3(3(1(x1))))))))))))))))))))))))))) 4(3(2(4(1(4(5(4(2(1(2(4(0(3(2(0(3(5(0(5(0(0(5(1(3(3(1(x1))))))))))))))))))))))))))) (87)
1(2(4(2(3(4(4(1(3(1(4(3(2(5(2(0(3(2(2(4(1(5(2(1(4(2(4(0(x1)))))))))))))))))))))))))))) 1(2(4(2(3(4(4(1(3(1(4(3(5(2(2(0(3(2(2(4(1(5(2(1(4(2(4(0(x1)))))))))))))))))))))))))))) (88)
2(2(4(1(2(0(5(0(0(4(0(1(3(0(5(5(0(3(5(4(4(3(3(0(3(4(5(0(x1)))))))))))))))))))))))))))) 2(2(4(1(2(0(5(0(0(4(0(1(3(0(5(5(0(3(5(4(4(3(3(0(4(3(5(0(x1)))))))))))))))))))))))))))) (89)
2(3(4(5(5(1(1(2(2(5(1(3(4(4(5(2(3(1(2(1(4(2(3(3(5(0(0(3(x1)))))))))))))))))))))))))))) 2(3(4(5(5(1(1(2(2(5(1(3(4(4(5(2(3(1(2(1(2(4(3(3(0(5(0(3(x1)))))))))))))))))))))))))))) (90)
3(1(4(1(3(1(2(0(2(0(2(3(2(4(4(3(5(1(5(0(2(5(3(0(1(5(3(0(x1)))))))))))))))))))))))))))) 3(2(1(1(2(0(3(2(4(4(1(3(2(1(2(5(0(3(1(0(3(0(5(0(5(4(3(5(x1)))))))))))))))))))))))))))) (91)
4(5(3(2(1(2(0(5(1(3(3(3(5(0(0(2(3(0(0(0(1(1(5(5(2(2(0(5(x1)))))))))))))))))))))))))))) 4(5(3(2(1(2(0(5(1(3(3(3(5(0(0(2(3(0(0(1(0(1(5(5(2(2(0(5(x1)))))))))))))))))))))))))))) (92)
1(4(5(3(0(2(2(3(3(5(2(5(0(0(0(5(2(0(4(4(1(1(2(0(4(1(5(0(1(x1))))))))))))))))))))))))))))) 1(4(5(3(0(2(2(3(3(5(2(5(0(0(0(5(2(0(4(4(1(2(1(0(4(1(5(0(1(x1))))))))))))))))))))))))))))) (93)
4(0(0(0(2(3(1(5(3(2(1(4(2(0(0(3(4(0(1(2(2(5(1(1(1(2(0(4(2(x1))))))))))))))))))))))))))))) 4(0(0(0(3(2(1(3(5(2(1(4(2(0(0(3(4(0(1(2(2(5(1(1(1(2(0(4(2(x1))))))))))))))))))))))))))))) (94)
3(5(5(3(1(3(1(4(3(5(1(0(2(1(3(1(2(3(2(2(0(5(3(4(1(4(1(3(1(1(x1)))))))))))))))))))))))))))))) 3(5(5(3(1(3(1(4(3(5(1(0(2(1(3(1(2(3(2(2(0(4(3(5(1(4(1(3(1(1(x1)))))))))))))))))))))))))))))) (95)
4(2(3(3(4(4(0(3(5(3(1(0(3(3(0(5(5(5(0(4(1(2(2(0(5(3(3(4(5(2(x1)))))))))))))))))))))))))))))) 4(2(3(3(4(4(0(3(5(3(1(0(3(3(0(5(5(5(0(4(2(1(2(0(5(3(3(4(5(2(x1)))))))))))))))))))))))))))))) (96)

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 +
20
[4(x1)] = x1 +
20
[3(x1)] = x1 +
24
[2(x1)] = x1 +
20
[1(x1)] = x1 +
21
[0(x1)] = x1 +
21
all of the following rules can be deleted.
0(1(3(1(1(3(2(3(3(2(x1)))))))))) 2(5(4(2(5(1(2(0(5(4(x1)))))))))) (9)
0(2(1(4(0(2(5(3(3(4(x1)))))))))) 2(4(5(4(4(5(4(5(4(2(x1)))))))))) (10)
1(0(3(5(2(3(4(2(1(0(x1)))))))))) 5(2(4(2(3(2(5(2(2(5(x1)))))))))) (11)
1(2(4(4(1(5(3(1(4(1(x1)))))))))) 5(2(1(4(0(2(2(5(5(1(x1)))))))))) (12)
1(3(0(3(0(3(0(1(2(2(x1)))))))))) 4(3(5(4(2(5(4(3(3(5(x1)))))))))) (13)
2(1(1(3(1(5(2(3(4(0(x1)))))))))) 0(2(4(2(5(4(4(4(5(3(x1)))))))))) (15)
2(2(4(3(2(2(5(3(3(2(x1)))))))))) 1(4(5(2(4(1(2(0(4(2(x1)))))))))) (16)
2(3(1(0(3(5(1(5(2(4(x1)))))))))) 3(4(0(1(3(4(2(2(2(4(x1)))))))))) (17)
3(1(5(1(3(0(3(1(3(2(x1)))))))))) 4(0(5(1(1(4(0(1(5(3(x1)))))))))) (18)
3(3(3(1(4(0(1(4(3(1(x1)))))))))) 5(4(1(3(4(0(1(1(5(1(x1)))))))))) (19)
5(3(1(4(3(0(1(0(5(1(x1)))))))))) 5(2(0(1(3(5(4(2(2(5(x1)))))))))) (20)
0(1(1(4(2(0(4(5(5(1(4(x1))))))))))) 3(3(4(4(4(4(0(3(1(4(x1)))))))))) (21)
0(1(5(4(3(3(4(0(2(0(3(x1))))))))))) 3(2(3(5(0(4(1(5(1(0(x1)))))))))) (22)
0(2(1(0(5(1(3(5(2(2(1(x1))))))))))) 2(1(5(3(3(4(2(0(0(0(x1)))))))))) (23)
0(3(2(0(3(5(4(3(0(0(2(x1))))))))))) 1(0(3(4(3(2(5(5(4(1(x1)))))))))) (24)
0(4(0(4(5(1(3(3(2(2(1(x1))))))))))) 2(2(4(5(1(5(3(3(4(5(x1)))))))))) (25)
0(4(3(3(5(1(0(3(1(1(3(x1))))))))))) 3(0(2(0(2(3(1(0(2(4(x1)))))))))) (26)
1(1(1(0(3(5(2(2(1(0(5(x1))))))))))) 1(0(3(5(4(4(1(3(1(5(x1)))))))))) (27)
1(1(1(2(0(5(0(2(3(3(5(x1))))))))))) 2(3(5(0(4(3(2(0(1(5(x1)))))))))) (28)
1(1(3(4(3(2(4(4(4(5(5(x1))))))))))) 0(5(1(2(2(4(1(5(5(5(x1)))))))))) (29)
1(1(5(5(5(4(1(2(1(0(1(x1))))))))))) 4(1(5(2(0(2(3(0(2(1(x1)))))))))) (30)
1(2(1(4(5(4(4(0(1(0(0(x1))))))))))) 5(2(4(4(3(2(3(5(1(1(x1)))))))))) (31)
1(3(0(0(5(1(3(0(4(3(5(x1))))))))))) 0(2(4(1(5(5(4(3(1(4(x1)))))))))) (32)
1(4(1(3(5(0(2(5(2(3(2(x1))))))))))) 5(1(1(1(0(2(3(1(3(2(x1)))))))))) (34)
1(4(2(4(1(4(3(5(1(4(1(x1))))))))))) 3(5(2(1(1(4(3(1(5(5(x1)))))))))) (35)
2(3(2(0(5(0(4(5(4(3(1(x1))))))))))) 5(3(3(3(5(2(5(3(3(1(x1)))))))))) (37)
2(3(2(2(5(0(0(4(2(5(1(x1))))))))))) 2(1(1(5(1(1(5(1(2(5(x1)))))))))) (38)
2(4(0(3(5(2(0(4(2(5(5(x1))))))))))) 5(1(3(3(1(1(4(2(2(0(x1)))))))))) (39)
3(1(4(0(5(0(3(3(2(2(0(x1))))))))))) 1(5(0(4(2(5(3(3(4(3(x1)))))))))) (41)
3(3(1(1(4(3(5(3(0(1(5(x1))))))))))) 2(3(4(3(1(3(2(3(2(0(x1)))))))))) (42)
3(3(4(0(3(2(4(4(3(5(4(x1))))))))))) 4(5(3(0(4(3(4(1(0(0(x1)))))))))) (43)
3(4(3(0(3(2(0(0(4(4(1(x1))))))))))) 3(2(3(1(1(1(5(5(2(2(x1)))))))))) (44)
4(3(4(1(0(2(3(1(0(3(5(x1))))))))))) 2(5(2(0(1(4(2(3(4(0(x1)))))))))) (45)
4(4(2(3(4(1(0(3(4(1(5(x1))))))))))) 4(0(1(4(0(3(4(0(0(1(x1)))))))))) (46)
4(4(2(4(3(3(3(5(2(2(0(x1))))))))))) 5(0(5(1(0(1(1(4(2(4(x1)))))))))) (47)
5(0(1(3(5(5(3(3(5(2(4(x1))))))))))) 2(2(4(1(4(0(1(1(4(1(x1)))))))))) (48)
5(0(3(0(5(4(3(4(0(3(1(x1))))))))))) 0(4(2(1(0(3(0(5(4(5(x1)))))))))) (49)
5(0(3(1(1(1(1(0(4(1(5(x1))))))))))) 3(3(5(4(1(1(2(0(0(0(x1)))))))))) (50)
5(2(3(1(4(3(4(1(4(2(2(x1))))))))))) 2(2(5(4(5(4(5(1(3(1(x1)))))))))) (51)
5(4(1(0(1(0(1(4(2(3(3(x1))))))))))) 3(4(1(0(1(0(4(5(4(4(x1)))))))))) (52)
5(5(1(1(0(1(0(5(1(5(3(x1))))))))))) 4(5(5(2(2(3(2(2(3(2(x1)))))))))) (53)
0(4(4(4(5(5(5(0(4(1(3(0(x1)))))))))))) 1(2(1(3(0(3(3(2(1(3(x1)))))))))) (55)
0(4(5(4(2(5(5(0(5(0(5(1(x1)))))))))))) 5(3(4(5(3(0(5(0(5(4(x1)))))))))) (56)
1(0(4(2(2(5(5(0(0(4(2(4(x1)))))))))))) 5(2(3(5(0(0(3(1(3(5(x1)))))))))) (57)
2(1(0(0(1(4(4(4(4(4(2(2(x1)))))))))))) 0(0(3(0(1(5(5(3(0(3(x1)))))))))) (58)
3(2(4(5(0(1(4(0(4(0(5(2(x1)))))))))))) 2(0(3(3(3(3(3(0(3(0(x1)))))))))) (59)
3(4(4(0(4(0(0(1(5(4(3(2(x1)))))))))))) 0(3(1(0(0(5(2(1(5(5(x1)))))))))) (60)
3(5(5(0(4(3(1(0(1(3(4(2(x1)))))))))))) 0(5(0(2(2(1(3(5(1(0(x1)))))))))) (61)
4(0(4(2(4(0(4(0(5(4(2(3(x1)))))))))))) 1(5(2(0(4(0(0(2(3(0(x1)))))))))) (62)
4(2(3(4(4(0(4(3(2(4(1(4(x1)))))))))))) 4(2(0(4(0(1(3(0(5(0(x1)))))))))) (63)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 276 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 1656 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 +
0
[52(x1)] = x1 +
1
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
0
[40(x1)] = x1 +
8
[41(x1)] = x1 +
1
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
1
[45(x1)] = x1 +
1
[30(x1)] = x1 +
0
[31(x1)] = x1 +
1
[32(x1)] = x1 +
1
[33(x1)] = x1 +
20
[34(x1)] = x1 +
8
[35(x1)] = x1 +
0
[20(x1)] = x1 +
8
[21(x1)] = x1 +
1
[22(x1)] = x1 +
0
[23(x1)] = x1 +
8
[24(x1)] = x1 +
0
[25(x1)] = x1 +
1
[10(x1)] = x1 +
20
[11(x1)] = x1 +
0
[12(x1)] = x1 +
8
[13(x1)] = x1 +
1
[14(x1)] = x1 +
1
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
1
[03(x1)] = x1 +
22
[04(x1)] = x1 +
0
[05(x1)] = x1 +
8
all of the following rules can be deleted.

There are 1620 ruless (increase limit for explicit display).

1.1.1.1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2029)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2030)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2031)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2032)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2033)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2034)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2035)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2036)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2037)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2038)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2039)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2040)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2041)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2042)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2043)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2044)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2045)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2046)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2047)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2048)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2049)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2050)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2051)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2052)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2053)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2054)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2055)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2056)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2057)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2058)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2059)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2060)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2061)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2062)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2063)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2064)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 10#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2065)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2066)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 10#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2067)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2068)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 10#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2069)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2070)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 10#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2071)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2072)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 10#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2073)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2074)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 10#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2075)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2076)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 11#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2077)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2078)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 11#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2079)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2080)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 11#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2081)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2082)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 11#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2083)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2084)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 11#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2085)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2086)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 11#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2087)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2088)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2089)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2090)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2091)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2092)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2093)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2094)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2095)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2096)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2097)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2098)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2099)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2100)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2101)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 13#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2102)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2103)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 13#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2104)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2105)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 13#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2106)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2107)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 13#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2108)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2109)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 13#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2110)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2111)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 13#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2112)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2113)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 14#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2114)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2115)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 14#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2116)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2117)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 14#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2118)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2119)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 14#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2120)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2121)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 14#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2122)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2123)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 14#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2124)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2125)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 15#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2126)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2127)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 15#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2128)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2129)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 15#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2130)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2131)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 15#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2132)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2133)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 15#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2134)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2135)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 15#(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2136)

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
[51(x1)] = x1 +
0
[54(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 +
1
[33(x1)] = x1 +
0
[34(x1)] = x1 +
1
[21(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
1
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[05(x1)] = x1 +
0
[10#(x1)] = x1 +
1
[11#(x1)] = x1 +
1
[12#(x1)] = x1 +
0
[13#(x1)] = x1 +
1
[14#(x1)] = x1 +
1
[15#(x1)] = x1 +
1
together with the usable rules
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2029)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2030)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2031)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2032)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2033)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) (2034)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2035)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2036)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2037)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2038)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2039)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) (2040)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2041)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2042)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2043)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2044)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2045)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) (2046)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2047)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2048)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2049)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2050)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2051)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) (2052)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2053)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2054)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2055)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2056)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2057)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) (2058)
15(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 15(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2059)
14(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 14(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2060)
13(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 13(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2061)
12(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2062)
11(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 11(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2063)
10(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 10(34(32(12(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) (2064)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2066)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2068)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2070)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2072)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2074)
10#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2076)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2078)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2080)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2082)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2084)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2086)
11#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2088)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2089)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2091)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2093)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2095)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2097)
12#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2099)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2101)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2103)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2105)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2107)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2109)
13#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2111)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2113)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2115)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2117)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2119)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2121)
14#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2123)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(51(x1))))))))))))))))))))))))) (2125)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(41(x1))))))))))))))))))))))))) (2127)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(31(x1))))))))))))))))))))))))) (2129)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(21(x1))))))))))))))))))))))))) (2131)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(11(x1))))))))))))))))))))))))) (2133)
15#(34(32(12(54(00(55(00(05(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1)))))))))))))))))))))))))))) 12#(54(00(05(55(00(55(30(02(25(33(02(45(21(13(24(43(51(40(11(44(21(33(42(01(x1))))))))))))))))))))))))) (2135)
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.