Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26933)

The rewrite relation of the following TRS is considered.

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

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 +
14
[51(x1)] = x1 +
13
[52(x1)] = x1 +
5
[53(x1)] = x1 +
0
[54(x1)] = x1 +
2
[55(x1)] = x1 +
1
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[42(x1)] = x1 +
13
[43(x1)] = x1 +
2
[44(x1)] = x1 +
5
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
5
[32(x1)] = x1 +
14
[33(x1)] = x1 +
2
[34(x1)] = x1 +
0
[35(x1)] = x1 +
2
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
2
[23(x1)] = x1 +
0
[24(x1)] = x1 +
1
[25(x1)] = x1 +
0
[10(x1)] = x1 +
1
[11(x1)] = x1 +
2
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
1
[00(x1)] = x1 +
0
[01(x1)] = x1 +
5
[02(x1)] = x1 +
13
[03(x1)] = x1 +
1
[04(x1)] = x1 +
1
[05(x1)] = x1 +
0
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
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2029)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2030)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2031)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2032)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2033)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2034)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2035)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2036)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2037)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2038)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2039)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2040)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2041)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2042)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2043)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2044)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2045)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2046)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2047)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2048)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2049)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2050)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2051)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2052)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2053)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2054)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2055)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2056)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2057)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2058)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2059)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2060)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2061)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2062)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2063)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2064)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2065)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2066)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2067)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2068)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2069)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2070)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2071)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2072)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2073)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2074)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2075)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2076)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2077)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2078)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2079)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2080)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2081)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2082)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2083)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2084)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2085)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2086)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2087)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2088)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2089)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2090)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2091)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2092)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2093)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2094)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2095)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2096)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2097)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2098)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2099)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2100)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2101)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2102)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2103)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2104)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2105)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2106)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2107)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2108)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2109)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2110)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2111)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2112)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2113)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2114)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2115)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2116)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2117)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2118)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2119)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2120)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2121)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2122)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2123)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2124)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2125)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2126)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2127)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2128)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2129)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2130)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2131)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2132)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2133)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2134)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2135)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(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
[50(x1)] = x1 +
0
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
1
[40(x1)] = x1 +
1
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
0
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[20(x1)] = x1 +
1
[22(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
1
[12(x1)] = x1 +
0
[14(x1)] = x1 +
1
[00(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
1
[04(x1)] = x1 +
1
[40#(x1)] = x1 +
0
[41#(x1)] = x1 +
1
[42#(x1)] = x1 +
1
[43#(x1)] = x1 +
1
[44#(x1)] = x1 +
1
[45#(x1)] = x1 +
1
together with the usable rules
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2029)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2030)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2031)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2032)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2033)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))))))))))) (2034)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2035)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2036)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2037)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2038)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2039)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))))))))))) (2040)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2041)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2042)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2043)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2044)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2045)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))))))))))) (2046)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2047)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2048)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2049)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2050)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2051)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))))))))))) (2052)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2053)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2054)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2055)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2056)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2057)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))))))))))) (2058)
45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 45(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2059)
44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 44(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2060)
43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 43(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2061)
42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 42(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2062)
41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 41(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2063)
40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))))))))))) (2064)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2065)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2067)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2069)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2071)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2073)
40#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2075)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2077)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2079)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2081)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2083)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2085)
41#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2087)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2089)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2091)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2093)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2095)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2097)
42#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2099)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2101)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2103)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2105)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2107)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2109)
43#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2111)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2113)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2115)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2117)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2119)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2121)
44#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(x1)))))))))))))))) (2123)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(50(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(50(x1)))))))))))))))) (2125)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(40(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(40(x1)))))))))))))))) (2127)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(30(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(30(x1)))))))))))))))) (2129)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(20(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(20(x1)))))))))))))))) (2131)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(10(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(10(x1)))))))))))))))) (2133)
45#(11(14(04(55(20(03(55(40(11(34(12(54(20(53(20(33(22(33(32(02(55(50(00(x1)))))))))))))))))))))))) 40#(11(34(12(54(20(53(20(33(32(22(33(02(55(50(00(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.