Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26132)

The rewrite relation of the following TRS is considered.

0(1(2(3(3(4(x1)))))) 0(2(1(3(3(4(x1)))))) (1)
4(4(3(0(4(2(4(x1))))))) 4(4(3(4(0(2(4(x1))))))) (2)
3(1(2(0(0(4(3(2(x1)))))))) 3(1(0(2(0(4(3(2(x1)))))))) (3)
0(1(2(4(3(0(2(0(3(x1))))))))) 0(2(1(4(3(0(2(0(3(x1))))))))) (4)
0(5(5(3(5(3(0(5(3(3(x1)))))))))) 0(5(5(3(3(5(0(5(3(3(x1)))))))))) (5)
2(1(2(4(5(4(1(2(5(0(x1)))))))))) 3(1(1(1(0(1(4(1(5(0(x1)))))))))) (6)
2(4(4(2(0(2(1(5(4(5(x1)))))))))) 1(1(2(1(5(5(5(2(4(5(x1)))))))))) (7)
4(1(1(1(0(0(0(0(2(0(x1)))))))))) 4(1(1(0(1(0(0(0(2(0(x1)))))))))) (8)
4(4(1(5(1(1(0(0(4(3(x1)))))))))) 4(2(1(3(2(1(0(0(4(3(x1)))))))))) (9)
0(0(5(3(1(3(0(2(2(2(3(x1))))))))))) 4(1(2(0(2(3(1(4(3(0(x1)))))))))) (10)
0(5(1(0(4(5(5(3(4(1(3(x1))))))))))) 1(3(2(2(1(3(0(0(0(3(x1)))))))))) (11)
0(5(1(4(5(2(2(4(4(5(1(x1))))))))))) 1(0(1(2(5(0(1(0(0(4(x1)))))))))) (12)
0(5(3(2(4(4(3(1(1(5(0(x1))))))))))) 3(5(0(3(0(5(1(0(4(1(x1)))))))))) (13)
1(1(4(5(3(4(5(5(3(2(0(x1))))))))))) 5(3(0(2(1(5(1(0(3(3(x1)))))))))) (14)
1(2(4(3(0(2(3(0(0(5(1(x1))))))))))) 1(1(3(1(5(2(5(0(4(3(x1)))))))))) (15)
1(5(1(3(4(4(3(3(5(4(2(x1))))))))))) 3(4(0(0(2(1(3(3(2(0(x1)))))))))) (16)
2(0(0(0(4(1(1(2(4(3(3(x1))))))))))) 5(5(2(2(2(4(5(0(1(5(x1)))))))))) (17)
2(0(4(5(4(4(4(5(3(2(4(x1))))))))))) 3(4(0(0(3(4(2(3(0(1(x1)))))))))) (18)
2(2(3(1(1(4(4(5(5(3(5(x1))))))))))) 1(2(1(0(3(4(4(3(1(5(x1)))))))))) (19)
2(5(5(1(4(4(0(2(0(4(2(x1))))))))))) 5(4(0(1(3(3(4(5(5(4(x1)))))))))) (20)
3(0(0(4(3(1(5(4(2(2(1(x1))))))))))) 3(4(2(3(4(0(1(4(2(5(x1)))))))))) (21)
3(0(5(5(1(4(5(1(0(2(2(x1))))))))))) 5(4(1(4(5(2(0(4(0(3(x1)))))))))) (22)
3(1(0(2(2(5(0(0(2(3(2(x1))))))))))) 4(0(5(2(4(0(5(3(1(2(x1)))))))))) (23)
3(1(3(5(3(3(5(1(2(2(5(x1))))))))))) 1(4(2(1(5(3(3(1(0(2(x1)))))))))) (24)
3(2(1(2(4(3(4(2(5(0(1(x1))))))))))) 5(1(3(5(1(1(0(4(2(3(x1)))))))))) (25)
3(3(1(5(4(5(1(2(4(4(3(x1))))))))))) 2(3(3(5(2(4(2(1(0(2(x1)))))))))) (26)
3(4(4(2(0(1(1(4(0(2(3(x1))))))))))) 5(5(2(2(2(0(4(5(5(2(x1)))))))))) (27)
3(4(5(5(0(4(0(3(0(0(5(x1))))))))))) 3(2(2(2(1(5(0(3(1(2(x1)))))))))) (28)
4(0(5(3(2(0(0(1(3(3(2(x1))))))))))) 2(0(3(2(5(4(5(3(5(1(x1)))))))))) (29)
4(0(5(4(1(0(1(2(2(3(5(x1))))))))))) 3(1(0(3(1(5(1(0(2(2(x1)))))))))) (30)
4(1(2(3(5(4(2(0(1(3(5(x1))))))))))) 3(5(4(2(1(5(2(4(5(5(x1)))))))))) (31)
4(1(2(5(3(0(5(2(5(2(0(x1))))))))))) 4(1(3(3(3(5(5(4(2(3(x1)))))))))) (32)
4(2(2(1(5(2(2(2(3(3(4(x1))))))))))) 5(3(0(1(3(0(0(0(1(2(x1)))))))))) (33)
4(5(1(1(1(2(2(0(0(1(2(x1))))))))))) 4(5(1(1(2(1(2(0(0(1(2(x1))))))))))) (34)
4(5(2(2(1(1(1(1(2(3(1(x1))))))))))) 1(5(1(5(0(3(4(3(3(1(x1)))))))))) (35)
4(5(3(1(3(3(1(4(2(4(5(x1))))))))))) 2(1(5(5(2(2(2(1(1(2(x1)))))))))) (36)
5(0(1(5(3(1(0(3(5(3(5(x1))))))))))) 5(0(1(3(5(1(0(3(5(3(5(x1))))))))))) (37)
5(0(5(0(1(3(0(0(4(4(4(x1))))))))))) 0(4(4(3(5(5(0(0(5(4(x1)))))))))) (38)
5(1(2(0(1(0(3(5(5(1(4(x1))))))))))) 5(1(5(3(5(0(4(5(0(0(x1)))))))))) (39)
5(2(3(2(4(2(1(5(3(5(1(x1))))))))))) 1(0(1(4(1(5(1(3(5(0(x1)))))))))) (40)
5(2(4(2(4(3(0(3(2(5(2(x1))))))))))) 5(2(4(2(4(3(0(2(3(5(2(x1))))))))))) (41)
5(2(4(5(5(5(0(0(0(1(4(x1))))))))))) 1(3(0(1(4(0(5(0(1(3(x1)))))))))) (42)
5(3(1(0(3(1(4(4(2(3(0(x1))))))))))) 0(2(4(4(4(5(5(1(4(2(x1)))))))))) (43)
5(4(2(4(2(5(0(1(4(2(3(x1))))))))))) 4(0(1(4(5(3(3(1(0(2(x1)))))))))) (44)
5(5(4(3(3(4(2(3(0(0(4(x1))))))))))) 5(2(4(0(3(5(0(0(5(4(x1)))))))))) (45)
0(1(3(4(1(3(1(2(0(3(0(5(x1)))))))))))) 2(2(3(5(2(1(4(4(3(4(x1)))))))))) (46)
0(4(0(2(5(5(5(5(0(1(1(4(x1)))))))))))) 0(4(0(2(5(5(5(5(1(0(1(4(x1)))))))))))) (47)
0(5(2(3(3(5(3(3(0(0(2(4(x1)))))))))))) 4(4(0(0(4(2(5(5(0(2(x1)))))))))) (48)
1(1(1(5(3(2(4(3(1(4(0(1(x1)))))))))))) 4(4(4(5(0(2(4(4(4(2(x1)))))))))) (49)
1(2(4(1(3(0(5(0(3(3(3(5(x1)))))))))))) 3(0(4(5(0(5(4(3(2(0(x1)))))))))) (50)
1(3(5(2(1(0(4(2(4(5(5(1(x1)))))))))))) 4(0(2(0(1(0(5(3(3(2(x1)))))))))) (51)
2(0(0(1(1(4(5(1(3(1(5(1(x1)))))))))))) 3(4(5(3(0(3(2(1(0(2(x1)))))))))) (52)
2(3(1(5(1(0(2(4(3(1(0(5(x1)))))))))))) 0(2(0(4(5(4(4(4(3(3(x1)))))))))) (53)
2(4(1(3(0(1(2(2(5(0(5(2(x1)))))))))))) 5(5(0(5(3(1(0(5(4(4(x1)))))))))) (54)
2(4(1(4(1(0(4(2(2(5(1(1(x1)))))))))))) 1(2(1(5(2(4(0(5(4(4(x1)))))))))) (55)
2(4(5(3(2(4(1(1(0(0(3(3(x1)))))))))))) 0(3(0(1(4(3(5(4(1(5(x1)))))))))) (56)
3(2(3(4(5(4(4(1(3(2(5(5(x1)))))))))))) 0(0(5(0(5(5(3(0(1(5(x1)))))))))) (57)
4(0(3(2(3(2(0(4(1(1(0(5(x1)))))))))))) 5(2(3(0(1(4(5(4(4(0(x1)))))))))) (58)
4(1(1(3(1(3(2(5(5(2(0(1(x1)))))))))))) 0(1(3(2(5(3(2(4(5(5(x1)))))))))) (59)
4(3(5(4(1(2(2(5(4(1(5(2(x1)))))))))))) 4(3(5(2(1(4(2(5(4(5(1(2(x1)))))))))))) (60)
5(3(5(0(1(3(4(1(4(5(5(5(x1)))))))))))) 4(4(2(0(2(0(4(3(1(2(x1)))))))))) (61)
3(2(5(4(0(5(5(5(5(5(1(2(2(x1))))))))))))) 3(2(0(4(5(5(5(5(5(5(1(2(2(x1))))))))))))) (62)
4(2(5(1(0(1(1(2(3(0(3(2(3(x1))))))))))))) 4(2(5(1(0(1(1(3(2(0(3(2(3(x1))))))))))))) (63)
0(0(2(3(4(3(5(1(5(4(2(2(4(5(x1)))))))))))))) 0(0(2(3(4(3(5(5(1(4(2(2(4(5(x1)))))))))))))) (64)
4(1(5(5(4(1(2(4(3(5(1(2(2(3(x1)))))))))))))) 4(1(5(5(4(1(2(3(4(5(1(2(2(3(x1)))))))))))))) (65)
0(0(0(1(2(3(0(2(3(3(3(2(4(5(1(x1))))))))))))))) 0(0(1(0(2(3(0(2(3(3(3(2(4(5(1(x1))))))))))))))) (66)
5(2(5(4(2(2(4(1(5(3(2(2(1(3(3(x1))))))))))))))) 2(4(5(5(1(4(5(2(2(2(3(2(1(3(3(x1))))))))))))))) (67)
5(4(5(4(2(0(1(0(4(4(2(0(5(3(2(x1))))))))))))))) 5(4(5(4(0(2(1(0(4(4(2(0(5(3(2(x1))))))))))))))) (68)
2(3(0(1(1(4(5(4(5(0(0(3(2(2(4(4(x1)))))))))))))))) 2(3(0(1(1(5(4(5(4(0(0(3(2(2(4(4(x1)))))))))))))))) (69)
0(0(0(2(1(3(5(0(2(1(0(1(3(1(0(1(1(x1))))))))))))))))) 0(0(0(2(1(3(0(5(2(1(0(1(3(1(0(1(1(x1))))))))))))))))) (70)
0(0(4(5(3(4(4(2(2(2(1(1(0(1(4(3(1(x1))))))))))))))))) 0(0(4(5(3(4(4(2(2(2(1(1(1(0(4(3(1(x1))))))))))))))))) (71)
0(1(3(5(1(0(1(5(0(5(0(5(3(0(0(5(1(x1))))))))))))))))) 0(1(3(5(1(0(1(0(0(5(5(5(3(5(0(0(1(x1))))))))))))))))) (72)
0(4(2(1(2(5(1(3(1(4(4(1(1(5(0(0(0(x1))))))))))))))))) 0(4(2(5(2(1(3(1(1(4(4(1(5(0(1(0(0(x1))))))))))))))))) (73)
0(4(5(4(1(0(2(1(4(3(1(3(5(2(3(1(2(x1))))))))))))))))) 0(4(5(4(1(0(2(1(4(1(3(3(5(2(3(1(2(x1))))))))))))))))) (74)
5(3(1(3(1(4(1(1(1(3(2(4(0(2(4(4(3(0(x1)))))))))))))))))) 5(3(1(3(1(1(4(1(1(3(2(4(0(2(4(4(3(0(x1)))))))))))))))))) (75)
0(0(5(0(4(5(5(5(3(0(5(4(0(3(0(0(3(2(4(x1))))))))))))))))))) 0(0(5(0(4(5(5(5(0(3(5(4(0(3(0(0(3(2(4(x1))))))))))))))))))) (76)
4(2(1(0(5(0(5(5(0(1(2(5(1(1(4(4(4(4(4(x1))))))))))))))))))) 4(2(1(0(0(5(5(5(0(1(2(5(1(1(4(4(4(4(4(x1))))))))))))))))))) (77)
4(5(1(1(5(3(5(4(1(0(5(1(2(4(0(4(0(4(5(x1))))))))))))))))))) 4(5(3(1(1(4(5(5(1(5(2(0(1(0(4(4(0(4(5(x1))))))))))))))))))) (78)
2(0(0(1(0(0(5(1(3(1(0(4(2(5(4(4(4(2(4(3(x1)))))))))))))))))))) 2(0(0(1(0(0(5(1(3(1(0(2(4(5(4(4(4(2(4(3(x1)))))))))))))))))))) (79)
3(3(0(4(0(2(4(2(1(3(5(4(0(2(3(2(5(3(5(5(x1)))))))))))))))))))) 3(3(0(4(0(2(4(2(1(3(5(4(0(2(3(2(3(5(5(5(x1)))))))))))))))))))) (80)
3(0(1(4(3(3(5(1(5(0(2(0(4(0(0(1(3(0(5(0(3(x1))))))))))))))))))))) 3(0(4(1(3(3(1(5(5(0(2(0(4(0(0(1(3(0(5(0(3(x1))))))))))))))))))))) (81)
3(0(2(5(4(4(0(0(2(0(4(4(2(1(5(2(2(3(2(5(4(3(1(x1))))))))))))))))))))))) 3(0(2(5(4(4(0(0(2(0(4(4(2(1(5(2(2(3(5(2(4(3(1(x1))))))))))))))))))))))) (82)
2(0(0(4(2(4(5(1(1(4(3(4(0(0(1(4(1(3(1(2(2(4(2(3(x1)))))))))))))))))))))))) 2(0(0(4(2(4(5(1(1(3(4(4(0(0(1(4(1(3(1(2(2(4(2(3(x1)))))))))))))))))))))))) (83)
3(4(1(5(3(5(1(3(4(0(5(2(0(1(4(1(2(3(2(5(0(5(3(3(x1)))))))))))))))))))))))) 3(4(1(5(3(1(3(5(4(5(0(2(4(0(1(1(2(3(5(2(0(3(5(3(x1)))))))))))))))))))))))) (84)
0(5(2(4(3(2(5(2(5(5(3(4(0(5(4(5(3(1(5(5(1(0(3(0(2(x1))))))))))))))))))))))))) 0(5(2(4(3(2(5(2(5(5(3(4(5(0(4(5(3(1(5(5(1(0(3(0(2(x1))))))))))))))))))))))))) (85)
1(1(0(5(0(5(3(2(5(0(2(3(3(4(5(1(4(1(5(3(1(0(2(3(3(4(x1)))))))))))))))))))))))))) 1(1(0(5(0(3(5(2(5(0(2(3(3(4(5(1(4(1(5(3(1(0(2(3(3(4(x1)))))))))))))))))))))))))) (86)
5(0(4(0(1(1(0(2(1(4(1(0(3(3(0(3(2(0(2(3(5(2(5(4(0(1(x1)))))))))))))))))))))))))) 5(0(4(0(1(1(0(2(1(4(0(1(3(3(0(3(2(0(2(3(5(2(5(4(0(1(x1)))))))))))))))))))))))))) (87)
5(5(5(4(5(4(1(0(4(5(0(5(3(0(2(5(4(4(2(3(2(0(2(0(1(5(x1)))))))))))))))))))))))))) 5(5(5(4(4(5(1(0(4(5(0(5(3(0(2(5(4(4(2(3(2(0(2(0(1(5(x1)))))))))))))))))))))))))) (88)
2(4(2(2(1(0(3(5(1(3(2(2(3(4(3(3(3(5(0(1(3(4(2(2(5(3(2(x1))))))))))))))))))))))))))) 2(4(2(2(1(0(3(5(1(3(2(2(3(4(3(3(3(5(0(1(3(2(4(2(5(3(2(x1))))))))))))))))))))))))))) (89)
2(4(3(3(1(0(5(3(5(1(0(3(3(0(0(5(2(0(4(2(0(0(3(4(5(0(1(x1))))))))))))))))))))))))))) 2(4(3(3(1(0(5(3(5(1(0(3(3(0(0(5(2(0(4(2(0(0(4(3(5(0(1(x1))))))))))))))))))))))))))) (90)
1(2(4(1(2(1(0(3(3(3(3(1(2(5(5(5(4(2(0(2(1(2(1(5(4(1(5(0(x1)))))))))))))))))))))))))))) 1(2(1(4(2(1(0(3(3(3(3(1(2(5(5(5(4(2(0(2(1(2(1(5(4(1(5(0(x1)))))))))))))))))))))))))))) (91)
1(3(4(3(1(0(1(1(2(4(1(2(0(5(1(1(0(2(3(0(1(4(3(3(3(1(3(2(x1)))))))))))))))))))))))))))) 1(3(4(3(1(0(1(2(1(4(1(2(0(5(1(1(0(2(3(0(1(4(3(3(3(1(3(2(x1)))))))))))))))))))))))))))) (92)
5(3(4(4(0(2(3(5(1(0(5(1(2(5(0(2(4(4(2(5(2(1(5(3(2(4(5(4(x1)))))))))))))))))))))))))))) 5(3(4(4(0(2(3(5(1(0(5(1(2(0(5(2(4(4(2(5(2(1(5(3(2(4(5(4(x1)))))))))))))))))))))))))))) (93)
0(3(1(2(3(2(4(2(2(5(4(2(0(2(3(2(5(3(1(2(3(3(2(2(2(1(2(0(5(x1))))))))))))))))))))))))))))) 0(3(1(2(3(2(4(2(2(5(4(2(0(2(3(2(5(1(3(2(3(3(2(2(2(1(2(0(5(x1))))))))))))))))))))))))))))) (94)
3(2(5(0(1(3(4(3(4(0(1(2(3(0(0(0(1(0(1(1(2(4(1(5(3(1(1(3(3(x1))))))))))))))))))))))))))))) 3(2(5(0(1(3(4(3(4(1(0(2(3(0(0(0(1(0(1(1(2(4(1(5(3(1(1(3(3(x1))))))))))))))))))))))))))))) (95)
2(0(2(0(3(4(0(1(2(1(5(2(5(4(2(4(1(2(1(5(0(1(2(3(2(5(1(5(1(5(x1)))))))))))))))))))))))))))))) 2(0(2(0(3(4(0(1(2(1(5(5(2(4(2(4(1(2(1(5(0(1(2(3(2(5(1(5(1(5(x1)))))))))))))))))))))))))))))) (96)
3(5(4(2(0(2(2(2(5(5(5(3(3(0(0(2(2(1(5(2(4(0(2(3(1(5(1(4(4(0(x1)))))))))))))))))))))))))))))) 3(5(4(2(0(2(2(2(5(5(5(3(3(0(2(0(2(1(5(2(4(0(2(3(1(5(1(4(4(0(x1)))))))))))))))))))))))))))))) (97)
3(5(4(4(3(1(1(5(3(3(5(0(3(4(1(5(4(0(2(0(4(4(1(4(5(0(3(0(2(5(x1)))))))))))))))))))))))))))))) 3(5(4(4(3(1(1(5(3(3(5(0(3(4(1(5(4(0(2(0(4(1(4(4(5(0(3(0(2(5(x1)))))))))))))))))))))))))))))) (98)
5(3(3(2(4(5(2(2(3(3(0(0(0(5(1(5(1(5(4(1(2(4(4(4(5(4(3(3(5(5(x1)))))))))))))))))))))))))))))) 5(3(3(2(4(5(2(2(3(3(0(0(0(5(1(5(1(4(5(1(2(4(4(4(5(4(3(3(5(5(x1)))))))))))))))))))))))))))))) (99)

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 +
5
[4(x1)] = x1 +
6
[3(x1)] = x1 +
5
[2(x1)] = x1 +
5
[1(x1)] = x1 +
5
[0(x1)] = x1 +
5
all of the following rules can be deleted.
2(1(2(4(5(4(1(2(5(0(x1)))))))))) 3(1(1(1(0(1(4(1(5(0(x1)))))))))) (6)
2(4(4(2(0(2(1(5(4(5(x1)))))))))) 1(1(2(1(5(5(5(2(4(5(x1)))))))))) (7)
4(4(1(5(1(1(0(0(4(3(x1)))))))))) 4(2(1(3(2(1(0(0(4(3(x1)))))))))) (9)
0(0(5(3(1(3(0(2(2(2(3(x1))))))))))) 4(1(2(0(2(3(1(4(3(0(x1)))))))))) (10)
0(5(1(0(4(5(5(3(4(1(3(x1))))))))))) 1(3(2(2(1(3(0(0(0(3(x1)))))))))) (11)
0(5(1(4(5(2(2(4(4(5(1(x1))))))))))) 1(0(1(2(5(0(1(0(0(4(x1)))))))))) (12)
0(5(3(2(4(4(3(1(1(5(0(x1))))))))))) 3(5(0(3(0(5(1(0(4(1(x1)))))))))) (13)
1(1(4(5(3(4(5(5(3(2(0(x1))))))))))) 5(3(0(2(1(5(1(0(3(3(x1)))))))))) (14)
1(2(4(3(0(2(3(0(0(5(1(x1))))))))))) 1(1(3(1(5(2(5(0(4(3(x1)))))))))) (15)
1(5(1(3(4(4(3(3(5(4(2(x1))))))))))) 3(4(0(0(2(1(3(3(2(0(x1)))))))))) (16)
2(0(0(0(4(1(1(2(4(3(3(x1))))))))))) 5(5(2(2(2(4(5(0(1(5(x1)))))))))) (17)
2(0(4(5(4(4(4(5(3(2(4(x1))))))))))) 3(4(0(0(3(4(2(3(0(1(x1)))))))))) (18)
2(2(3(1(1(4(4(5(5(3(5(x1))))))))))) 1(2(1(0(3(4(4(3(1(5(x1)))))))))) (19)
2(5(5(1(4(4(0(2(0(4(2(x1))))))))))) 5(4(0(1(3(3(4(5(5(4(x1)))))))))) (20)
3(0(0(4(3(1(5(4(2(2(1(x1))))))))))) 3(4(2(3(4(0(1(4(2(5(x1)))))))))) (21)
3(0(5(5(1(4(5(1(0(2(2(x1))))))))))) 5(4(1(4(5(2(0(4(0(3(x1)))))))))) (22)
3(1(0(2(2(5(0(0(2(3(2(x1))))))))))) 4(0(5(2(4(0(5(3(1(2(x1)))))))))) (23)
3(1(3(5(3(3(5(1(2(2(5(x1))))))))))) 1(4(2(1(5(3(3(1(0(2(x1)))))))))) (24)
3(2(1(2(4(3(4(2(5(0(1(x1))))))))))) 5(1(3(5(1(1(0(4(2(3(x1)))))))))) (25)
3(3(1(5(4(5(1(2(4(4(3(x1))))))))))) 2(3(3(5(2(4(2(1(0(2(x1)))))))))) (26)
3(4(4(2(0(1(1(4(0(2(3(x1))))))))))) 5(5(2(2(2(0(4(5(5(2(x1)))))))))) (27)
3(4(5(5(0(4(0(3(0(0(5(x1))))))))))) 3(2(2(2(1(5(0(3(1(2(x1)))))))))) (28)
4(0(5(3(2(0(0(1(3(3(2(x1))))))))))) 2(0(3(2(5(4(5(3(5(1(x1)))))))))) (29)
4(0(5(4(1(0(1(2(2(3(5(x1))))))))))) 3(1(0(3(1(5(1(0(2(2(x1)))))))))) (30)
4(1(2(3(5(4(2(0(1(3(5(x1))))))))))) 3(5(4(2(1(5(2(4(5(5(x1)))))))))) (31)
4(1(2(5(3(0(5(2(5(2(0(x1))))))))))) 4(1(3(3(3(5(5(4(2(3(x1)))))))))) (32)
4(2(2(1(5(2(2(2(3(3(4(x1))))))))))) 5(3(0(1(3(0(0(0(1(2(x1)))))))))) (33)
4(5(2(2(1(1(1(1(2(3(1(x1))))))))))) 1(5(1(5(0(3(4(3(3(1(x1)))))))))) (35)
4(5(3(1(3(3(1(4(2(4(5(x1))))))))))) 2(1(5(5(2(2(2(1(1(2(x1)))))))))) (36)
5(0(5(0(1(3(0(0(4(4(4(x1))))))))))) 0(4(4(3(5(5(0(0(5(4(x1)))))))))) (38)
5(1(2(0(1(0(3(5(5(1(4(x1))))))))))) 5(1(5(3(5(0(4(5(0(0(x1)))))))))) (39)
5(2(3(2(4(2(1(5(3(5(1(x1))))))))))) 1(0(1(4(1(5(1(3(5(0(x1)))))))))) (40)
5(2(4(5(5(5(0(0(0(1(4(x1))))))))))) 1(3(0(1(4(0(5(0(1(3(x1)))))))))) (42)
5(3(1(0(3(1(4(4(2(3(0(x1))))))))))) 0(2(4(4(4(5(5(1(4(2(x1)))))))))) (43)
5(4(2(4(2(5(0(1(4(2(3(x1))))))))))) 4(0(1(4(5(3(3(1(0(2(x1)))))))))) (44)
5(5(4(3(3(4(2(3(0(0(4(x1))))))))))) 5(2(4(0(3(5(0(0(5(4(x1)))))))))) (45)
0(1(3(4(1(3(1(2(0(3(0(5(x1)))))))))))) 2(2(3(5(2(1(4(4(3(4(x1)))))))))) (46)
0(5(2(3(3(5(3(3(0(0(2(4(x1)))))))))))) 4(4(0(0(4(2(5(5(0(2(x1)))))))))) (48)
1(1(1(5(3(2(4(3(1(4(0(1(x1)))))))))))) 4(4(4(5(0(2(4(4(4(2(x1)))))))))) (49)
1(2(4(1(3(0(5(0(3(3(3(5(x1)))))))))))) 3(0(4(5(0(5(4(3(2(0(x1)))))))))) (50)
1(3(5(2(1(0(4(2(4(5(5(1(x1)))))))))))) 4(0(2(0(1(0(5(3(3(2(x1)))))))))) (51)
2(0(0(1(1(4(5(1(3(1(5(1(x1)))))))))))) 3(4(5(3(0(3(2(1(0(2(x1)))))))))) (52)
2(3(1(5(1(0(2(4(3(1(0(5(x1)))))))))))) 0(2(0(4(5(4(4(4(3(3(x1)))))))))) (53)
2(4(1(3(0(1(2(2(5(0(5(2(x1)))))))))))) 5(5(0(5(3(1(0(5(4(4(x1)))))))))) (54)
2(4(1(4(1(0(4(2(2(5(1(1(x1)))))))))))) 1(2(1(5(2(4(0(5(4(4(x1)))))))))) (55)
2(4(5(3(2(4(1(1(0(0(3(3(x1)))))))))))) 0(3(0(1(4(3(5(4(1(5(x1)))))))))) (56)
3(2(3(4(5(4(4(1(3(2(5(5(x1)))))))))))) 0(0(5(0(5(5(3(0(1(5(x1)))))))))) (57)
4(0(3(2(3(2(0(4(1(1(0(5(x1)))))))))))) 5(2(3(0(1(4(5(4(4(0(x1)))))))))) (58)
4(1(1(3(1(3(2(5(5(2(0(1(x1)))))))))))) 0(1(3(2(5(3(2(4(5(5(x1)))))))))) (59)
5(3(5(0(1(3(4(1(4(5(5(5(x1)))))))))))) 4(4(2(0(2(0(4(3(1(2(x1)))))))))) (61)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 294 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 1764 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[51(x1)] = x1 +
1
[52(x1)] = x1 +
34
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
3
[40(x1)] = x1 +
3
[41(x1)] = x1 +
0
[42(x1)] = x1 +
20
[43(x1)] = x1 +
10
[44(x1)] = x1 +
10
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
6
[20(x1)] = x1 +
34
[21(x1)] = x1 +
20
[22(x1)] = x1 +
0
[23(x1)] = x1 +
21
[24(x1)] = x1 +
0
[25(x1)] = x1 +
10
[10(x1)] = x1 +
1
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[13(x1)] = x1 +
20
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
6
[01(x1)] = x1 +
0
[02(x1)] = x1 +
21
[03(x1)] = x1 +
10
[04(x1)] = x1 +
1
[05(x1)] = x1 +
3
all of the following rules can be deleted.

There are 1692 ruless (increase limit for explicit display).

1.1.1.1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2158)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2159)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2160)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2161)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2162)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2163)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2164)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2165)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2166)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2167)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2168)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2169)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2170)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2171)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2172)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2173)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2174)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2175)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2176)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2177)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2178)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2179)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2180)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2181)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2182)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2183)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2184)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2185)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2186)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2187)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2188)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2189)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2190)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2191)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2192)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2193)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2194)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2195)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2196)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2197)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2198)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2199)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2200)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2201)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2202)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2203)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2204)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2205)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2206)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2207)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2208)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2209)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2210)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2211)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2212)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2213)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2214)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2215)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2216)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2217)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2218)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2219)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2220)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2221)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2222)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2223)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2224)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2225)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2226)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2227)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2228)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2229)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 216 ruless (increase limit for explicit display).

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[51(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[55(x1)] = x1 +
1
[40(x1)] = x1 +
0
[41(x1)] = x1 +
1
[42(x1)] = x1 +
1
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
1
[20(x1)] = x1 +
1
[21(x1)] = x1 +
1
[22(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
0
[12(x1)] = x1 +
0
[14(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
0
[02(x1)] = x1 +
1
[03(x1)] = x1 +
1
[04(x1)] = x1 +
0
[05(x1)] = x1 +
0
[50#(x1)] = x1 +
1
[51#(x1)] = x1 +
1
[52#(x1)] = x1 +
1
[53#(x1)] = x1 +
1
[54#(x1)] = x1 +
1
[55#(x1)] = x1 +
0
[00#(x1)] = x1 +
1
[01#(x1)] = x1 +
1
[02#(x1)] = x1 +
0
[03#(x1)] = x1 +
0
[04#(x1)] = x1 +
1
[05#(x1)] = x1 +
1
together with the usable rules
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2158)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2159)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2160)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2161)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2162)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(00(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(00(x1))))))))))))))))))) (2163)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2164)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2165)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2166)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2167)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2168)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(10(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(10(x1))))))))))))))))))) (2169)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2170)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2171)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2172)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2173)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2174)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(20(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(20(x1))))))))))))))))))) (2175)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2176)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2177)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2178)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2179)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2180)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(30(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(30(x1))))))))))))))))))) (2181)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2182)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2183)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2184)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2185)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2186)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(40(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(40(x1))))))))))))))))))) (2187)
05(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 05(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2188)
04(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 04(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2189)
03(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 03(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2190)
02(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 02(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2191)
01(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 01(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2192)
00(35(42(41(21(03(45(21(33(12(14(14(44(11(34(12(34(52(50(x1))))))))))))))))))) 00(35(42(41(21(03(45(21(33(12(14(44(11(14(34(12(34(52(50(x1))))))))))))))))))) (2193)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2194)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2195)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2196)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2197)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2198)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(02(x1))))))))))))))))))))))))))))))) (2199)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2200)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2201)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2202)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2203)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2204)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(12(x1))))))))))))))))))))))))))))))) (2205)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2206)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2207)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2208)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2209)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2210)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(22(x1))))))))))))))))))))))))))))))) (2211)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2212)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2213)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2214)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2215)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2216)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(32(x1))))))))))))))))))))))))))))))) (2217)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2218)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2219)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2220)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2221)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2222)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(42(x1))))))))))))))))))))))))))))))) (2223)
55(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 55(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2224)
54(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 54(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2225)
53(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 53(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2226)
52(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 52(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2227)
51(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 51(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2228)
50(20(03(35(02(55(40(11(44(41(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) 50(20(03(35(02(55(40(41(11(44(01(25(03(45(51(10(44(31(02(55(30(32(52(10(14(34(42(41(51(30(52(x1))))))))))))))))))))))))))))))) (2229)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

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

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.