Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/26986)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
14
[4(x1)] = x1 +
8
[3(x1)] = x1 +
14
[2(x1)] = x1 +
15
[1(x1)] = x1 +
14
[0(x1)] = x1 +
14
all of the following rules can be deleted.
0(0(0(3(2(4(3(2(5(2(1(x1))))))))))) 0(4(1(0(5(5(2(4(0(3(x1)))))))))) (8)
0(0(1(1(1(5(2(2(5(0(3(x1))))))))))) 1(2(5(3(0(5(1(1(1(5(x1)))))))))) (9)
0(2(1(4(4(4(1(3(2(5(1(x1))))))))))) 1(4(1(1(0(0(2(3(3(5(x1)))))))))) (10)
0(2(2(2(3(2(2(3(4(2(0(x1))))))))))) 1(2(2(5(0(2(3(5(2(2(x1)))))))))) (11)
0(3(0(1(5(5(5(3(2(0(1(x1))))))))))) 2(4(2(0(4(4(4(3(4(0(x1)))))))))) (12)
0(3(0(2(4(0(2(4(5(4(2(x1))))))))))) 2(5(3(3(3(5(5(3(3(4(x1)))))))))) (13)
0(4(3(2(3(4(3(4(2(0(0(x1))))))))))) 3(0(2(0(3(3(5(4(5(3(x1)))))))))) (15)
0(5(4(3(0(0(3(1(4(0(1(x1))))))))))) 0(4(1(2(3(1(3(1(2(5(x1)))))))))) (16)
1(0(2(1(5(5(0(4(4(4(4(x1))))))))))) 2(4(3(3(4(4(4(0(4(5(x1)))))))))) (17)
1(0(2(3(5(3(2(0(3(5(3(x1))))))))))) 1(2(5(2(4(5(1(3(2(5(x1)))))))))) (18)
1(0(3(1(1(5(5(5(1(2(4(x1))))))))))) 3(0(1(5(3(4(1(3(2(3(x1)))))))))) (19)
1(2(1(5(3(3(3(0(5(1(0(x1))))))))))) 5(0(2(1(5(5(5(1(1(3(x1)))))))))) (20)
1(2(2(5(2(0(3(3(4(5(1(x1))))))))))) 2(2(3(1(1(5(5(0(3(4(x1)))))))))) (21)
1(3(3(2(3(5(4(4(0(2(5(x1))))))))))) 3(2(4(0(3(2(1(4(5(0(x1)))))))))) (22)
1(3(5(2(2(5(1(0(1(0(2(x1))))))))))) 0(5(0(0(4(0(1(5(4(4(x1)))))))))) (23)
1(4(2(1(1(2(3(4(0(1(2(x1))))))))))) 5(0(4(3(1(4(3(0(3(0(x1)))))))))) (24)
1(4(2(3(0(3(3(0(0(2(5(x1))))))))))) 3(4(1(1(0(2(0(5(3(1(x1)))))))))) (25)
1(5(2(4(5(5(5(4(0(3(2(x1))))))))))) 0(4(1(4(0(2(3(5(0(4(x1)))))))))) (26)
2(0(5(2(3(3(1(3(1(5(0(x1))))))))))) 2(1(2(4(1(0(2(5(4(5(x1)))))))))) (27)
2(1(1(0(1(0(2(4(5(0(4(x1))))))))))) 0(1(1(3(0(0(5(1(4(0(x1)))))))))) (28)
2(3(1(4(4(3(5(1(5(2(3(x1))))))))))) 5(2(3(0(5(1(2(4(1(2(x1)))))))))) (29)
2(5(0(1(2(4(4(3(5(3(5(x1))))))))))) 1(0(5(3(0(2(3(2(4(3(x1)))))))))) (31)
2(5(3(1(1(5(4(2(3(0(2(x1))))))))))) 4(0(1(4(5(3(0(0(5(3(x1)))))))))) (32)
2(5(4(2(4(1(5(0(3(5(5(x1))))))))))) 4(4(4(0(2(0(0(1(5(5(x1)))))))))) (33)
3(2(0(4(5(1(3(5(0(4(1(x1))))))))))) 0(4(4(0(0(0(3(3(5(2(x1)))))))))) (34)
3(3(1(0(2(0(2(3(2(5(1(x1))))))))))) 2(4(2(5(2(5(4(4(3(2(x1)))))))))) (35)
3(3(2(0(1(2(5(5(4(2(0(x1))))))))))) 1(5(0(3(2(3(2(1(5(2(x1)))))))))) (36)
3(3(4(0(5(0(4(2(4(4(0(x1))))))))))) 4(3(1(0(2(3(0(4(5(5(x1)))))))))) (37)
4(2(1(5(2(1(5(4(0(0(2(x1))))))))))) 3(0(3(2(4(5(1(5(1(0(x1)))))))))) (39)
4(2(2(4(1(4(1(3(2(3(4(x1))))))))))) 4(2(4(4(2(2(0(5(2(4(x1)))))))))) (40)
4(3(5(4(3(2(0(1(4(0(0(x1))))))))))) 0(0(2(4(1(5(5(1(1(3(x1)))))))))) (41)
4(4(3(0(2(5(0(0(5(5(3(x1))))))))))) 5(5(2(2(5(0(4(5(3(4(x1)))))))))) (42)
4(4(5(5(2(1(1(5(2(5(5(x1))))))))))) 3(3(0(3(5(0(3(4(1(2(x1)))))))))) (43)
4(5(1(5(2(5(5(5(3(0(5(x1))))))))))) 5(4(5(3(1(0(1(1(2(2(x1)))))))))) (44)
5(1(3(1(2(0(0(5(2(3(4(x1))))))))))) 3(2(5(1(3(3(1(5(3(0(x1)))))))))) (45)
5(2(3(5(1(5(2(0(3(1(0(x1))))))))))) 5(0(5(0(2(5(3(0(2(2(x1)))))))))) (46)
5(2(5(4(5(2(1(2(0(4(3(x1))))))))))) 2(2(4(2(0(5(2(1(2(3(x1)))))))))) (47)
5(4(1(2(0(5(3(2(0(0(3(x1))))))))))) 5(5(5(4(0(3(4(0(0(4(x1)))))))))) (48)
5(4(5(3(1(5(4(4(5(0(0(x1))))))))))) 3(1(5(2(4(5(4(3(4(5(x1)))))))))) (49)
5(5(1(4(2(3(1(1(2(2(3(x1))))))))))) 5(0(2(2(4(4(3(0(2(3(x1)))))))))) (50)
5(5(5(2(3(2(2(5(3(5(5(x1))))))))))) 2(4(2(0(0(2(5(1(1(5(x1)))))))))) (51)
0(0(1(2(3(1(1(1(1(2(3(2(x1)))))))))))) 4(4(4(1(3(4(1(3(2(1(x1)))))))))) (52)
0(0(2(0(2(5(5(5(3(2(2(1(x1)))))))))))) 3(1(0(0(2(4(3(3(3(4(x1)))))))))) (53)
0(4(4(2(1(5(2(4(4(0(3(2(x1)))))))))))) 4(5(1(2(0(1(3(0(0(0(x1)))))))))) (54)
0(4(5(5(4(3(1(1(4(5(0(5(x1)))))))))))) 1(3(3(2(4(1(3(1(1(2(x1)))))))))) (55)
2(4(3(5(5(1(2(5(5(3(2(1(x1)))))))))))) 5(0(3(3(3(0(3(4(0(1(x1)))))))))) (57)
3(5(3(5(4(3(2(3(0(4(5(0(x1)))))))))))) 1(4(0(0(1(1(4(4(1(4(x1)))))))))) (58)
4(3(3(2(0(0(5(0(3(2(1(3(x1)))))))))))) 0(3(4(5(3(2(4(0(0(5(x1)))))))))) (59)
4(5(3(2(3(3(2(2(3(3(4(2(x1)))))))))))) 4(2(2(4(0(0(0(5(4(4(x1)))))))))) (60)
5(1(2(3(1(4(3(5(4(2(1(2(x1)))))))))))) 0(0(0(4(1(1(4(4(0(0(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 258 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,5}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 6):

[5(x1)] = 6x1 + 0
[4(x1)] = 6x1 + 1
[3(x1)] = 6x1 + 2
[2(x1)] = 6x1 + 3
[1(x1)] = 6x1 + 4
[0(x1)] = 6x1 + 5

We obtain the labeled TRS

There are 1548 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
13
[51(x1)] = x1 +
0
[52(x1)] = x1 +
2
[53(x1)] = x1 +
5
[54(x1)] = x1 +
2
[55(x1)] = x1 +
0
[40(x1)] = x1 +
5
[41(x1)] = x1 +
1
[42(x1)] = x1 +
2
[43(x1)] = x1 +
5
[44(x1)] = x1 +
0
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
5
[33(x1)] = x1 +
0
[34(x1)] = x1 +
0
[35(x1)] = x1 +
2
[20(x1)] = x1 +
0
[21(x1)] = x1 +
13
[22(x1)] = x1 +
5
[23(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
2
[10(x1)] = x1 +
0
[11(x1)] = x1 +
2
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
0
[15(x1)] = x1 +
2
[00(x1)] = x1 +
2
[01(x1)] = x1 +
0
[02(x1)] = x1 +
0
[03(x1)] = x1 +
2
[04(x1)] = x1 +
5
[05(x1)] = x1 +
1
all of the following rules can be deleted.

There are 1548 ruless (increase limit for explicit display).

1.1.1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.