Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/96642)

The rewrite relation of the following TRS is considered.

0(1(2(1(2(2(x1)))))) 0(3(4(3(5(2(x1)))))) (1)
4(0(1(0(3(0(x1)))))) 2(5(0(5(5(0(x1)))))) (2)
2(1(3(0(3(3(5(x1))))))) 2(5(2(2(5(5(2(x1))))))) (3)
3(3(0(0(0(5(2(x1))))))) 5(3(3(1(2(5(2(x1))))))) (4)
3(3(3(0(1(1(0(x1))))))) 5(3(3(0(2(1(0(x1))))))) (5)
4(0(2(3(1(4(1(x1))))))) 1(4(3(2(5(4(x1)))))) (6)
4(1(5(0(0(5(2(1(3(x1))))))))) 4(5(0(3(5(2(2(2(3(x1))))))))) (7)
5(2(5(1(5(0(3(0(4(2(x1)))))))))) 3(3(2(5(1(3(3(5(0(2(x1)))))))))) (8)
2(1(4(2(2(0(3(0(1(0(5(x1))))))))))) 2(2(5(4(2(4(1(4(3(1(x1)))))))))) (9)
3(3(0(1(3(4(2(1(1(2(1(x1))))))))))) 5(2(4(4(3(5(3(5(5(1(1(x1))))))))))) (10)
5(3(2(3(5(0(4(0(2(3(4(5(x1)))))))))))) 3(5(2(1(1(5(2(1(0(5(4(x1))))))))))) (11)
5(2(3(5(5(0(0(0(3(4(0(2(5(x1))))))))))))) 5(5(5(2(4(3(5(1(1(2(5(0(x1)))))))))))) (12)
5(5(3(4(3(2(4(0(5(2(1(2(2(x1))))))))))))) 5(5(4(4(0(1(0(1(3(1(4(2(x1)))))))))))) (13)
1(4(5(1(5(0(1(1(1(0(3(2(3(3(1(x1))))))))))))))) 1(1(3(2(3(4(3(5(4(4(3(5(3(1(x1)))))))))))))) (14)
3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1))))))))))))))) 3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1))))))))))))))) (15)
3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1)))))))))))))))) 3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1)))))))))))))))) (16)
5(0(2(5(5(1(3(2(5(2(0(4(4(0(4(1(x1)))))))))))))))) 5(1(1(0(0(2(2(2(1(3(4(3(2(5(4(x1))))))))))))))) (17)
3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1)))))))))))))))))) 3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1)))))))))))))))))) (18)
4(5(3(3(2(5(5(1(3(5(1(5(0(0(2(5(5(1(x1)))))))))))))))))) 4(5(5(2(2(3(0(3(3(0(4(1(3(1(1(1(x1)))))))))))))))) (19)
0(0(5(3(2(0(5(1(3(3(5(2(0(2(5(3(4(4(5(x1))))))))))))))))))) 0(0(5(3(5(5(0(1(3(5(0(1(3(1(3(4(2(4(x1)))))))))))))))))) (20)
2(5(1(2(2(3(2(3(2(1(4(2(0(5(5(1(0(3(3(x1))))))))))))))))))) 2(3(0(4(5(0(4(3(1(3(2(0(4(1(2(4(1(3(x1)))))))))))))))))) (21)
3(2(1(3(3(1(5(1(2(0(2(0(4(1(4(2(5(5(1(5(x1)))))))))))))))))))) 5(1(0(1(3(1(1(4(2(0(0(2(3(2(5(3(5(1(2(x1))))))))))))))))))) (22)
3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1)))))))))))))))))))) 3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1)))))))))))))))))))) (23)
0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1))))))))))))))))))))) 2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1))))))))))))))))))))) (24)
1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1))))))))))))))))))))) 3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1))))))))))))))))))))) (25)

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 +
1
[4(x1)] = x1 +
1
[3(x1)] = x1 +
1
[2(x1)] = x1 +
1
[1(x1)] = x1 +
1
[0(x1)] = x1 +
1
all of the following rules can be deleted.
4(0(2(3(1(4(1(x1))))))) 1(4(3(2(5(4(x1)))))) (6)
2(1(4(2(2(0(3(0(1(0(5(x1))))))))))) 2(2(5(4(2(4(1(4(3(1(x1)))))))))) (9)
5(3(2(3(5(0(4(0(2(3(4(5(x1)))))))))))) 3(5(2(1(1(5(2(1(0(5(4(x1))))))))))) (11)
5(2(3(5(5(0(0(0(3(4(0(2(5(x1))))))))))))) 5(5(5(2(4(3(5(1(1(2(5(0(x1)))))))))))) (12)
5(5(3(4(3(2(4(0(5(2(1(2(2(x1))))))))))))) 5(5(4(4(0(1(0(1(3(1(4(2(x1)))))))))))) (13)
1(4(5(1(5(0(1(1(1(0(3(2(3(3(1(x1))))))))))))))) 1(1(3(2(3(4(3(5(4(4(3(5(3(1(x1)))))))))))))) (14)
5(0(2(5(5(1(3(2(5(2(0(4(4(0(4(1(x1)))))))))))))))) 5(1(1(0(0(2(2(2(1(3(4(3(2(5(4(x1))))))))))))))) (17)
4(5(3(3(2(5(5(1(3(5(1(5(0(0(2(5(5(1(x1)))))))))))))))))) 4(5(5(2(2(3(0(3(3(0(4(1(3(1(1(1(x1)))))))))))))))) (19)
0(0(5(3(2(0(5(1(3(3(5(2(0(2(5(3(4(4(5(x1))))))))))))))))))) 0(0(5(3(5(5(0(1(3(5(0(1(3(1(3(4(2(4(x1)))))))))))))))))) (20)
2(5(1(2(2(3(2(3(2(1(4(2(0(5(5(1(0(3(3(x1))))))))))))))))))) 2(3(0(4(5(0(4(3(1(3(2(0(4(1(2(4(1(3(x1)))))))))))))))))) (21)
3(2(1(3(3(1(5(1(2(0(2(0(4(1(4(2(5(5(1(5(x1)))))))))))))))))))) 5(1(0(1(3(1(1(4(2(0(0(2(3(2(5(3(5(1(2(x1))))))))))))))))))) (22)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS
5(0(1(2(1(2(2(x1))))))) 5(0(3(4(3(5(2(x1))))))) (26)
5(4(0(1(0(3(0(x1))))))) 5(2(5(0(5(5(0(x1))))))) (27)
5(2(1(3(0(3(3(5(x1)))))))) 5(2(5(2(2(5(5(2(x1)))))))) (28)
5(3(3(0(0(0(5(2(x1)))))))) 5(5(3(3(1(2(5(2(x1)))))))) (29)
5(3(3(3(0(1(1(0(x1)))))))) 5(5(3(3(0(2(1(0(x1)))))))) (30)
5(4(1(5(0(0(5(2(1(3(x1)))))))))) 5(4(5(0(3(5(2(2(2(3(x1)))))))))) (31)
5(5(2(5(1(5(0(3(0(4(2(x1))))))))))) 5(3(3(2(5(1(3(3(5(0(2(x1))))))))))) (32)
5(3(3(0(1(3(4(2(1(1(2(1(x1)))))))))))) 5(5(2(4(4(3(5(3(5(5(1(1(x1)))))))))))) (33)
5(3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1)))))))))))))))) 5(3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1)))))))))))))))) (34)
5(3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1))))))))))))))))) 5(3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1))))))))))))))))) (35)
5(3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1))))))))))))))))))) 5(3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1))))))))))))))))))) (36)
5(3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1))))))))))))))))))))) 5(3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1))))))))))))))))))))) (37)
5(0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1)))))))))))))))))))))) 5(2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1)))))))))))))))))))))) (38)
5(1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1)))))))))))))))))))))) 5(3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1)))))))))))))))))))))) (39)
4(0(1(2(1(2(2(x1))))))) 4(0(3(4(3(5(2(x1))))))) (40)
4(4(0(1(0(3(0(x1))))))) 4(2(5(0(5(5(0(x1))))))) (41)
4(2(1(3(0(3(3(5(x1)))))))) 4(2(5(2(2(5(5(2(x1)))))))) (42)
4(3(3(0(0(0(5(2(x1)))))))) 4(5(3(3(1(2(5(2(x1)))))))) (43)
4(3(3(3(0(1(1(0(x1)))))))) 4(5(3(3(0(2(1(0(x1)))))))) (44)
4(4(1(5(0(0(5(2(1(3(x1)))))))))) 4(4(5(0(3(5(2(2(2(3(x1)))))))))) (45)
4(5(2(5(1(5(0(3(0(4(2(x1))))))))))) 4(3(3(2(5(1(3(3(5(0(2(x1))))))))))) (46)
4(3(3(0(1(3(4(2(1(1(2(1(x1)))))))))))) 4(5(2(4(4(3(5(3(5(5(1(1(x1)))))))))))) (47)
4(3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1)))))))))))))))) 4(3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1)))))))))))))))) (48)
4(3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1))))))))))))))))) 4(3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1))))))))))))))))) (49)
4(3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1))))))))))))))))))) 4(3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1))))))))))))))))))) (50)
4(3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1))))))))))))))))))))) 4(3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1))))))))))))))))))))) (51)
4(0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1)))))))))))))))))))))) 4(2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1)))))))))))))))))))))) (52)
4(1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1)))))))))))))))))))))) 4(3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1)))))))))))))))))))))) (53)
3(0(1(2(1(2(2(x1))))))) 3(0(3(4(3(5(2(x1))))))) (54)
3(4(0(1(0(3(0(x1))))))) 3(2(5(0(5(5(0(x1))))))) (55)
3(2(1(3(0(3(3(5(x1)))))))) 3(2(5(2(2(5(5(2(x1)))))))) (56)
3(3(3(0(0(0(5(2(x1)))))))) 3(5(3(3(1(2(5(2(x1)))))))) (57)
3(3(3(3(0(1(1(0(x1)))))))) 3(5(3(3(0(2(1(0(x1)))))))) (58)
3(4(1(5(0(0(5(2(1(3(x1)))))))))) 3(4(5(0(3(5(2(2(2(3(x1)))))))))) (59)
3(5(2(5(1(5(0(3(0(4(2(x1))))))))))) 3(3(3(2(5(1(3(3(5(0(2(x1))))))))))) (60)
3(3(3(0(1(3(4(2(1(1(2(1(x1)))))))))))) 3(5(2(4(4(3(5(3(5(5(1(1(x1)))))))))))) (61)
3(3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1)))))))))))))))) 3(3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1)))))))))))))))) (62)
3(3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1))))))))))))))))) 3(3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1))))))))))))))))) (63)
3(3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1))))))))))))))))))) 3(3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1))))))))))))))))))) (64)
3(3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1))))))))))))))))))))) 3(3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1))))))))))))))))))))) (65)
3(0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1)))))))))))))))))))))) 3(2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1)))))))))))))))))))))) (66)
3(1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1)))))))))))))))))))))) 3(3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1)))))))))))))))))))))) (67)
2(0(1(2(1(2(2(x1))))))) 2(0(3(4(3(5(2(x1))))))) (68)
2(4(0(1(0(3(0(x1))))))) 2(2(5(0(5(5(0(x1))))))) (69)
2(2(1(3(0(3(3(5(x1)))))))) 2(2(5(2(2(5(5(2(x1)))))))) (70)
2(3(3(0(0(0(5(2(x1)))))))) 2(5(3(3(1(2(5(2(x1)))))))) (71)
2(3(3(3(0(1(1(0(x1)))))))) 2(5(3(3(0(2(1(0(x1)))))))) (72)
2(4(1(5(0(0(5(2(1(3(x1)))))))))) 2(4(5(0(3(5(2(2(2(3(x1)))))))))) (73)
2(5(2(5(1(5(0(3(0(4(2(x1))))))))))) 2(3(3(2(5(1(3(3(5(0(2(x1))))))))))) (74)
2(3(3(0(1(3(4(2(1(1(2(1(x1)))))))))))) 2(5(2(4(4(3(5(3(5(5(1(1(x1)))))))))))) (75)
2(3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1)))))))))))))))) 2(3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1)))))))))))))))) (76)
2(3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1))))))))))))))))) 2(3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1))))))))))))))))) (77)
2(3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1))))))))))))))))))) 2(3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1))))))))))))))))))) (78)
2(3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1))))))))))))))))))))) 2(3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1))))))))))))))))))))) (79)
2(0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1)))))))))))))))))))))) 2(2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1)))))))))))))))))))))) (80)
2(1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1)))))))))))))))))))))) 2(3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1)))))))))))))))))))))) (81)
1(0(1(2(1(2(2(x1))))))) 1(0(3(4(3(5(2(x1))))))) (82)
1(4(0(1(0(3(0(x1))))))) 1(2(5(0(5(5(0(x1))))))) (83)
1(2(1(3(0(3(3(5(x1)))))))) 1(2(5(2(2(5(5(2(x1)))))))) (84)
1(3(3(0(0(0(5(2(x1)))))))) 1(5(3(3(1(2(5(2(x1)))))))) (85)
1(3(3(3(0(1(1(0(x1)))))))) 1(5(3(3(0(2(1(0(x1)))))))) (86)
1(4(1(5(0(0(5(2(1(3(x1)))))))))) 1(4(5(0(3(5(2(2(2(3(x1)))))))))) (87)
1(5(2(5(1(5(0(3(0(4(2(x1))))))))))) 1(3(3(2(5(1(3(3(5(0(2(x1))))))))))) (88)
1(3(3(0(1(3(4(2(1(1(2(1(x1)))))))))))) 1(5(2(4(4(3(5(3(5(5(1(1(x1)))))))))))) (89)
1(3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1)))))))))))))))) 1(3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1)))))))))))))))) (90)
1(3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1))))))))))))))))) 1(3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1))))))))))))))))) (91)
1(3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1))))))))))))))))))) 1(3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1))))))))))))))))))) (92)
1(3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1))))))))))))))))))))) 1(3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1))))))))))))))))))))) (93)
1(0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1)))))))))))))))))))))) 1(2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1)))))))))))))))))))))) (94)
1(1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1)))))))))))))))))))))) 1(3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1)))))))))))))))))))))) (95)
0(0(1(2(1(2(2(x1))))))) 0(0(3(4(3(5(2(x1))))))) (96)
0(4(0(1(0(3(0(x1))))))) 0(2(5(0(5(5(0(x1))))))) (97)
0(2(1(3(0(3(3(5(x1)))))))) 0(2(5(2(2(5(5(2(x1)))))))) (98)
0(3(3(0(0(0(5(2(x1)))))))) 0(5(3(3(1(2(5(2(x1)))))))) (99)
0(3(3(3(0(1(1(0(x1)))))))) 0(5(3(3(0(2(1(0(x1)))))))) (100)
0(4(1(5(0(0(5(2(1(3(x1)))))))))) 0(4(5(0(3(5(2(2(2(3(x1)))))))))) (101)
0(5(2(5(1(5(0(3(0(4(2(x1))))))))))) 0(3(3(2(5(1(3(3(5(0(2(x1))))))))))) (102)
0(3(3(0(1(3(4(2(1(1(2(1(x1)))))))))))) 0(5(2(4(4(3(5(3(5(5(1(1(x1)))))))))))) (103)
0(3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1)))))))))))))))) 0(3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1)))))))))))))))) (104)
0(3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1))))))))))))))))) 0(3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1))))))))))))))))) (105)
0(3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1))))))))))))))))))) 0(3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1))))))))))))))))))) (106)
0(3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1))))))))))))))))))))) 0(3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1))))))))))))))))))))) (107)
0(0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1)))))))))))))))))))))) 0(2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1)))))))))))))))))))))) (108)
0(1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1)))))))))))))))))))))) 0(3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1)))))))))))))))))))))) (109)

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 504 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 +
0
[52(x1)] = x1 +
1
[53(x1)] = x1 +
0
[54(x1)] = x1 +
6
[55(x1)] = x1 +
0
[40(x1)] = x1 +
1
[41(x1)] = x1 +
6
[42(x1)] = x1 +
6
[43(x1)] = x1 +
7
[44(x1)] = x1 +
24
[45(x1)] = x1 +
6
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
6
[34(x1)] = x1 +
7
[35(x1)] = x1 +
6
[20(x1)] = x1 +
1
[21(x1)] = x1 +
6
[22(x1)] = x1 +
6
[23(x1)] = x1 +
0
[24(x1)] = x1 +
6
[25(x1)] = x1 +
6
[10(x1)] = x1 +
7
[11(x1)] = x1 +
6
[12(x1)] = x1 +
6
[13(x1)] = x1 +
0
[14(x1)] = x1 +
6
[15(x1)] = x1 +
1
[00(x1)] = x1 +
6
[01(x1)] = x1 +
7
[02(x1)] = x1 +
0
[03(x1)] = x1 +
6
[04(x1)] = x1 +
14
[05(x1)] = x1 +
7
all of the following rules can be deleted.

There are 504 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.