Certification Problem

Input (TPDB SRS_Standard/Trafo_06/un18)

The rewrite relation of the following TRS is considered.

b(b(a(a(a(b(x1)))))) b(a(a(a(b(a(b(x1))))))) (1)
b(b(x1)) b(a(b(a(b(a(b(x1))))))) (2)
b(a(b(a(a(a(b(a(b(x1))))))))) b(b(a(a(b(x1))))) (3)
b(a(a(b(x1)))) b(a(a(a(b(x1))))) (4)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Closure Under Flat Contexts

Using the flat contexts

{b(), a()}

We obtain the transformed TRS
b(b(b(a(a(a(b(x1))))))) b(b(a(a(a(b(a(b(x1)))))))) (5)
b(b(b(x1))) b(b(a(b(a(b(a(b(x1)))))))) (6)
b(b(a(b(a(a(a(b(a(b(x1)))))))))) b(b(b(a(a(b(x1)))))) (7)
b(b(a(a(b(x1))))) b(b(a(a(a(b(x1)))))) (8)
a(b(b(a(a(a(b(x1))))))) a(b(a(a(a(b(a(b(x1)))))))) (9)
a(b(b(x1))) a(b(a(b(a(b(a(b(x1)))))))) (10)
a(b(a(b(a(a(a(b(a(b(x1)))))))))) a(b(b(a(a(b(x1)))))) (11)
a(b(a(a(b(x1))))) a(b(a(a(a(b(x1)))))) (12)

1.1 Closure Under Flat Contexts

Using the flat contexts

{b(), a()}

We obtain the transformed TRS
b(b(b(b(a(a(a(b(x1)))))))) b(b(b(a(a(a(b(a(b(x1))))))))) (13)
b(b(b(b(x1)))) b(b(b(a(b(a(b(a(b(x1))))))))) (14)
b(b(b(a(b(a(a(a(b(a(b(x1))))))))))) b(b(b(b(a(a(b(x1))))))) (15)
b(b(b(a(a(b(x1)))))) b(b(b(a(a(a(b(x1))))))) (16)
b(a(b(b(a(a(a(b(x1)))))))) b(a(b(a(a(a(b(a(b(x1))))))))) (17)
b(a(b(b(x1)))) b(a(b(a(b(a(b(a(b(x1))))))))) (18)
b(a(b(a(b(a(a(a(b(a(b(x1))))))))))) b(a(b(b(a(a(b(x1))))))) (19)
b(a(b(a(a(b(x1)))))) b(a(b(a(a(a(b(x1))))))) (20)
a(b(b(b(a(a(a(b(x1)))))))) a(b(b(a(a(a(b(a(b(x1))))))))) (21)
a(b(b(b(x1)))) a(b(b(a(b(a(b(a(b(x1))))))))) (22)
a(b(b(a(b(a(a(a(b(a(b(x1))))))))))) a(b(b(b(a(a(b(x1))))))) (23)
a(b(b(a(a(b(x1)))))) a(b(b(a(a(a(b(x1))))))) (24)
a(a(b(b(a(a(a(b(x1)))))))) a(a(b(a(a(a(b(a(b(x1))))))))) (25)
a(a(b(b(x1)))) a(a(b(a(b(a(b(a(b(x1))))))))) (26)
a(a(b(a(b(a(a(a(b(a(b(x1))))))))))) a(a(b(b(a(a(b(x1))))))) (27)
a(a(b(a(a(b(x1)))))) a(a(b(a(a(a(b(x1))))))) (28)

1.1.1 Closure Under Flat Contexts

Using the flat contexts

{b(), a()}

We obtain the transformed TRS
b(b(b(b(b(a(a(a(b(x1))))))))) b(b(b(b(a(a(a(b(a(b(x1)))))))))) (29)
b(b(b(b(b(x1))))) b(b(b(b(a(b(a(b(a(b(x1)))))))))) (30)
b(b(b(b(a(b(a(a(a(b(a(b(x1)))))))))))) b(b(b(b(b(a(a(b(x1)))))))) (31)
b(b(b(b(a(a(b(x1))))))) b(b(b(b(a(a(a(b(x1)))))))) (32)
b(b(a(b(b(a(a(a(b(x1))))))))) b(b(a(b(a(a(a(b(a(b(x1)))))))))) (33)
b(b(a(b(b(x1))))) b(b(a(b(a(b(a(b(a(b(x1)))))))))) (34)
b(b(a(b(a(b(a(a(a(b(a(b(x1)))))))))))) b(b(a(b(b(a(a(b(x1)))))))) (35)
b(b(a(b(a(a(b(x1))))))) b(b(a(b(a(a(a(b(x1)))))))) (36)
b(a(b(b(b(a(a(a(b(x1))))))))) b(a(b(b(a(a(a(b(a(b(x1)))))))))) (37)
b(a(b(b(b(x1))))) b(a(b(b(a(b(a(b(a(b(x1)))))))))) (38)
b(a(b(b(a(b(a(a(a(b(a(b(x1)))))))))))) b(a(b(b(b(a(a(b(x1)))))))) (39)
b(a(b(b(a(a(b(x1))))))) b(a(b(b(a(a(a(b(x1)))))))) (40)
b(a(a(b(b(a(a(a(b(x1))))))))) b(a(a(b(a(a(a(b(a(b(x1)))))))))) (41)
b(a(a(b(b(x1))))) b(a(a(b(a(b(a(b(a(b(x1)))))))))) (42)
b(a(a(b(a(b(a(a(a(b(a(b(x1)))))))))))) b(a(a(b(b(a(a(b(x1)))))))) (43)
b(a(a(b(a(a(b(x1))))))) b(a(a(b(a(a(a(b(x1)))))))) (44)
a(b(b(b(b(a(a(a(b(x1))))))))) a(b(b(b(a(a(a(b(a(b(x1)))))))))) (45)
a(b(b(b(b(x1))))) a(b(b(b(a(b(a(b(a(b(x1)))))))))) (46)
a(b(b(b(a(b(a(a(a(b(a(b(x1)))))))))))) a(b(b(b(b(a(a(b(x1)))))))) (47)
a(b(b(b(a(a(b(x1))))))) a(b(b(b(a(a(a(b(x1)))))))) (48)
a(b(a(b(b(a(a(a(b(x1))))))))) a(b(a(b(a(a(a(b(a(b(x1)))))))))) (49)
a(b(a(b(b(x1))))) a(b(a(b(a(b(a(b(a(b(x1)))))))))) (50)
a(b(a(b(a(b(a(a(a(b(a(b(x1)))))))))))) a(b(a(b(b(a(a(b(x1)))))))) (51)
a(b(a(b(a(a(b(x1))))))) a(b(a(b(a(a(a(b(x1)))))))) (52)
a(a(b(b(b(a(a(a(b(x1))))))))) a(a(b(b(a(a(a(b(a(b(x1)))))))))) (53)
a(a(b(b(b(x1))))) a(a(b(b(a(b(a(b(a(b(x1)))))))))) (54)
a(a(b(b(a(b(a(a(a(b(a(b(x1)))))))))))) a(a(b(b(b(a(a(b(x1)))))))) (55)
a(a(b(b(a(a(b(x1))))))) a(a(b(b(a(a(a(b(x1)))))))) (56)
a(a(a(b(b(a(a(a(b(x1))))))))) a(a(a(b(a(a(a(b(a(b(x1)))))))))) (57)
a(a(a(b(b(x1))))) a(a(a(b(a(b(a(b(a(b(x1)))))))))) (58)
a(a(a(b(a(b(a(a(a(b(a(b(x1)))))))))))) a(a(a(b(b(a(a(b(x1)))))))) (59)
a(a(a(b(a(a(b(x1))))))) a(a(a(b(a(a(a(b(x1)))))))) (60)

1.1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,7}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 8):

[b(x1)] = 2x1 + 0
[a(x1)] = 2x1 + 1

We obtain the labeled TRS

There are 256 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[b0(x1)] = x1 +
1
[b4(x1)] = x1 +
1
[b2(x1)] = x1 +
1
[b6(x1)] = x1 +
0
[b1(x1)] = x1 +
0
[b5(x1)] = x1 +
0
[b3(x1)] = x1 +
0
[b7(x1)] = x1 +
0
[a0(x1)] = x1 +
0
[a4(x1)] = x1 +
0
[a2(x1)] = x1 +
0
[a6(x1)] = x1 +
0
[a1(x1)] = x1 +
0
[a5(x1)] = x1 +
0
[a3(x1)] = x1 +
0
all of the following rules can be deleted.
b0(b0(b4(b6(b7(a3(a1(a0(b0(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (61)
b0(b0(b4(b6(b7(a3(a1(a0(b4(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (62)
b0(b0(b4(b6(b7(a3(a1(a4(b2(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (63)
b0(b0(b4(b6(b7(a3(a1(a4(b6(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (64)
b0(b0(b4(b6(b7(a3(a5(a2(b1(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (65)
b0(b0(b4(b6(b7(a3(a5(a2(b5(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (66)
b0(b0(b4(b6(b7(a3(a5(a6(b3(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (67)
b0(b0(b4(b6(b7(a3(a5(a6(b7(x1))))))))) b0(b4(b6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (68)
b1(a0(b4(b6(b7(a3(a1(a0(b0(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (77)
b1(a0(b4(b6(b7(a3(a1(a0(b4(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (78)
b1(a0(b4(b6(b7(a3(a1(a4(b2(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (79)
b1(a0(b4(b6(b7(a3(a1(a4(b6(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (80)
b1(a0(b4(b6(b7(a3(a5(a2(b1(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (81)
b1(a0(b4(b6(b7(a3(a5(a2(b5(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (82)
b1(a0(b4(b6(b7(a3(a5(a6(b3(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (83)
b1(a0(b4(b6(b7(a3(a5(a6(b7(x1))))))))) b1(a4(b6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (84)
a0(b0(b4(b6(b7(a3(a1(a0(b0(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (93)
a0(b0(b4(b6(b7(a3(a1(a0(b4(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (94)
a0(b0(b4(b6(b7(a3(a1(a4(b2(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (95)
a0(b0(b4(b6(b7(a3(a1(a4(b6(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (96)
a0(b0(b4(b6(b7(a3(a5(a2(b1(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (97)
a0(b0(b4(b6(b7(a3(a5(a2(b5(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (98)
a0(b0(b4(b6(b7(a3(a5(a6(b3(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (99)
a0(b0(b4(b6(b7(a3(a5(a6(b7(x1))))))))) a0(b4(b6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (100)
a1(a0(b4(b6(b7(a3(a1(a0(b0(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (109)
a1(a0(b4(b6(b7(a3(a1(a0(b4(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (110)
a1(a0(b4(b6(b7(a3(a1(a4(b2(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (111)
a1(a0(b4(b6(b7(a3(a1(a4(b6(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (112)
a1(a0(b4(b6(b7(a3(a5(a2(b1(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (113)
a1(a0(b4(b6(b7(a3(a5(a2(b5(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (114)
a1(a0(b4(b6(b7(a3(a5(a6(b3(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (115)
a1(a0(b4(b6(b7(a3(a5(a6(b7(x1))))))))) a1(a4(b6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (116)
b0(b0(b0(b0(b0(x1))))) b0(b4(b2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (125)
b0(b0(b0(b0(b4(x1))))) b0(b4(b2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (126)
b0(b0(b0(b4(b2(x1))))) b0(b4(b2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (127)
b0(b0(b0(b4(b6(x1))))) b0(b4(b2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (128)
b0(b0(b4(b2(b1(x1))))) b0(b4(b2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (129)
b0(b0(b4(b2(b5(x1))))) b0(b4(b2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (130)
b2(b1(a0(b0(b0(x1))))) b2(b5(a2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (133)
b2(b1(a0(b0(b4(x1))))) b2(b5(a2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (134)
b2(b1(a0(b4(b2(x1))))) b2(b5(a2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (135)
b2(b1(a0(b4(b6(x1))))) b2(b5(a2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (136)
b2(b1(a4(b2(b1(x1))))) b2(b5(a2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (137)
b2(b1(a4(b2(b5(x1))))) b2(b5(a2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (138)
b1(a0(b0(b0(b0(x1))))) b1(a4(b2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (141)
b1(a0(b0(b0(b4(x1))))) b1(a4(b2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (142)
b1(a0(b0(b4(b2(x1))))) b1(a4(b2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (143)
b1(a0(b0(b4(b6(x1))))) b1(a4(b2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (144)
b1(a0(b4(b2(b1(x1))))) b1(a4(b2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (145)
b1(a0(b4(b2(b5(x1))))) b1(a4(b2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (146)
b3(a1(a0(b0(b0(x1))))) b3(a5(a2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (149)
b3(a1(a0(b0(b4(x1))))) b3(a5(a2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (150)
b3(a1(a0(b4(b2(x1))))) b3(a5(a2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (151)
b3(a1(a0(b4(b6(x1))))) b3(a5(a2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (152)
b3(a1(a4(b2(b1(x1))))) b3(a5(a2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (153)
b3(a1(a4(b2(b5(x1))))) b3(a5(a2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (154)
a0(b0(b0(b0(b0(x1))))) a0(b4(b2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (157)
a0(b0(b0(b0(b4(x1))))) a0(b4(b2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (158)
a0(b0(b0(b4(b2(x1))))) a0(b4(b2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (159)
a0(b0(b0(b4(b6(x1))))) a0(b4(b2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (160)
a0(b0(b4(b2(b1(x1))))) a0(b4(b2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (161)
a0(b0(b4(b2(b5(x1))))) a0(b4(b2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (162)
a2(b1(a0(b0(b0(x1))))) a2(b5(a2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (165)
a2(b1(a0(b0(b4(x1))))) a2(b5(a2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (166)
a2(b1(a0(b4(b2(x1))))) a2(b5(a2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (167)
a2(b1(a0(b4(b6(x1))))) a2(b5(a2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (168)
a2(b1(a4(b2(b1(x1))))) a2(b5(a2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (169)
a2(b1(a4(b2(b5(x1))))) a2(b5(a2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (170)
a1(a0(b0(b0(b0(x1))))) a1(a4(b2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (173)
a1(a0(b0(b0(b4(x1))))) a1(a4(b2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (174)
a1(a0(b0(b4(b2(x1))))) a1(a4(b2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (175)
a1(a0(b0(b4(b6(x1))))) a1(a4(b2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (176)
a1(a0(b4(b2(b1(x1))))) a1(a4(b2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (177)
a1(a0(b4(b2(b5(x1))))) a1(a4(b2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (178)
a3(a1(a0(b0(b0(x1))))) a3(a5(a2(b5(a2(b5(a2(b1(a0(b0(x1)))))))))) (181)
a3(a1(a0(b0(b4(x1))))) a3(a5(a2(b5(a2(b5(a2(b1(a0(b4(x1)))))))))) (182)
a3(a1(a0(b4(b2(x1))))) a3(a5(a2(b5(a2(b5(a2(b1(a4(b2(x1)))))))))) (183)
a3(a1(a0(b4(b6(x1))))) a3(a5(a2(b5(a2(b5(a2(b1(a4(b6(x1)))))))))) (184)
a3(a1(a4(b2(b1(x1))))) a3(a5(a2(b5(a2(b5(a2(b5(a2(b1(x1)))))))))) (185)
a3(a1(a4(b2(b5(x1))))) a3(a5(a2(b5(a2(b5(a2(b5(a2(b5(x1)))))))))) (186)

1.1.1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the naturals
[b0(x1)] =
2
· x1 +
1
[b4(x1)] =
2
· x1 +
1
[b2(x1)] =
1
· x1 +
0
[b6(x1)] =
1
· x1 +
1
[b1(x1)] =
2
· x1 +
0
[b5(x1)] =
1
· x1 +
0
[b3(x1)] =
2
· x1 +
1
[b7(x1)] =
2
· x1 +
1
[a0(x1)] =
1
· x1 +
0
[a4(x1)] =
1
· x1 +
1
[a2(x1)] =
1
· x1 +
1
[a6(x1)] =
2
· x1 +
0
[a1(x1)] =
2
· x1 +
0
[a5(x1)] =
1
· x1 +
0
[a3(x1)] =
1
· x1 +
0
all of the following rules can be deleted.
b0(b0(b4(b6(b3(x1))))) b0(b4(b2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (131)
b0(b0(b4(b6(b7(x1))))) b0(b4(b2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (132)
b2(b1(a4(b6(b3(x1))))) b2(b5(a2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (139)
b2(b1(a4(b6(b7(x1))))) b2(b5(a2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (140)
b3(a1(a4(b6(b3(x1))))) b3(a5(a2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (155)
b3(a1(a4(b6(b7(x1))))) b3(a5(a2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (156)
a0(b0(b4(b6(b3(x1))))) a0(b4(b2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (163)
a0(b0(b4(b6(b7(x1))))) a0(b4(b2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (164)
a2(b1(a4(b6(b3(x1))))) a2(b5(a2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (171)
a2(b1(a4(b6(b7(x1))))) a2(b5(a2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (172)
a3(a1(a4(b6(b3(x1))))) a3(a5(a2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (187)
a3(a1(a4(b6(b7(x1))))) a3(a5(a2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (188)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) b0(b0(b4(b6(b3(a1(a0(b0(x1)))))))) (189)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) b0(b0(b4(b6(b3(a1(a0(b4(x1)))))))) (190)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) b0(b0(b4(b6(b3(a1(a4(b2(x1)))))))) (191)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) b0(b0(b4(b6(b3(a1(a4(b6(x1)))))))) (192)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) b0(b0(b4(b6(b3(a5(a2(b1(x1)))))))) (193)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) b0(b0(b4(b6(b3(a5(a2(b5(x1)))))))) (194)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) b0(b0(b4(b6(b3(a5(a6(b3(x1)))))))) (195)
b0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) b0(b0(b4(b6(b3(a5(a6(b7(x1)))))))) (196)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) b2(b1(a4(b6(b3(a1(a0(b0(x1)))))))) (197)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) b2(b1(a4(b6(b3(a1(a0(b4(x1)))))))) (198)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) b2(b1(a4(b6(b3(a1(a4(b2(x1)))))))) (199)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) b2(b1(a4(b6(b3(a1(a4(b6(x1)))))))) (200)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) b2(b1(a4(b6(b3(a5(a2(b1(x1)))))))) (201)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) b2(b1(a4(b6(b3(a5(a2(b5(x1)))))))) (202)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) b2(b1(a4(b6(b3(a5(a6(b3(x1)))))))) (203)
b2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) b2(b1(a4(b6(b3(a5(a6(b7(x1)))))))) (204)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) b1(a0(b4(b6(b3(a1(a0(b0(x1)))))))) (205)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) b1(a0(b4(b6(b3(a1(a0(b4(x1)))))))) (206)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) b1(a0(b4(b6(b3(a1(a4(b2(x1)))))))) (207)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) b1(a0(b4(b6(b3(a1(a4(b6(x1)))))))) (208)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) b1(a0(b4(b6(b3(a5(a2(b1(x1)))))))) (209)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) b1(a0(b4(b6(b3(a5(a2(b5(x1)))))))) (210)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) b1(a0(b4(b6(b3(a5(a6(b3(x1)))))))) (211)
b1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) b1(a0(b4(b6(b3(a5(a6(b7(x1)))))))) (212)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) b3(a1(a4(b6(b3(a1(a0(b0(x1)))))))) (213)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) b3(a1(a4(b6(b3(a1(a0(b4(x1)))))))) (214)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) b3(a1(a4(b6(b3(a1(a4(b2(x1)))))))) (215)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) b3(a1(a4(b6(b3(a1(a4(b6(x1)))))))) (216)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) b3(a1(a4(b6(b3(a5(a2(b1(x1)))))))) (217)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) b3(a1(a4(b6(b3(a5(a2(b5(x1)))))))) (218)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) b3(a1(a4(b6(b3(a5(a6(b3(x1)))))))) (219)
b3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) b3(a1(a4(b6(b3(a5(a6(b7(x1)))))))) (220)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) a0(b0(b4(b6(b3(a1(a0(b0(x1)))))))) (221)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) a0(b0(b4(b6(b3(a1(a0(b4(x1)))))))) (222)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) a0(b0(b4(b6(b3(a1(a4(b2(x1)))))))) (223)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) a0(b0(b4(b6(b3(a1(a4(b6(x1)))))))) (224)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) a0(b0(b4(b6(b3(a5(a2(b1(x1)))))))) (225)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) a0(b0(b4(b6(b3(a5(a2(b5(x1)))))))) (226)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) a0(b0(b4(b6(b3(a5(a6(b3(x1)))))))) (227)
a0(b4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) a0(b0(b4(b6(b3(a5(a6(b7(x1)))))))) (228)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) a2(b1(a4(b6(b3(a1(a0(b0(x1)))))))) (229)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) a2(b1(a4(b6(b3(a1(a0(b4(x1)))))))) (230)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) a2(b1(a4(b6(b3(a1(a4(b2(x1)))))))) (231)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) a2(b1(a4(b6(b3(a1(a4(b6(x1)))))))) (232)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) a2(b1(a4(b6(b3(a5(a2(b1(x1)))))))) (233)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) a2(b1(a4(b6(b3(a5(a2(b5(x1)))))))) (234)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) a2(b1(a4(b6(b3(a5(a6(b3(x1)))))))) (235)
a2(b5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) a2(b1(a4(b6(b3(a5(a6(b7(x1)))))))) (236)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) a1(a0(b4(b6(b3(a1(a0(b0(x1)))))))) (237)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) a1(a0(b4(b6(b3(a1(a0(b4(x1)))))))) (238)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) a1(a0(b4(b6(b3(a1(a4(b2(x1)))))))) (239)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) a1(a0(b4(b6(b3(a1(a4(b6(x1)))))))) (240)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) a1(a0(b4(b6(b3(a5(a2(b1(x1)))))))) (241)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) a1(a0(b4(b6(b3(a5(a2(b5(x1)))))))) (242)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) a1(a0(b4(b6(b3(a5(a6(b3(x1)))))))) (243)
a1(a4(b2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) a1(a0(b4(b6(b3(a5(a6(b7(x1)))))))) (244)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))))) a3(a1(a4(b6(b3(a1(a0(b0(x1)))))))) (245)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))))) a3(a1(a4(b6(b3(a1(a0(b4(x1)))))))) (246)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))))) a3(a1(a4(b6(b3(a1(a4(b2(x1)))))))) (247)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))))) a3(a1(a4(b6(b3(a1(a4(b6(x1)))))))) (248)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))))) a3(a1(a4(b6(b3(a5(a2(b1(x1)))))))) (249)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))))) a3(a1(a4(b6(b3(a5(a2(b5(x1)))))))) (250)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))))) a3(a1(a4(b6(b3(a5(a6(b3(x1)))))))) (251)
a3(a5(a2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))))) a3(a1(a4(b6(b3(a5(a6(b7(x1)))))))) (252)

1.1.1.1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[b0(x1)] = x1 +
0
[b4(x1)] = x1 +
1
[b2(x1)] = x1 +
0
[b6(x1)] = x1 +
1
[b1(x1)] = x1 +
0
[b5(x1)] = x1 +
0
[b3(x1)] = x1 +
1
[b7(x1)] = x1 +
0
[a0(x1)] = x1 +
1
[a4(x1)] = x1 +
0
[a2(x1)] = x1 +
0
[a6(x1)] = x1 +
0
[a1(x1)] = x1 +
1
[a5(x1)] = x1 +
0
[a3(x1)] = x1 +
0
all of the following rules can be deleted.
b2(b1(a4(b6(b7(a3(a1(a0(b0(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (69)
b2(b1(a4(b6(b7(a3(a1(a0(b4(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (70)
b2(b1(a4(b6(b7(a3(a1(a4(b2(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (71)
b2(b1(a4(b6(b7(a3(a1(a4(b6(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (72)
b2(b1(a4(b6(b7(a3(a5(a2(b1(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (73)
b2(b1(a4(b6(b7(a3(a5(a2(b5(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (74)
b2(b1(a4(b6(b7(a3(a5(a6(b3(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (75)
b2(b1(a4(b6(b7(a3(a5(a6(b7(x1))))))))) b2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (76)
b3(a1(a4(b6(b7(a3(a1(a0(b0(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (85)
b3(a1(a4(b6(b7(a3(a1(a0(b4(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (86)
b3(a1(a4(b6(b7(a3(a1(a4(b2(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (87)
b3(a1(a4(b6(b7(a3(a1(a4(b6(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (88)
b3(a1(a4(b6(b7(a3(a5(a2(b1(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (89)
b3(a1(a4(b6(b7(a3(a5(a2(b5(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (90)
b3(a1(a4(b6(b7(a3(a5(a6(b3(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (91)
b3(a1(a4(b6(b7(a3(a5(a6(b7(x1))))))))) b3(a5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (92)
a2(b1(a4(b6(b7(a3(a1(a0(b0(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (101)
a2(b1(a4(b6(b7(a3(a1(a0(b4(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (102)
a2(b1(a4(b6(b7(a3(a1(a4(b2(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (103)
a2(b1(a4(b6(b7(a3(a1(a4(b6(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (104)
a2(b1(a4(b6(b7(a3(a5(a2(b1(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (105)
a2(b1(a4(b6(b7(a3(a5(a2(b5(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (106)
a2(b1(a4(b6(b7(a3(a5(a6(b3(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (107)
a2(b1(a4(b6(b7(a3(a5(a6(b7(x1))))))))) a2(b5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (108)
a3(a1(a4(b6(b7(a3(a1(a0(b0(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b1(a0(b0(x1)))))))))) (117)
a3(a1(a4(b6(b7(a3(a1(a0(b4(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b1(a0(b4(x1)))))))))) (118)
a3(a1(a4(b6(b7(a3(a1(a4(b2(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b1(a4(b2(x1)))))))))) (119)
a3(a1(a4(b6(b7(a3(a1(a4(b6(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b1(a4(b6(x1)))))))))) (120)
a3(a1(a4(b6(b7(a3(a5(a2(b1(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b5(a2(b1(x1)))))))))) (121)
a3(a1(a4(b6(b7(a3(a5(a2(b5(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b5(a2(b5(x1)))))))))) (122)
a3(a1(a4(b6(b7(a3(a5(a6(b3(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b5(a6(b3(x1)))))))))) (123)
a3(a1(a4(b6(b7(a3(a5(a6(b7(x1))))))))) a3(a5(a6(b7(a3(a5(a2(b5(a6(b7(x1)))))))))) (124)
b1(a0(b4(b6(b3(x1))))) b1(a4(b2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (147)
b1(a0(b4(b6(b7(x1))))) b1(a4(b2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (148)
a1(a0(b4(b6(b3(x1))))) a1(a4(b2(b5(a2(b5(a2(b5(a6(b3(x1)))))))))) (179)
a1(a0(b4(b6(b7(x1))))) a1(a4(b2(b5(a2(b5(a2(b5(a6(b7(x1)))))))))) (180)
b0(b4(b6(b3(a1(a0(b0(x1))))))) b0(b4(b6(b7(a3(a1(a0(b0(x1)))))))) (253)
b0(b4(b6(b3(a1(a0(b4(x1))))))) b0(b4(b6(b7(a3(a1(a0(b4(x1)))))))) (254)
b0(b4(b6(b3(a1(a4(b2(x1))))))) b0(b4(b6(b7(a3(a1(a4(b2(x1)))))))) (255)
b0(b4(b6(b3(a1(a4(b6(x1))))))) b0(b4(b6(b7(a3(a1(a4(b6(x1)))))))) (256)
b0(b4(b6(b3(a5(a2(b1(x1))))))) b0(b4(b6(b7(a3(a5(a2(b1(x1)))))))) (257)
b0(b4(b6(b3(a5(a2(b5(x1))))))) b0(b4(b6(b7(a3(a5(a2(b5(x1)))))))) (258)
b0(b4(b6(b3(a5(a6(b3(x1))))))) b0(b4(b6(b7(a3(a5(a6(b3(x1)))))))) (259)
b0(b4(b6(b3(a5(a6(b7(x1))))))) b0(b4(b6(b7(a3(a5(a6(b7(x1)))))))) (260)
b2(b5(a6(b3(a1(a0(b0(x1))))))) b2(b5(a6(b7(a3(a1(a0(b0(x1)))))))) (261)
b2(b5(a6(b3(a1(a0(b4(x1))))))) b2(b5(a6(b7(a3(a1(a0(b4(x1)))))))) (262)
b2(b5(a6(b3(a1(a4(b2(x1))))))) b2(b5(a6(b7(a3(a1(a4(b2(x1)))))))) (263)
b2(b5(a6(b3(a1(a4(b6(x1))))))) b2(b5(a6(b7(a3(a1(a4(b6(x1)))))))) (264)
b2(b5(a6(b3(a5(a2(b1(x1))))))) b2(b5(a6(b7(a3(a5(a2(b1(x1)))))))) (265)
b2(b5(a6(b3(a5(a2(b5(x1))))))) b2(b5(a6(b7(a3(a5(a2(b5(x1)))))))) (266)
b2(b5(a6(b3(a5(a6(b3(x1))))))) b2(b5(a6(b7(a3(a5(a6(b3(x1)))))))) (267)
b2(b5(a6(b3(a5(a6(b7(x1))))))) b2(b5(a6(b7(a3(a5(a6(b7(x1)))))))) (268)
b1(a4(b6(b3(a1(a0(b0(x1))))))) b1(a4(b6(b7(a3(a1(a0(b0(x1)))))))) (269)
b1(a4(b6(b3(a1(a0(b4(x1))))))) b1(a4(b6(b7(a3(a1(a0(b4(x1)))))))) (270)
b1(a4(b6(b3(a1(a4(b2(x1))))))) b1(a4(b6(b7(a3(a1(a4(b2(x1)))))))) (271)
b1(a4(b6(b3(a1(a4(b6(x1))))))) b1(a4(b6(b7(a3(a1(a4(b6(x1)))))))) (272)
b1(a4(b6(b3(a5(a2(b1(x1))))))) b1(a4(b6(b7(a3(a5(a2(b1(x1)))))))) (273)
b1(a4(b6(b3(a5(a2(b5(x1))))))) b1(a4(b6(b7(a3(a5(a2(b5(x1)))))))) (274)
b1(a4(b6(b3(a5(a6(b3(x1))))))) b1(a4(b6(b7(a3(a5(a6(b3(x1)))))))) (275)
b1(a4(b6(b3(a5(a6(b7(x1))))))) b1(a4(b6(b7(a3(a5(a6(b7(x1)))))))) (276)
b3(a5(a6(b3(a1(a0(b0(x1))))))) b3(a5(a6(b7(a3(a1(a0(b0(x1)))))))) (277)
b3(a5(a6(b3(a1(a0(b4(x1))))))) b3(a5(a6(b7(a3(a1(a0(b4(x1)))))))) (278)
b3(a5(a6(b3(a1(a4(b2(x1))))))) b3(a5(a6(b7(a3(a1(a4(b2(x1)))))))) (279)
b3(a5(a6(b3(a1(a4(b6(x1))))))) b3(a5(a6(b7(a3(a1(a4(b6(x1)))))))) (280)
b3(a5(a6(b3(a5(a2(b1(x1))))))) b3(a5(a6(b7(a3(a5(a2(b1(x1)))))))) (281)
b3(a5(a6(b3(a5(a2(b5(x1))))))) b3(a5(a6(b7(a3(a5(a2(b5(x1)))))))) (282)
b3(a5(a6(b3(a5(a6(b3(x1))))))) b3(a5(a6(b7(a3(a5(a6(b3(x1)))))))) (283)
b3(a5(a6(b3(a5(a6(b7(x1))))))) b3(a5(a6(b7(a3(a5(a6(b7(x1)))))))) (284)
a0(b4(b6(b3(a1(a0(b0(x1))))))) a0(b4(b6(b7(a3(a1(a0(b0(x1)))))))) (285)
a0(b4(b6(b3(a1(a0(b4(x1))))))) a0(b4(b6(b7(a3(a1(a0(b4(x1)))))))) (286)
a0(b4(b6(b3(a1(a4(b2(x1))))))) a0(b4(b6(b7(a3(a1(a4(b2(x1)))))))) (287)
a0(b4(b6(b3(a1(a4(b6(x1))))))) a0(b4(b6(b7(a3(a1(a4(b6(x1)))))))) (288)
a0(b4(b6(b3(a5(a2(b1(x1))))))) a0(b4(b6(b7(a3(a5(a2(b1(x1)))))))) (289)
a0(b4(b6(b3(a5(a2(b5(x1))))))) a0(b4(b6(b7(a3(a5(a2(b5(x1)))))))) (290)
a0(b4(b6(b3(a5(a6(b3(x1))))))) a0(b4(b6(b7(a3(a5(a6(b3(x1)))))))) (291)
a0(b4(b6(b3(a5(a6(b7(x1))))))) a0(b4(b6(b7(a3(a5(a6(b7(x1)))))))) (292)
a2(b5(a6(b3(a1(a0(b0(x1))))))) a2(b5(a6(b7(a3(a1(a0(b0(x1)))))))) (293)
a2(b5(a6(b3(a1(a0(b4(x1))))))) a2(b5(a6(b7(a3(a1(a0(b4(x1)))))))) (294)
a2(b5(a6(b3(a1(a4(b2(x1))))))) a2(b5(a6(b7(a3(a1(a4(b2(x1)))))))) (295)
a2(b5(a6(b3(a1(a4(b6(x1))))))) a2(b5(a6(b7(a3(a1(a4(b6(x1)))))))) (296)
a2(b5(a6(b3(a5(a2(b1(x1))))))) a2(b5(a6(b7(a3(a5(a2(b1(x1)))))))) (297)
a2(b5(a6(b3(a5(a2(b5(x1))))))) a2(b5(a6(b7(a3(a5(a2(b5(x1)))))))) (298)
a2(b5(a6(b3(a5(a6(b3(x1))))))) a2(b5(a6(b7(a3(a5(a6(b3(x1)))))))) (299)
a2(b5(a6(b3(a5(a6(b7(x1))))))) a2(b5(a6(b7(a3(a5(a6(b7(x1)))))))) (300)
a1(a4(b6(b3(a1(a0(b0(x1))))))) a1(a4(b6(b7(a3(a1(a0(b0(x1)))))))) (301)
a1(a4(b6(b3(a1(a0(b4(x1))))))) a1(a4(b6(b7(a3(a1(a0(b4(x1)))))))) (302)
a1(a4(b6(b3(a1(a4(b2(x1))))))) a1(a4(b6(b7(a3(a1(a4(b2(x1)))))))) (303)
a1(a4(b6(b3(a1(a4(b6(x1))))))) a1(a4(b6(b7(a3(a1(a4(b6(x1)))))))) (304)
a1(a4(b6(b3(a5(a2(b1(x1))))))) a1(a4(b6(b7(a3(a5(a2(b1(x1)))))))) (305)
a1(a4(b6(b3(a5(a2(b5(x1))))))) a1(a4(b6(b7(a3(a5(a2(b5(x1)))))))) (306)
a1(a4(b6(b3(a5(a6(b3(x1))))))) a1(a4(b6(b7(a3(a5(a6(b3(x1)))))))) (307)
a1(a4(b6(b3(a5(a6(b7(x1))))))) a1(a4(b6(b7(a3(a5(a6(b7(x1)))))))) (308)
a3(a5(a6(b3(a1(a0(b0(x1))))))) a3(a5(a6(b7(a3(a1(a0(b0(x1)))))))) (309)
a3(a5(a6(b3(a1(a0(b4(x1))))))) a3(a5(a6(b7(a3(a1(a0(b4(x1)))))))) (310)
a3(a5(a6(b3(a1(a4(b2(x1))))))) a3(a5(a6(b7(a3(a1(a4(b2(x1)))))))) (311)
a3(a5(a6(b3(a1(a4(b6(x1))))))) a3(a5(a6(b7(a3(a1(a4(b6(x1)))))))) (312)
a3(a5(a6(b3(a5(a2(b1(x1))))))) a3(a5(a6(b7(a3(a5(a2(b1(x1)))))))) (313)
a3(a5(a6(b3(a5(a2(b5(x1))))))) a3(a5(a6(b7(a3(a5(a2(b5(x1)))))))) (314)
a3(a5(a6(b3(a5(a6(b3(x1))))))) a3(a5(a6(b7(a3(a5(a6(b3(x1)))))))) (315)
a3(a5(a6(b3(a5(a6(b7(x1))))))) a3(a5(a6(b7(a3(a5(a6(b7(x1)))))))) (316)

1.1.1.1.1.1.1.1 R is empty

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