Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-47)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
x1 |
(1) |
|
a(x1) |
→ |
b(c(x1)) |
(2) |
|
c(b(b(b(x1)))) |
→ |
b(a(b(a(x1)))) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Looping derivation
There is a looping derivation.
c b b b b b b b b b →+ b b c b b b b b b b b b c c
The derivation can be derived as follows.
-
c b b b →+ b a b a:
This is an original rule (OC1).
-
a →+ b c:
This is an original rule (OC1).
-
c b b b →+ b b c b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b b →+ b a b a
-
a →+ b c
-
a →+ ε:
This is an original rule (OC1).
-
c b b b →+ b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b b →+ b a b a
-
a →+ ε
-
c b b b →+ b b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b →+ b b a
-
a →+ b c
-
a b b b →+ b b b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b c
-
c b b b →+ b b b c
-
c b b b b b b →+ b a b b b b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b →+ b a b a
-
a b b b →+ b b b b c
-
a b b b b b b →+ b b a b b b b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b c
-
c b b b b b b →+ b a b b b b b c
-
c b b b →+ b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b →+ b a b a
-
a →+ ε
-
a b b b →+ b b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b c
-
c b b b →+ b a b
-
a b b b b b b →+ b b b b a b b b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b →+ b b a b b b b b c
-
a b b b →+ b b a b
-
c b b b →+ b a b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b →+ b a b a
-
a →+ b c
-
a b b b →+ b b a b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b c
-
c b b b →+ b a b b c
-
a b b b b b b →+ b b b b b b a b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b →+ b b b b a b b b c
-
a b b b →+ b b a b b c
-
c b b b b b b b b b →+ b b c b b b b b b b a b b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b →+ b b c b a
-
a b b b b b b →+ b b b b b b a b b c c
-
c b b b b b b b b b →+ b b c b b b b b b b b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b b b b b b b b →+ b b c b b b b b b b a b b c c
-
a →+ ε