Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-224)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
x1 |
(1) |
|
a(b(x1)) |
→ |
b(b(c(a(c(x1))))) |
(2) |
|
c(c(x1)) |
→ |
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.
a b c b b c →+ b b c b b b b b b b b b b b b b b b a b c b b c a c
The derivation can be derived as follows.
-
a b →+ b b c a c:
This is an original rule (OC1).
-
c c →+ b a:
This is an original rule (OC1).
-
a b c →+ b b c a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b b c a c
-
c c →+ b a
-
a b c →+ b b c b b c a c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c →+ b b c a b a
-
a b →+ b b c a c
-
a →+ ε:
This is an original rule (OC1).
-
a b c →+ b b c b b c c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c →+ b b c b b c a c a
-
a →+ ε
-
a b →+ b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b →+ b b c b b c c b b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b b c b b c c a
-
a b →+ b b c c
-
a b c b →+ b b c b b c c b b b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b →+ b b c b b c c b b c c
-
c c →+ b a
-
a b c b →+ b b c b b b a b b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b →+ b b c b b c c b b b a
-
c c →+ b a
-
a b →+ b b b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b b c c
-
c c →+ b a
-
a b c b →+ b b c b b b b b b a b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b →+ b b c b b b a b b b a
-
a b →+ b b b a
-
a b c b →+ b b c b b b b b b b b b a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b →+ b b c b b b b b b a b b a
-
a b →+ b b b a
-
a b c b →+ b b c b b b b b b b b b b b b a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b →+ b b c b b b b b b b b b a b a
-
a b →+ b b b a
-
a b c b b →+ b b c b b b b b b b b b b b b a b b c a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b →+ b b c b b b b b b b b b b b b a a
-
a b →+ b b c a c
-
a b c b b →+ b b c b b b b b b b b b b b b b b c a c b c a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b c b b b b b b b b b b b b a b b c a c
-
a b →+ b b c a c
-
a b c b b →+ b b c b b b b b b b b b b b b b b c c b c a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b c b b b b b b b b b b b b b b c a c b c a c
-
a →+ ε
-
c c →+ b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b b c →+ b b c b b b b b b b b b b b b b b c c b c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b b →+ b b c b b b b b b b b b b b b b b c c b c a c
-
c c →+ b
-
a b c b b c →+ b b c b b b b b b b b b b b b b b b a b c a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b c →+ b b c b b b b b b b b b b b b b b c c b c a b
-
c c →+ b a
-
a b c b b c →+ b b c b b b b b b b b b b b b b b b a b c b b c a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b b c →+ b b c b b b b b b b b b b b b b b b a b c a b
-
a b →+ b b c a c