Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-522)
The rewrite relation of the following TRS is considered.
|
a(a(b(x1))) |
→ |
a(c(c(a(a(a(x1)))))) |
(1) |
|
a(c(x1)) |
→ |
b(x1) |
(2) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Looping derivation
There is a looping derivation.
a a b a b c b c →+ b c b c b c a b c a a b a b c b c a a a
The derivation can be derived as follows.
-
a a b →+ a c c a a a:
This is an original rule (OC1).
-
a c →+ b:
This is an original rule (OC1).
-
a a b →+ b c a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b →+ a c c a a a
-
a c →+ b
-
a a b c →+ a c c a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b →+ a c c a a a
-
a c →+ b
-
a a b c →+ b c a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b c →+ a c c a a b
-
a c →+ b
-
a a b a b c →+ b c a a b c a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b →+ b c a a a
-
a a b c →+ b c a a b
-
a a b a b c →+ b c b c a a b a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b c →+ b c a a b c a a b
-
a a b c →+ b c a a b
-
a a b a b c →+ b c b c a a b b c a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b a b c →+ b c b c a a b a a b
-
a a b →+ b c a a a
-
a a b a b c →+ b c b c b c a a a b c a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b c →+ b c b c a a b b c a a a
-
a a b →+ b c a a a
-
a a b a b c →+ b c b c b c a b c a a b a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b c →+ b c b c b c a a a b c a a a
-
a a b c →+ b c a a b
-
a a b c →+ b c a c c a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b c →+ b c a a b
-
a a b →+ a c c a a a
-
a a b a b c b c →+ b c b c b c a b c a a b a b c a c c a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b a b c →+ b c b c b c a b c a a b a a a
-
a a b c →+ b c a c c a a a
-
a a b a b c b c →+ b c b c b c a b c a a b a b c b c a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b c b c →+ b c b c b c a b c a a b a b c a c c a a a
-
a c →+ b