Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-2-num-20)
The rewrite relation of the following TRS is considered.
a(x1) |
→ |
x1 |
(1) |
a(a(b(x1))) |
→ |
b(a(b(a(x1)))) |
(2) |
b(b(b(x1))) |
→ |
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 a b a b a b a b a b a b →+ ε a a b a b a b a b a b a b a
The derivation can be derived as follows.
-
a a b →+ b a b a:
This is an original rule (OC1).
-
a →+ ε:
This is an original rule (OC1).
-
a a b →+ b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b →+ b b b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b →+ b b a
-
a a b →+ b a b a
-
b b b →+ a:
This is an original rule (OC1).
-
a a b a b →+ a a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b →+ b b b a b a
-
b b b →+ a
-
a a b a b →+ b a b b b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b →+ b a b a
-
a a b →+ b b a
-
a a b a b →+ b a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b →+ b a b b b a
-
b b b →+ a
-
a a b a b a b a b →+ a a b b a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b a b →+ a a b a
-
a a b a b →+ b a a a
-
a a b a b a b a b a b →+ a a b b a a b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b a b a b a b →+ a a b b a a a
-
a a b →+ b a b a
-
a a b a b a b a b a b →+ a a b b b a b a a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a b a b →+ a a b b a a b a b a
-
a a b →+ b a b a
-
a a b a b a b a b a b →+ a a a a b a a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a b a b →+ a a b b b a b a a b a
-
b b b →+ a
-
a a b a b a b a b a b →+ a a b a b a a a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a b a b →+ a a a a b a a b a
-
a a b →+ b a b a
-
a a b a b a b a b a b →+ a a b a b a b a b a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a b a b →+ a a b a b a a a b a
-
a a b →+ b a b a
-
a a b a b a b a b a b a b →+ a a b a b a b a b a b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b a b a b a b a b →+ a a b a b a b a b a a
-
a a b →+ b a b a