Certification Problem
Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-4)
The rewrite relation of the following TRS is considered.
|
a(a(a(a(x1)))) |
→ |
b(a(a(a(x1)))) |
(1) |
|
b(b(x1)) |
→ |
a(a(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.
b b b b b →+ ε b b b b b a a a b
The derivation can be derived as follows.
-
b b →+ a a b:
This is an original rule (OC1).
-
b b b →+ a a a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b →+ a a b
-
b b →+ a a b
-
a a a a →+ b a a a:
This is an original rule (OC1).
-
b b b →+ b a a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b b →+ a a a a b
-
a a a a →+ b a a a
-
b b b b →+ b a a a a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b b →+ b a a a b
-
b b →+ a a b
-
b b b b →+ b b a a a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b b b →+ b a a a a a b
-
a a a a →+ b a a a
-
b b b b →+ b b b a a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b b b →+ b b a a a a b
-
a a a a →+ b a a a
-
b b b b b →+ b b b a a a a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b b b →+ b b b a a a b
-
b b →+ a a b
-
b b b b b →+ b b b b a a a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b b b b →+ b b b a a a a a b
-
a a a a →+ b a a a
-
b b b b b →+ b b b b b a a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b b b b →+ b b b b a a a a b
-
a a a a →+ b a a a