Certification Problem
Input (TPDB SRS_Standard/Zantema_06/loop1)
The rewrite relation of the following TRS is considered.
|
a(b(b(x1))) |
→ |
b(b(a(a(x1)))) |
(1) |
|
a(a(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 b b b b b b →+ b b a b b b b b b ε
The derivation can be derived as follows.
-
a b b →+ b b a a:
This is an original rule (OC1).
-
a a →+ b:
This is an original rule (OC1).
-
a b b →+ b b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b a a
-
a a →+ b
-
a b b b b →+ b b a b b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b a a
-
a b b →+ b b b
-
a b b b b →+ b b b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b →+ b b a b b b
-
a b b →+ b b b
-
a b b b b b b →+ b b a b b b b b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b a a
-
a b b b b →+ b b b b b b