Certification Problem
Input (TPDB SRS_Standard/Zantema_06/loop2)
The rewrite relation of the following TRS is considered.
|
b(b(b(x1))) |
→ |
a(a(x1)) |
(1) |
|
a(a(x1)) |
→ |
b(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.
a a b b a b b a →+ b a a b b a b b a b
The derivation can be derived as follows.
-
a a →+ b a b:
This is an original rule (OC1).
-
b b b →+ a a:
This is an original rule (OC1).
-
a a b b →+ b a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b
-
b b b →+ a a
-
a a b b →+ b b a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b b →+ b a a a
-
a a →+ b a b
-
b b b a b b →+ a b b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b b →+ a a
-
a a b b →+ b b a b a
-
a a b b a b b →+ b a a b b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b
-
b b b a b b →+ a b b a b a
-
a a b b a b b a →+ b a a b b a b b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b b a b b →+ b a a b b a b a
-
a a →+ b a b