Certification Problem
Input (TPDB SRS_Standard/Trafo_06/un04)
The rewrite relation of the following TRS is considered.
|
b(a(b(a(a(b(x1)))))) |
→ |
b(b(a(b(a(b(x1)))))) |
(1) |
|
b(a(b(b(x1)))) |
→ |
b(b(a(a(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.
b a b a a b b b a a b b →+ b b b a a b b a b b a a b a b a a b b b a a b b a b a b a b
The derivation can be derived as follows.
-
b a b a a b →+ b b a b a b:
This is an original rule (OC1).
-
b a b b →+ b b a a b a b:
This is an original rule (OC1).
-
b a b a a b b →+ b b a b b a a b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a b a a b →+ b b a b a b
-
b a b b →+ b b a a b a b
-
b a b a a b b →+ b b b a a b a b a a b a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a b a a b b →+ b b a b b a a b a b
-
b a b b →+ b b a a b a b
-
b a b a a b b →+ b b b a a b b a b a b a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a b a a b b →+ b b b a a b a b a a b a b
-
b a b a a b →+ b b a b a b
-
b a b a a b b b →+ b b b a a b b a b a b b a a b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a b a a b b →+ b b b a a b b a b a b a b
-
b a b b →+ b b a a b a b
-
b a b a a b b b →+ b b b a a b b a b b a a b a b a a b a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a b a a b b b →+ b b b a a b b a b a b b a a b a b
-
b a b b →+ b b a a b a b
-
b a b a a b b b a a b b →+ b b b a a b b a b b a a b a b a a b b b a a b b a b a b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a b a a b b b →+ b b b a a b b a b b a a b a b a a b a b
-
b a b a a b b →+ b b b a a b b a b a b a b