Certification Problem
Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-2)
The rewrite relation of the following TRS is considered.
|
a(a(a(a(x1)))) |
→ |
a(c(a(c(c(x1))))) |
(1) |
|
c(c(c(x1))) |
→ |
a(a(a(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 a a c a a a c a a c a →+ a c a a a a c a a a c a a c a c c
The derivation can be derived as follows.
-
a a a a →+ a c a c c:
This is an original rule (OC1).
-
c c c →+ a a a:
This is an original rule (OC1).
-
a a a a c →+ a c a a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a a a →+ a c a c c
-
c c c →+ a a a
-
c c c a →+ a c a c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c c →+ a a a
-
a a a a →+ a c a c c
-
a a a a c a →+ a c a a c a c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a a a →+ a c a c c
-
c c c a →+ a c a c c
-
c c c a a c a →+ a a c a a c a c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c c →+ a a a
-
a a a a c a →+ a c a a c a c c
-
a a a a c a a c a →+ a c a a a c a a c a c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a a a →+ a c a c c
-
c c c a a c a →+ a a c a a c a c c
-
a a a a c a a a c a a c a →+ a c a a a a c a a a c a a c a c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a a a c →+ a c a a a a
-
a a a a c a a c a →+ a c a a a c a a c a c c