Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-368)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
b(x1) |
(1) |
|
a(b(c(x1))) |
→ |
c(c(a(a(x1)))) |
(2) |
|
c(c(x1)) |
→ |
b(x1) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Looping derivation
There is a looping derivation.
a b c b c c c c c →+ b a b c b c c c c c a a
The derivation can be derived as follows.
-
a b c →+ c c a a:
This is an original rule (OC1).
-
c c →+ b:
This is an original rule (OC1).
-
a b c →+ b a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c →+ c c a a
-
c c →+ b
-
a →+ b:
This is an original rule (OC1).
-
a b c →+ b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c →+ b c c a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b a b
-
a b c →+ c c a a
-
a b c c →+ b c c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c →+ b c c a a
-
a →+ b
-
a b c c c →+ b c c c c a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c →+ b c c a b
-
a b c →+ c c a a
-
a b c c c →+ b c b c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c c c →+ b c c c c a a
-
c c →+ b
-
a b c c c →+ b c b c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c c →+ b c b c a a
-
a →+ b
-
a b c c c c →+ b c b c c c a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c c →+ b c b c a b
-
a b c →+ c c a a
-
a b c c c c →+ b c b c c c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c c c →+ b c b c c c a a
-
a →+ b
-
a b c b c c c c →+ b a b c b c c c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b a a
-
a b c c c c →+ b c b c c c a b
-
a b c b c c c c c →+ b a b c b c c c c c a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b c c c c →+ b a b c b c c c a b
-
a b c →+ c c a a