Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-450)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
b(c(x1)) |
(1) |
|
a(b(b(x1))) |
→ |
c(a(a(a(x1)))) |
(2) |
|
c(c(x1)) |
→ |
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 b b b c b c b →+ c a b b b b c b c b c
The derivation can be derived as follows.
-
a b b →+ c a a a:
This is an original rule (OC1).
-
a →+ b c:
This is an original rule (OC1).
-
c c →+ ε:
This is an original rule (OC1).
-
a c →+ b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b c →+ c a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ c a a a
-
a c →+ b
-
a b b c b →+ c a c a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b c →+ c a a b
-
a b b →+ c a a a
-
a b b c b →+ c b a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c b →+ c a c a a a
-
a c →+ b
-
a b b c b c b →+ c a c b a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b c →+ c a a b
-
a b b c b →+ c b a a a
-
a b b c b c b →+ c b b a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c b c b →+ c a c b a a a
-
a c →+ b
-
a b b b b c b c b →+ c a a c b b a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ c a a a
-
a b b c b c b →+ c b b a a a
-
a b b b b c b c b →+ c a b b b a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b c b c b →+ c a a c b b a a a
-
a c →+ b
-
a b b b b c b c b →+ c a b b b b c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b c b c b →+ c a b b b a a a
-
a →+ b c
-
a b b b b c b c b →+ c a b b b b c b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b c b c b →+ c a b b b b c a a
-
a →+ b c
-
a b b b b c b c b →+ c a b b b b c b c b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b b b c b c b →+ c a b b b b c b c a
-
a →+ b c