Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size11/size-11-alpha-3-num-1)
The rewrite relation of the following TRS is considered.
a(x1) |
→ |
x1 |
(1) |
a(b(x1)) |
→ |
c(x1) |
(2) |
c(c(x1)) |
→ |
b(c(b(a(a(x1))))) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Looping derivation
There is a looping derivation.
c c b c b c b c →+ b c b b c b b c b c c b c b c b c ε
The derivation can be derived as follows.
-
c c →+ b c b a a:
This is an original rule (OC1).
-
a b →+ c:
This is an original rule (OC1).
-
a b c →+ b c b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ c
-
c c →+ b c b a a
-
c c b c →+ b c b a b c b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c →+ b c b a a
-
a b c →+ b c b a a
-
a b c b c →+ b c b a b c b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ c
-
c c b c →+ b c b a b c b a a
-
a b c b c →+ b c b c c b a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b c →+ b c b a b c b a a
-
a b →+ c
-
c c b c b c →+ b c b a b c b c c b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c →+ b c b a a
-
a b c b c →+ b c b c c b a a
-
c c b c b c →+ b c b c c b c c b a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b c b c →+ b c b a b c b c c b a a
-
a b →+ c
-
a →+ ε:
This is an original rule (OC1).
-
c c →+ b c b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b c b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c b c →+ b c b a b c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c →+ b c b a a
-
a b c →+ b c b
-
c c b c →+ b c b c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b c →+ b c b a b c b
-
a b →+ c
-
c c b c b c →+ b c b b c b c c b c b a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b c b c →+ b c b c c b c c b a a
-
c c b c →+ b c b c c b
-
c c b →+ b c b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b →+ b c b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ c
-
c c b →+ b c b c
-
c c b c b →+ b c b a b c b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c →+ b c b a a
-
a b c b →+ b c b c
-
c c b c b →+ b c b c c b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b c b →+ b c b a b c b c
-
a b →+ c
-
c c b c b c →+ b c b b c b b c b c c b c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b c b c →+ b c b b c b c c b c b a a
-
c c b c b →+ b c b c c b c
-
c c b c b c b c →+ b c b b c b b c b c c b c a b c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c b c b c →+ b c b b c b b c b c c b c a a
-
a b c →+ b c b
-
c c b c b c b c →+ b c b b c b b c b c c b c c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b c b c b c →+ b c b b c b b c b c c b c a b c b
-
a b →+ c
-
c c b c b c b c →+ b c b b c b b c b c c b c b c b a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b c b c b c →+ b c b b c b b c b c c b c c c b
-
c c →+ b c b a
-
c c b c b c b c →+ b c b b c b b c b c c b c b c b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c b c b c b c →+ b c b b c b b c b c c b c b c b a b
-
a b →+ c