Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-564)
The rewrite relation of the following TRS is considered.
|
a(b(x1)) |
→ |
x1 |
(1) |
|
a(c(x1)) |
→ |
c(c(b(b(x1)))) |
(2) |
|
b(c(x1)) |
→ |
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.
b c c c c →+ c c b c c c c b b c b b b b b b b
The derivation can be derived as follows.
-
b c →+ a a:
This is an original rule (OC1).
-
a c →+ c c b b:
This is an original rule (OC1).
-
b c c →+ a c c b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c →+ a a
-
a c →+ c c b b
-
b c c →+ c c b b c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c →+ a c c b b
-
a c →+ c c b b
-
b c c →+ c c b a a b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c →+ c c b b c b b
-
b c →+ a a
-
a b →+ ε:
This is an original rule (OC1).
-
b c b →+ a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c b b →+ ε:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c →+ c c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c →+ c c b b c b b
-
b c b b →+ ε
-
b c c c c →+ c c b a a b c c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c →+ c c b a a b b
-
b c c →+ c c b
-
b c c c c →+ c c b a a a a c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b a a b c c b
-
b c →+ a a
-
b c c c c →+ c c b a a a c c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b a a a a c b
-
a c →+ c c b b
-
b c c c c →+ c c b a a c c b b c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b a a a c c b b b
-
a c →+ c c b b
-
b c c c c →+ c c b a c c b b c b b c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b a a c c b b c b b b
-
a c →+ c c b b
-
b c c c c →+ c c b c c b b c b b c b b c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b a c c b b c b b c b b b
-
a c →+ c c b b
-
b c c c c →+ c c b c c b b c b c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b c c b b c b b c b b c b b b
-
b c b b →+ ε
-
b c b c →+ c c b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c b →+ a
-
a c →+ c c b b
-
b c c c c →+ c c b c c b c c b b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b c c b b c b c b b b
-
b c b c →+ c c b b
-
b c c c c →+ c c b c c a c c b b b b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b c c b c c b b b b b
-
b c c →+ a c c b b
-
b c c c c →+ c c b c c c c b b c b b b b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c b c c a c c b b b b b b b
-
a c →+ c c b b