Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-566)
The rewrite relation of the following TRS is considered.
a(b(x1)) |
→ |
x1 |
(1) |
a(c(x1)) |
→ |
c(c(c(b(x1)))) |
(2) |
b(c(x1)) |
→ |
a(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.
b c c c c c c c c →+ c c c b c c c c c c c c b b b
The derivation can be derived as follows.
-
b c →+ a b:
This is an original rule (OC1).
-
a b →+ ε:
This is an original rule (OC1).
-
b c →+ ε:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c →+ a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c c →+ a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c →+ c c c b:
This is an original rule (OC1).
-
b c c c c →+ a c c c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c c →+ a a
-
a c →+ c c c b
-
b c c c c →+ c c c b c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ a c c c b
-
a c →+ c c c b
-
b c c c c →+ c c c a b c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c c b c c b
-
b c →+ a b
-
b c c c c →+ c c c a a b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c →+ c c c a b c b
-
b c →+ a b
-
b c c c c c c →+ c c c a a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c c c →+ c c c a a b b
-
b c c →+ a
-
b c c c c c c c →+ c c c a a b c c c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c c c c c →+ c c c a a b a
-
a c →+ c c c b
-
b c c c c c c c →+ c c c a a a b c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c a a b c c c b
-
b c →+ a b
-
b c c c c c c c →+ c c c a a a c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c a a a b c c b
-
b c →+ ε
-
b c c c c c c c →+ c c c a a c c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c a a a c b
-
a c →+ c c c b
-
b c c c c c c c →+ c c c a c c c b c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c a a c c c b b
-
a c →+ c c c b
-
b c c c c c c c →+ c c c a c c c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c a c c c b c c b b
-
b c →+ ε
-
b c c c c c c c →+ c c c c c c b c c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c a c c c c b b
-
a c →+ c c c b
-
b c c c c c c c →+ c c c c c c a b c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c c c c b c c c b b
-
b c →+ a b
-
b c c c c c c c →+ c c c c c c a c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c →+ c c c c c c a b c c b b
-
b c →+ ε
-
b c c c c c c c c →+ a c c c c c c a c b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c →+ a b
-
b c c c c c c c →+ c c c c c c a c b b
-
b c c c c c c c c →+ a c c c c c c c c c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c c →+ a c c c c c c a c b b
-
a c →+ c c c b
-
b c c c c c c c c →+ c c c b c c c c c c c c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c c c c →+ a c c c c c c c c c b b b
-
a c →+ c c c b