Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-21)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
x1 |
(1) |
|
a(x1) |
→ |
b(x1) |
(2) |
|
b(b(c(x1))) |
→ |
a(c(c(c(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.
a b c b c c →+ c c c c c c c c c a b c b c c c
The derivation can be derived as follows.
-
a →+ b:
This is an original rule (OC1).
-
b b c →+ a c c c a a:
This is an original rule (OC1).
-
a →+ ε:
This is an original rule (OC1).
-
b b c →+ c c c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b c →+ a c c c a a
-
a →+ ε
-
b b c →+ a c c c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b c →+ a c c c a a
-
a →+ b
-
b b c →+ b c c c a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b c →+ a c c c a b
-
a →+ b
-
b b c →+ b c c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b c →+ b c c c a b
-
a →+ b
-
a b c →+ b c c c b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b
-
b b c →+ b c c c b b
-
b b c b c →+ c c c a b c c c b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b c →+ c c c a a
-
a b c →+ b c c c b b
-
a b c b c →+ c c c a b c c c b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b
-
b b c b c →+ c c c a b c c c b b
-
b b c →+ c c c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b c →+ c c c a a
-
a →+ b
-
a b c →+ c c c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b
-
b b c →+ c c c a b
-
a b c b 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).
-
a b c b c →+ c c c a b c c c b b
-
a b c →+ c c c a b
-
a b c b c →+ c c c c c c c c c a b c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b c →+ c c c c c c a b c c b b
-
a b c →+ c c c a b
-
b b c →+ a c c c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b c →+ a c c c a a
-
a →+ ε
-
b b c →+ b c c c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b c →+ a c c c a
-
a →+ b
-
b b c →+ b c c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b c →+ b c c c a
-
a →+ ε
-
a b c b c c →+ c c c c c c c c c a b c b c c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b c →+ c c c c c c c c c a b c b b
-
b b c →+ b c c c