Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-402)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
b(x1) |
(1) |
|
b(b(a(c(x1)))) |
→ |
a(c(c(b(a(a(x1)))))) |
(2) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Looping derivation
There is a looping derivation.
b b a c b a c c a c c →+ a c c a c c a c c b a c c b b a c b a c c a c c b a a
The derivation can be derived as follows.
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b b a c →+ a c c b a a:
This is an original rule (OC1).
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a →+ b:
This is an original rule (OC1).
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b b a c →+ a c c b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
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b b a c →+ a c c b a a
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a →+ b
-
a b a c →+ a c c b b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a →+ b
-
b b a c →+ a c c b b a
-
b b a c b a c →+ a c c b b a c c b b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b a c →+ a c c b b a
-
a b a c →+ a c c b b a
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b b a c b a c →+ a c c a c c b a a c b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c →+ a c c b b a c c b b a
-
b b a c →+ a c c b a a
-
b b a c b a c →+ a c c a c c b b a c b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c →+ a c c a c c b a a c b b a
-
a →+ b
-
b b a c b a c →+ a c c a c c a c c b a a b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c →+ a c c a c c b b a c b b a
-
b b a c →+ a c c b a a
-
b b a c b a c →+ a c c a c c a c c b b a b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c →+ a c c a c c a c c b a a b b a
-
a →+ b
-
b b a c b a c →+ a c c a c c a c c b b b b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c →+ a c c a c c a c c b b a b b a
-
a →+ b
-
b b a c b a c c →+ a c c a c c a c c b b b a c c b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b a c b a c →+ a c c a c c a c c b b b b b a
-
b b a c →+ a c c b a a
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b b a c b a c c →+ a c c a c c a c c b b b a c c b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b a c b a c c →+ a c c a c c a c c b b b a c c b a a
-
a →+ b
-
b b a c b a c c →+ a c c a c c a c c b b b a c c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c c →+ a c c a c c a c c b b b a c c b a b
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a →+ b
-
b b a c b a c c →+ a c c a c c a c c b a c c b a a c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c c →+ a c c a c c a c c b b b a c c b b b
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b b a c →+ a c c b a a
-
b b a c b a c c →+ a c c a c c a c c b a c c b b a c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c c →+ a c c a c c a c c b a c c b a a c b b b
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a →+ b
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b b a c b a c c a c →+ a c c a c c a c c b a c c b b a c b a c c b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b a c b a c c →+ a c c a c c a c c b a c c b b a c b b b
-
b b a c →+ a c c b a a
-
b b a c b a c c a c →+ a c c a c c a c c b a c c b b a c b a c c b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b b a c b a c c a c →+ a c c a c c a c c b a c c b b a c b a c c b a a
-
a →+ b
-
b b a c b a c c a c c →+ a c c a c c a c c b a c c b b a c b a c c a c c b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b a c b a c c a c →+ a c c a c c a c c b a c c b b a c b a c c b b a
-
b b a c →+ a c c b a a