Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-493)
The rewrite relation of the following TRS is considered.
a(a(x1)) |
→ |
b(x1) |
(1) |
b(a(c(x1))) |
→ |
c(c(a(a(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 a c a a c c a c c →+ c c c c a c c b c c a b a c a a c c a c c a a a a
The derivation can be derived as follows.
-
b a c →+ c c a a a a:
This is an original rule (OC1).
-
a a →+ b:
This is an original rule (OC1).
-
b a c →+ c c b a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c →+ c c a a a a
-
a a →+ b
-
a a a c →+ c c a a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b
-
b a c →+ c c a a a a
-
a a a c →+ c c a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a c →+ c c a a a a
-
a a →+ b
-
b a c a a c →+ c c b a c c a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a c →+ c c b a a
-
a a a c →+ c c a b a
-
b a c a a c →+ c c c c a a a a c a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c a a c →+ c c b a c c a b a
-
b a c →+ c c a a a a
-
b a c a a c →+ c c c c a b a c a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c a a c →+ c c c c a a a a c a b a
-
a a →+ b
-
b a c →+ c c a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a c →+ c c a a a a
-
a a →+ b
-
b a c →+ c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c →+ c c a a b
-
a a →+ b
-
b a c a a c →+ c c c c a c c b b a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c a a c →+ c c c c a b a c a b a
-
b a c →+ c c b b
-
b a c a a c c →+ c c c c a c c b b a c c a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a c a a c →+ c c c c a c c b b a b a
-
b a c →+ c c a a b
-
b a c a a c c →+ c c c c a c c b c c a a a a c a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c a a c c →+ c c c c a c c b b a c c a a b
-
b a c →+ c c a a a a
-
b a c a a c c →+ c c c c a c c b c c a b a c a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c a a c c →+ c c c c a c c b c c a a a a c a a b
-
a a →+ b
-
b a c →+ c c a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b a c →+ c c a a a a
-
a a →+ b
-
b a c a a c c a c →+ c c c c a c c b c c a b a c a a c c a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a c a a c c →+ c c c c a c c b c c a b a c a a b
-
b a c →+ c c a b a
-
b a c a a c c a c c →+ c c c c a c c b c c a b a c a a c c a c c a a a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b a c a a c c a c →+ c c c c a c c b c c a b a c a a c c a b a
-
b a c →+ c c a a a a