Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-378)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
b(x1) |
(1) |
|
a(c(b(x1))) |
→ |
c(a(b(a(c(x1))))) |
(2) |
|
b(c(x1)) |
→ |
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 c b b b c c b b →+ c c a b a c b b b c c b b ε
The derivation can be derived as follows.
-
a c b →+ c a b a c:
This is an original rule (OC1).
-
a →+ b:
This is an original rule (OC1).
-
b c →+ ε:
This is an original rule (OC1).
-
a c →+ ε:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c b →+ c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c b →+ c a b a c
-
a c →+ ε
-
a c b b →+ c a b c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c b →+ c a b a c
-
a c b →+ c a b
-
a c b b →+ c a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b →+ c a b c a b
-
b c →+ ε
-
a c b b b →+ c a b c a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c b →+ c a b a c
-
a c b b →+ c a a b
-
a c b b b c →+ c a b c a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c b b b →+ c a b c a a b
-
b c →+ ε
-
a c b b b c →+ c a a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c →+ c a b c a a
-
b c →+ ε
-
a c b →+ c b b a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b →+ c a b a c
-
a →+ b
-
a c b b b c c b →+ c a a c b b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c b b b c →+ c a a a
-
a c b →+ c b b a c
-
a c b b b c c b →+ c a c a b a c b a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b →+ c a a c b b a c
-
a c b →+ c a b a c
-
a c b b b c c b →+ c a c a b c a b a c a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b →+ c a c a b a c b a c
-
a c b →+ c a b a c
-
a c b b b c c b →+ c a c a a b a c a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b →+ c a c a b c a b a c a c
-
b c →+ ε
-
a c b b b c c b b →+ c a c a a b a c c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a c b b b c c b →+ c a c a a b a c a c
-
a c b →+ c a b
-
a c b b b c c b b →+ c a c b a b a c c a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b b →+ c a c a a b a c c a b
-
a →+ b
-
a c b b b c c b b →+ c a c b b b a c c a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b b →+ c a c b a b a c c a b
-
a →+ b
-
a c b b b c c b b →+ c a c b b b b c c a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b b →+ c a c b b b a c c a b
-
a →+ b
-
a c b b b c c b b →+ c a c b b b b c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b b →+ c a c b b b b c c a b
-
a →+ b
-
a c b b b c c b b →+ c c a b a c b b b c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a c b b b c c b b →+ c a c b b b b c c b b
-
a c b →+ c a b a c