Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-497)
The rewrite relation of the following TRS is considered.
|
a(a(x1)) |
→ |
b(a(b(c(c(x1))))) |
(1) |
|
c(a(x1)) |
→ |
x1 |
(2) |
|
c(b(x1)) |
→ |
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 a b a b a b a a b →+ b a b b a b a a b a b a b a a b c c
The derivation can be derived as follows.
-
a a →+ b a b c c:
This is an original rule (OC1).
-
c b →+ a:
This is an original rule (OC1).
-
c b a →+ b a b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b →+ a
-
a a →+ b a b c c
-
a a b a →+ b a b c b a b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b c c
-
c b a →+ b a b c c
-
c b a b a →+ b a b c b a b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b →+ a
-
a a b a →+ b a b c b a b c c
-
c b a b a →+ b a b a a b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b a b a →+ b a b c b a b c c
-
c b →+ a
-
a a b a b a →+ b a b c b a b a a b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b c c
-
c b a b a →+ b a b a a b c c
-
a a b a b a →+ b a b a a b a a b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a →+ b a b c b a b a a b c c
-
c b →+ a
-
c a →+ ε:
This is an original rule (OC1).
-
a a a →+ b a b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b c c
-
c a →+ ε
-
a a a b →+ b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a a →+ b a b c
-
c b →+ a
-
c b a a b →+ b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b →+ a
-
a a a b →+ b a b a
-
a a b a a b →+ b a b c b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b c c
-
c b a a b →+ b a b a
-
a a b a a b →+ b a b a a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a a b →+ b a b c b a b a
-
c b →+ a
-
a a b a b a →+ b a b b a b a a b a c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a →+ b a b a a b a a b c c
-
a a b a a b →+ b a b a a b a
-
a a b a b a b a a b →+ b a b b a b a a b a c b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b a b a →+ b a b b a b a a b a c c
-
c b a a b →+ b a b a
-
a a b a b a b a a b →+ b a b b a b a a b a a a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a a b →+ b a b b a b a a b a c b a b a
-
c b →+ a
-
a a b a b a b a a b →+ b a b b a b a a b a b a b c c b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a a b →+ b a b b a b a a b a a a b a
-
a a →+ b a b c c
-
a a b a b a b a a b →+ b a b b a b a a b a b a b c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a a b →+ b a b b a b a a b a b a b c c b a
-
c b →+ a
-
a a b a b a b a a b →+ b a b b a b a a b a b a b c b a b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a b a b a b a a b →+ b a b b a b a a b a b a b c a a
-
a a →+ b a b c c
-
a a b a b a b a a b →+ b a b b a b a a b a b a b a a b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a b a b a b a a b →+ b a b b a b a a b a b a b c b a b c c
-
c b →+ a