Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-211)
The rewrite relation of the following TRS is considered.
a(x1) |
→ |
x1 |
(1) |
a(b(x1)) |
→ |
b(b(a(c(a(x1))))) |
(2) |
c(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 b c b b b b c b b →+ b b b b c b b a b c b b b b c b b a c a c
The derivation can be derived as follows.
-
a b →+ b b a c a:
This is an original rule (OC1).
-
a →+ ε:
This is an original rule (OC1).
-
a b →+ b b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c b →+ a:
This is an original rule (OC1).
-
a b →+ b b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b b →+ b b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c b →+ a
-
a b →+ b b c a
-
a b c b b →+ b b a b b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b b a c
-
c c b b →+ b b c a
-
a b c b b →+ b b b b a c a b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b a b b c a
-
a b →+ b b a c a
-
a b c b b →+ b b b b c a b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b b b a c a b c a
-
a →+ ε
-
a b →+ b b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b b b c b b c c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b b b c a b c a
-
a b →+ b b c
-
a b c b b b →+ b b b b c b b c c b b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b b →+ b b b b c b b c c a
-
a b →+ b b c a
-
a b c b b b →+ b b b b c b b a b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b b →+ b b b b c b b c c b b c a
-
c c b →+ a
-
c c b b →+ b b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c b →+ a
-
a b →+ b b a c
-
c c b b →+ b b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c b b →+ b b a c
-
a →+ ε
-
a b c b b →+ b b a b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b b a c
-
c c b b →+ b b c
-
a b c b b →+ b b b b a c a b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b a b b c
-
a b →+ b b a c a
-
a b c b b →+ b b b b c a b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b →+ b b b b a c a b c
-
a →+ ε
-
a b c b b b b c b b →+ b b b b c b b a b c b b b b c a b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b b b →+ b b b b c b b a b c a
-
a b c b b →+ b b b b c a b c
-
a b c b b b b c b b →+ b b b b c b b a b c b b b b c b b a c a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b b b b c b b →+ b b b b c b b a b c b b b b c a b c
-
a b →+ b b a c a