Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-298)
The rewrite relation of the following TRS is considered.
a(x1) |
→ |
x1 |
(1) |
a(b(b(x1))) |
→ |
b(b(b(a(c(a(x1)))))) |
(2) |
c(b(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 b b b b b b b b →+ b b b a b b b b b b b b c c c
The derivation can be derived as follows.
-
a b b →+ b b b a c a:
This is an original rule (OC1).
-
a →+ ε:
This is an original rule (OC1).
-
a b b →+ b b b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b b a c a
-
a →+ ε
-
a b b b b →+ b b b a c b b b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b b a c a
-
a b b →+ b b b a c
-
a b b b b →+ b b b a c b b b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b →+ b b b a c b b b a c
-
a →+ ε
-
c b →+ ε:
This is an original rule (OC1).
-
a b b b b →+ b b b a b b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b →+ b b b a c b b b c
-
c b →+ ε
-
a b b b b →+ b b b b b b a c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b →+ b b b a b b c
-
a b b →+ b b b a c
-
a b b b b b b →+ b b b a c b b b b b b a c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b b a c a
-
a b b b b →+ b b b b b b a c c
-
a b b b b b b →+ b b b a c b b b b b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b →+ b b b a c b b b b b b a c c
-
a →+ ε
-
a b b b b b b →+ b b b a b b b b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b →+ b b b a c b b b b b b c c
-
c b →+ ε
-
a b b b →+ b b b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b b a c
-
c b →+ ε
-
a b b b b b b →+ b b b b b b a b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b →+ b b b a b b b b b c c
-
a b b b →+ b b b a
-
a b b b b b b →+ b b b b b b b b b a c c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b →+ b b b b b b a b b c c
-
a b b →+ b b b a c
-
a b b b b b b b b →+ b b b a c b b b b b b b b b a c c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b b a c a
-
a b b b b b b →+ b b b b b b b b b a c c c
-
a b b b b b b b b →+ b b b a c b b b b b b b b b c c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b b b →+ b b b a c b b b b b b b b b a c c c
-
a →+ ε
-
a b b b b b b b b →+ b b b a b b b b b b b b c c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b b b b b b →+ b b b a c b b b b b b b b b c c c
-
c b →+ ε