Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-260)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
x1 |
(1) |
|
a(b(x1)) |
→ |
b(c(b(a(c(a(a(x1))))))) |
(2) |
|
c(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 b c b b c b →+ b c b b c b c a b c b b c b a c a a
The derivation can be derived as follows.
-
a b →+ b c b a c a a:
This is an original rule (OC1).
-
a →+ ε:
This is an original rule (OC1).
-
a b →+ b c b a c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c b a c a a
-
a →+ ε
-
a b →+ b c b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c b a c a
-
a →+ ε
-
c c →+ ε:
This is an original rule (OC1).
-
a b c →+ b c b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c b a c
-
c c →+ ε
-
a b →+ b c b c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b →+ b c b a c a a
-
a →+ ε
-
a b b →+ b c b c a b c b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c b c a a
-
a b →+ b c b a c
-
a b c b b →+ b c b b c b c a b c b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b c b a
-
a b b →+ b c b c a b c b a c
-
a b c b b c →+ b c b b c b c a b c b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b b →+ b c b b c b c a b c b a c
-
c c →+ ε
-
a b c b b c b →+ b c b b c b c a b c b b c b a c a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b b c →+ b c b b c b c a b c b a
-
a b →+ b c b a c a a