Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-353)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
b(x1) |
(1) |
|
a(b(x1)) |
→ |
b(b(a(c(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 a b b b c c b c c b
The derivation can be derived as follows.
-
a b →+ b b a c c a:
This is an original rule (OC1).
-
a b b →+ b b a c c b b a c c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b b a c c a
-
a b →+ b b a c c a
-
c b →+ ε:
This is an original rule (OC1).
-
a b b →+ b b a c b a c c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b →+ b b a c c b b a c c a
-
c b →+ ε
-
a b b →+ b b a a c c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b →+ b b a c b a c c a
-
c b →+ ε
-
a →+ b:
This is an original rule (OC1).
-
a b →+ b b a c c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b b a c c a
-
a →+ b
-
a b →+ b b b c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b →+ b b a c c b
-
a →+ b
-
a b b b →+ b b a a c c b b b c c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b b a a c c a
-
a b →+ b b b c c b
-
a b b b →+ b b a a c b b c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b →+ b b a a c c b b b c c b
-
c b →+ ε
-
a b b b →+ b b a a b c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b →+ b b a a c b b c c b
-
c b →+ ε
-
a b b b →+ b b a b b b c c b c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b b →+ b b a a b c c b
-
a b →+ b b b c c b