Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-83)
The rewrite relation of the following TRS is considered.
a(x1) |
→ |
x1 |
(1) |
a(a(x1)) |
→ |
b(a(b(c(x1)))) |
(2) |
c(x1) |
→ |
x1 |
(3) |
c(b(x1)) |
→ |
a(c(x1)) |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Looping derivation
There is a looping derivation.
c b b b b b a b →+ b b c b b b b b a b c
The derivation can be derived as follows.
-
c b →+ a c:
This is an original rule (OC1).
-
c b b →+ a a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b c:
This is an original rule (OC1).
-
c b b →+ b a b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b →+ a a c
-
a a →+ b a b c
-
a →+ ε:
This is an original rule (OC1).
-
c b b →+ b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b →+ b a b c c
-
a →+ ε
-
c →+ ε:
This is an original rule (OC1).
-
c b →+ a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a →+ b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b a →+ b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b a →+ b b c b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b →+ b b c c
-
c b a →+ b a b
-
c b b b a →+ b b a c a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b b a →+ b b c b a b
-
c b →+ a c
-
c b b b a →+ b b a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b b a →+ b b a c a b
-
c →+ ε
-
c b b b a →+ b b b a b c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b b a →+ b b a a b
-
a a →+ b a b c
-
c b b b a →+ b b b a b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b a →+ b b b a b c b
-
c b →+ a c
-
c b b b a →+ b b b b a c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c b b b a →+ b b b a b a c
-
a →+ ε
-
c b b b a b →+ b b b b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b a →+ b b b b a c
-
c b →+ a
-
c b b b b b a b →+ b b c b b b b a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b →+ b b c c
-
c b b b a b →+ b b b b a a
-
c b b b b b a b →+ b b c b b b b b a b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c b b b b b a b →+ b b c b b b b a a
-
a a →+ b a b c