Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-7)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
x1 |
(1) |
|
a(x1) |
→ |
b(x1) |
(2) |
|
a(b(c(x1))) |
→ |
c(b(a(c(a(x1))))) |
(3) |
|
c(x1) |
→ |
x1 |
(4) |
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 c c b c →+ b a b c b c c b c ε
The derivation can be derived as follows.
-
a b c →+ c b a c a:
This is an original rule (OC1).
-
c →+ ε:
This is an original rule (OC1).
-
a b c →+ b a c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c →+ c b a c a
-
c →+ ε
-
a →+ b:
This is an original rule (OC1).
-
a b c →+ b a c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a →+ ε:
This is an original rule (OC1).
-
a b c →+ c b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c →+ c b a c a
-
a →+ ε
-
a b c c →+ b c b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b a b
-
a b c →+ c b c a
-
a b c b c c →+ b a c b c b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b a c a
-
a b c c →+ b c b c a
-
a b c b c c →+ b a b c b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b c c →+ b a c b c b c a
-
c →+ ε
-
a b c →+ c b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ c b a c a
-
a →+ ε
-
a b c b c c b c →+ b a b c b c c b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c b c c →+ b a b c b c a
-
a b c →+ c b a c
-
a b c b c c b c →+ b a b c b c c b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c b c c b c →+ b a b c b c c b a c
-
a →+ ε