Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-100)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
x1 |
(1) |
|
a(a(a(x1))) |
→ |
b(x1) |
(2) |
|
b(c(x1)) |
→ |
c(a(c(b(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.
b c c c c c →+ ε b c c c c c b
The derivation can be derived as follows.
-
b c →+ c a c b:
This is an original rule (OC1).
-
c →+ ε:
This is an original rule (OC1).
-
b c →+ a c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c →+ a c a c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c →+ a c b
-
b c →+ a c b
-
b c c →+ a a c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c →+ a c a c b
-
c →+ ε
-
b c c c →+ a c a a c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c →+ a c b
-
b c c →+ a a c b
-
b c c c →+ a a a c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c →+ a c a a c b
-
c →+ ε
-
a a a →+ b:
This is an original rule (OC1).
-
b c c c →+ b c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c →+ a a a c b
-
a a a →+ b
-
a →+ ε:
This is an original rule (OC1).
-
b c →+ c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c →+ c c c a c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c →+ c c b
-
b c →+ c a c b
-
b c c c c c →+ b c c c c a c b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b c c c →+ b c b
-
b c c →+ c c c a c b
-
b c c c c c →+ b c c c c c b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
b c c c c c →+ b c c c c a c b
-
a →+ ε