Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-249)
The rewrite relation of the following TRS is considered.
a(x1) |
→ |
x1 |
(1) |
a(b(x1)) |
→ |
b(c(a(a(a(x1))))) |
(2) |
a(c(c(x1))) |
→ |
b(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 c c →+ b c b c a a b b c c ε
The derivation can be derived as follows.
-
a b →+ b c a a a:
This is an original rule (OC1).
-
a c c →+ b:
This is an original rule (OC1).
-
a b c c →+ b c a a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c a a a
-
a c c →+ b
-
a →+ ε:
This is an original rule (OC1).
-
a b →+ b c a a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c →+ b c a b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c c →+ b c a a b
-
a b →+ b c
-
a b c c →+ b c b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b c c →+ b c a b c
-
a b →+ b c
-
a b b c c →+ b c a a b c b c c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b c a a a
-
a b c c →+ b c b c c
-
a b b c c →+ b c a b c c b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c c →+ b c a a b c b c c
-
a b →+ b c
-
a b b c c →+ b c b c a a a c c b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c c →+ b c a b c c b c c
-
a b →+ b c a a a
-
a b b c c →+ b c b c a a b b c c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c c →+ b c b c a a a c c b c c
-
a c c →+ b