Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-488)
The rewrite relation of the following TRS is considered.
a(a(x1)) |
→ |
b(x1) |
(1) |
a(b(x1)) |
→ |
c(a(x1)) |
(2) |
c(c(x1)) |
→ |
b(a(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 b b a b b →+ b a b b b b a b b b a
The derivation can be derived as follows.
-
a b →+ c a:
This is an original rule (OC1).
-
a b b →+ c c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c →+ b a b:
This is an original rule (OC1).
-
a b b →+ b a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b →+ c c a
-
c c →+ b a b
-
c c →+ b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b →+ c c a
-
c c →+ b c a
-
a a →+ b:
This is an original rule (OC1).
-
a b b a →+ b c a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b c a a
-
a a →+ b
-
a b b a →+ b c c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b a →+ b c a b
-
a b →+ c a
-
a b b a →+ b b c a a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b a →+ b c c a
-
c c →+ b c a
-
a b b a b b →+ b b c a b a b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b a →+ b b c a a
-
a b b →+ b a b a
-
a b b a b b →+ b b c c a a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b a b b →+ b b c a b a b a
-
a b →+ c a
-
a b b a b b →+ b b c c b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b a b b →+ b b c c a a b a
-
a a →+ b
-
a b b a b b →+ b b b a b b b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b a b b →+ b b c c b b a
-
c c →+ b a b
-
a b b b b a b b →+ b a b b b b a b b b a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b →+ b a b a
-
a b b a b b →+ b b b a b b b a