Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-170)
The rewrite relation of the following TRS is considered.
a(x1) |
→ |
x1 |
(1) |
a(b(x1)) |
→ |
b(a(c(a(x1)))) |
(2) |
c(b(x1)) |
→ |
x1 |
(3) |
c(c(x1)) |
→ |
b(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 b c b b c →+ b b a b b c b b c ε
The derivation can be derived as follows.
-
a b →+ b a c a:
This is an original rule (OC1).
-
a →+ ε:
This is an original rule (OC1).
-
a b →+ b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c →+ b:
This is an original rule (OC1).
-
a b c →+ b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b c →+ b a c b a b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b a c a
-
a b c →+ b a b
-
c b →+ ε:
This is an original rule (OC1).
-
a b b c →+ b a a b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c →+ b a c b a b
-
c b →+ ε
-
a b →+ b c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c →+ b a b c a:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b c →+ b a a b
-
a b →+ b c a
-
a b b c →+ b b a c c a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c →+ b a b c a
-
a b →+ b a c
-
a b b c →+ b b a b a:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c →+ b b a c c a
-
c c →+ b
-
a b c →+ b b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b c →+ b a b
-
a b →+ b a c
-
a b b c →+ b a c b b a c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b →+ b a c a
-
a b c →+ b b a c
-
a b b c →+ b a c b b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c →+ b a c b b a c
-
a →+ ε
-
a b b c b b c →+ b b a b b a c b b c:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a b b c →+ b b a b a
-
a b b c →+ b a c b b c
-
a b b c b b c →+ b b a b b c b b c:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a b b c b b c →+ b b a b b a c b b c
-
a →+ ε