Term Rewriting System R:
[x]
f(f(x)) -> g(f(x))
g(g(x)) -> f(x)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(f(x)) -> G(f(x))
G(g(x)) -> F(x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
Dependency Pairs:
G(g(x)) -> F(x)
F(f(x)) -> G(f(x))
Rules:
f(f(x)) -> g(f(x))
g(g(x)) -> f(x)
On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule
F(f(x)) -> G(f(x))
one new Dependency Pair
is created:
F(f(f(x''))) -> G(g(f(x'')))
The transformation is resulting in one new DP problem:
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pairs:
F(f(f(x''))) -> G(g(f(x'')))
G(g(x)) -> F(x)
Rules:
f(f(x)) -> g(f(x))
g(g(x)) -> f(x)
Termination of R could not be shown.
Duration:
0:00 minutes