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