Term Rewriting System R:
[x]
f(x, x) -> f(g(x), x)
g(x) -> s(x)
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x, x) -> F(g(x), x)
F(x, x) -> G(x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Usable Rules (Innermost)
Dependency Pair:
F(x, x) -> F(g(x), x)
Rules:
f(x, x) -> f(g(x), x)
g(x) -> s(x)
Strategy:
innermost
As we are in the innermost case, we can delete all 1 non-usable-rules.
R
↳DPs
→DP Problem 1
↳UsableRules
→DP Problem 2
↳Rewriting Transformation
Dependency Pair:
F(x, x) -> F(g(x), x)
Rule:
g(x) -> s(x)
Strategy:
innermost
On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule
F(x, x) -> F(g(x), x)
one new Dependency Pair
is created:
F(x, x) -> F(s(x), x)
The transformation is resulting in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes