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