Term Rewriting System R:
[x, y]
f(f(x, a), y) -> f(y, f(x, y))
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(f(x, a), y) -> F(y, f(x, y))
F(f(x, a), y) -> F(x, y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Usable Rules (Innermost)
Dependency Pair:
F(f(x, a), y) -> F(y, f(x, y))
Rule:
f(f(x, a), y) -> f(y, f(x, y))
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
↳Instantiation Transformation
Dependency Pair:
F(f(x, a), y) -> F(y, f(x, y))
Rule:
none
Strategy:
innermost
On this DP problem, an Instantiation SCC transformation can be performed.
As a result of transforming the rule
F(f(x, a), y) -> F(y, f(x, y))
one new Dependency Pair
is created:
F(f(x0, a), f(x'', f(x0, a))) -> F(f(x'', f(x0, a)), f(x0, f(x'', f(x0, a))))
The transformation is resulting in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes