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