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