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