f(f(a, a),

R

↳Dependency Pair Analysis

F(f(a, a),x) -> F(f(x, f(a, f(a, a))), a)

F(f(a, a),x) -> F(x, f(a, f(a, a)))

F(f(a, a),x) -> F(a, f(a, a))

Furthermore,

R

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

**F(f(a, a), x) -> F(x, f(a, f(a, a)))**

f(f(a, a),x) -> f(f(x, f(a, f(a, a))), a)

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

**F(f(a, a), x) -> F(x, f(a, f(a, a)))**

none

innermost

On this DP problem, an Instantiation SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

F(f(a, a),x) -> F(x, f(a, f(a, a)))

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.

Duration:

0:00 minutes