f(a, f(

R

↳Dependency Pair Analysis

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

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

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

innermost

As we are in the innermost case, we can delete all 1 non-usable-rules.

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↳DPs

→DP Problem 1

↳UsableRules

→DP Problem 2

↳Instantiation Transformation

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

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

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

The transformation is resulting in no new DP problems.

Duration:

0:00 minutes