f(a, f(

R

↳Dependency Pair Analysis

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

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

↳Narrowing Transformation

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

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

innermost

On this DP problem, a Narrowing 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(a, f(f(a, a),x)))

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

The transformation is resulting in one new DP problem:

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↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Narrowing Transformation

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

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

innermost

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

no new Dependency Pairs are created.

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 3

↳Narrowing Transformation

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

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

innermost

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

no new Dependency Pairs are created.

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 4

↳Remaining Obligation(s)

The following remains to be proven:

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

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

innermost

Duration:

0:00 minutes