f(a, f(f(a, a),

R

↳Dependency Pair Analysis

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Forward Instantiation Transformation

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

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

innermost

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

As a result of transforming the rule

two new Dependency Pairs are created:

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Remaining Obligation(s)

The following remains to be proven:

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

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

innermost

Duration:

0:00 minutes