f(f(a, a),

R

↳Dependency Pair Analysis

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

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

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

innermost

On this DP problem, a Forward 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, a)

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

innermost

Duration:

0:00 minutes