f(f(a,

R

↳Dependency Pair Analysis

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

innermost

Duration:

0:00 minutes