f(f(

R

↳Dependency Pair Analysis

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Forward Instantiation Transformation

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

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Narrowing Transformation

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

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

The transformation is resulting in no new DP problems.

Duration:

0:00 minutes