f(f(

R

↳Dependency Pair Analysis

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

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

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

On this DP problem, a Forward Instantiation 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, a), f(x, a))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Narrowing Transformation

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

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Nar

...

→DP Problem 3

↳Remaining Obligation(s)

The following remains to be proven:

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

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

Duration:

0:00 minutes