f(

R

↳Dependency Pair Analysis

F(x) -> F(g(x))

Furthermore,

R

↳DPs

→DP Problem 1

↳Instantiation Transformation

**F( x) -> F(g(x))**

f(x) -> f(g(x))

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

F(x) -> F(g(x))

F(g(x'')) -> F(g(g(x'')))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Instantiation Transformation

**F(g( x'')) -> F(g(g(x'')))**

f(x) -> f(g(x))

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

F(g(x'')) -> F(g(g(x'')))

F(g(g(x''''))) -> F(g(g(g(x''''))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 3

↳Instantiation Transformation

**F(g(g( x''''))) -> F(g(g(g(x''''))))**

f(x) -> f(g(x))

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

F(g(g(x''''))) -> F(g(g(g(x''''))))

F(g(g(g(x'''''')))) -> F(g(g(g(g(x'''''')))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 4

↳Instantiation Transformation

**F(g(g(g( x'''''')))) -> F(g(g(g(g(x'''''')))))**

f(x) -> f(g(x))

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

F(g(g(g(x'''''')))) -> F(g(g(g(g(x'''''')))))

F(g(g(g(g(x''''''''))))) -> F(g(g(g(g(g(x''''''''))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 5

↳Instantiation Transformation

**F(g(g(g(g( x''''''''))))) -> F(g(g(g(g(g(x''''''''))))))**

f(x) -> f(g(x))

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

F(g(g(g(g(x''''''''))))) -> F(g(g(g(g(g(x''''''''))))))

F(g(g(g(g(g(x'''''''''')))))) -> F(g(g(g(g(g(g(x'''''''''')))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 6

↳Remaining Obligation(s)

The following remains to be proven:

**F(g(g(g(g(g( x'''''''''')))))) -> F(g(g(g(g(g(g(x'''''''''')))))))**

f(x) -> f(g(x))

innermost

Duration:

0:00 minutes