f(

f(

R

↳Dependency Pair Analysis

F(x, g(y)) -> F(g(x),y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Instantiation Transformation

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

f(x, a) ->x

f(x, g(y)) -> f(g(x),y)

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, g(y)) -> F(g(x),y)

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Instantiation Transformation

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

f(x, a) ->x

f(x, g(y)) -> f(g(x),y)

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 3

↳Polynomial Ordering

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

f(x, a) ->x

f(x, g(y)) -> f(g(x),y)

innermost

The following dependency pair can be strictly oriented:

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

There are no usable rules for innermost w.r.t. to the implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1}, x_{2})= x _{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 4

↳Dependency Graph

f(x, a) ->x

f(x, g(y)) -> f(g(x),y)

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes