f(

f(g(

R

↳Dependency Pair Analysis

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

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

f(x,x) -> a

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Forward Instantiation Transformation

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

f(x,x) -> a

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Polynomial Ordering

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

f(x,x) -> a

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

The following dependency pair can be strictly oriented:

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

There are no usable rules 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})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳FwdInst

...

→DP Problem 4

↳Dependency Graph

f(x,x) -> a

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes