*(

R

↳Dependency Pair Analysis

*'(x, *(minus(y),y)) -> *'(minus(*(y,y)),x)

*'(x, *(minus(y),y)) -> *'(y,y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

***'( x, *(minus(y), y)) -> *'(y, y)**

*(x, *(minus(y),y)) -> *(minus(*(y,y)),x)

The following dependency pair can be strictly oriented:

*'(x, *(minus(y),y)) -> *'(y,y)

Additionally, the following usable rule w.r.t. to the implicit AFS can be oriented:

*(x, *(minus(y),y)) -> *(minus(*(y,y)),x)

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(*'(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(*(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(minus(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Instantiation Transformation

***'( x, *(minus(y), y)) -> *'(minus(*(y, y)), x)**

*(x, *(minus(y),y)) -> *(minus(*(y,y)),x)

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

As a result of transforming the rule

one new Dependency Pair is created:

*'(x, *(minus(y),y)) -> *'(minus(*(y,y)),x)

*'(minus(x'''), *(minus(y'),y')) -> *'(minus(*(y',y')), minus(x'''))

The transformation is resulting in no new DP problems.

Duration:

0:00 minutes