*(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

innermost

The following dependency pair can be strictly oriented:

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

The following usable rule for innermost can be oriented:

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(*'(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(*(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(minus)= 0 _{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

*'(x,_{1}x) -> *'(_{2}x,_{1}x)_{2}

*(x,_{1}x) -> *(_{2}x,_{1}x)_{2}

minus(x) -> minus_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes