*(

R

↳Dependency Pair Analysis

*'(x, +(y,z)) -> *'(x,y)

*'(x, +(y,z)) -> *'(x,z)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

***'( x, +(y, z)) -> *'(x, z)**

*(x, +(y,z)) -> +(*(x,y), *(x,z))

The following dependency pairs can be strictly oriented:

*'(x, +(y,z)) -> *'(x,z)

*'(x, +(y,z)) -> *'(x,y)

There are no usable rules using the Ce-refinement that need to be oriented.

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}_{ }^{ }

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}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

*(x, +(y,z)) -> +(*(x,y), *(x,z))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes