+(*(

*(*(

R

↳Dependency Pair Analysis

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

innermost

The following dependency pair can be strictly oriented:

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

There are no usable rules for innermost 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), *(a,y)) -> *(+(x, a),y)

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes