*(

*(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

*(x,x) ->x

The following dependency pair can be strictly oriented:

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

The following usable rules w.r.t. to the AFS can be oriented:

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

*(x,x) ->x

Used ordering: Polynomial ordering with Polynomial interpretation:

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

↳Argument Filtering and Ordering

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

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

*(x,x) ->x

The following dependency pair can be strictly oriented:

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

There are no usable rules w.r.t. to the AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }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_{2}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

...

→DP Problem 3

↳Dependency Graph

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

*(x,x) ->x

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes