+(

+(*(

+(*(

R

↳Dependency Pair Analysis

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

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

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

innermost

The following dependency pairs can be strictly oriented:

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

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

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}_{ }^{ }_{ }^{ }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}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes