+(-(

-(+(

R

↳Dependency Pair Analysis

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

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

The following dependency pair can be strictly oriented:

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

The following rules can be oriented:

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(-(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(+'(x)_{1}, x_{2})= 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,z),y)

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes