+(*(

+(+(

+(*(

R

↳Dependency Pair Analysis

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

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

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

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

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

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

innermost

The following dependency pairs can be strictly oriented:

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

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

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

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

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

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

+'(x,_{1}x) ->_{2}x_{1}

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

+(+(x,y),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