+(+(

+(f(

+(f(

R

↳Dependency Pair Analysis

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

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

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

innermost

The following dependency pairs can be strictly oriented:

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

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

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

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

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

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

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

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

f(x) -> f(_{1}x)_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes