minus(0) -> 0

minus(minus(

+(

+(0,

+(minus(1), 1) -> 0

+(

+(

+(minus(+(

R

↳Dependency Pair Analysis

+'(x, minus(y)) -> MINUS(+(minus(x),y))

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

+'(x, minus(y)) -> MINUS(x)

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

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

+'(minus(+(x, 1)), 1) -> MINUS(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

minus(0) -> 0

minus(minus(x)) ->x

+(x, 0) ->x

+(0,y) ->y

+(minus(1), 1) -> 0

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

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

+(minus(+(x, 1)), 1) -> minus(x)

innermost

The following dependency pair can be strictly oriented:

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

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

minus(0) -> 0

minus(minus(x)) ->x

Used ordering: Homeomorphic Embedding Order with EMB

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}

minus(x) ->_{1}x_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

minus(0) -> 0

minus(minus(x)) ->x

+(x, 0) ->x

+(0,y) ->y

+(minus(1), 1) -> 0

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

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

+(minus(+(x, 1)), 1) -> minus(x)

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes