+(0,

+(s(

+(s(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

+(0,y) ->y

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

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

The following dependency pairs can be strictly oriented:

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

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

The following rules can be oriented:

+(0,y) ->y

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

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

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

+' > s

+ > s

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

+(0,y) ->y

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

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes