+(

+(

+(0, s(

s(+(0,

R

↳Dependency Pair Analysis

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

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

S(+(0,y)) -> S(y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳Remaining

**S(+(0, y)) -> S(y)**

+(x, 0) ->x

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

+(0, s(y)) -> s(y)

s(+(0,y)) -> s(y)

The following dependency pair can be strictly oriented:

S(+(0,y)) -> S(y)

The following rules can be oriented:

+(x, 0) ->x

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

+(0, s(y)) -> s(y)

s(+(0,y)) -> s(y)

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Remaining

+(x, 0) ->x

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

+(0, s(y)) -> s(y)

s(+(0,y)) -> s(y)

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

+(x, 0) ->x

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

+(0, s(y)) -> s(y)

s(+(0,y)) -> s(y)

Duration:

0:00 minutes