+(0,

+(s(

+(s(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**+'(s( x), s(y)) -> +'(s(x), +(y, 0))**

+(0,y) ->y

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

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

innermost

The following dependency pair can be strictly oriented:

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

The following usable rules for innermost can be oriented:

+(0,y) ->y

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(+'(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }

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), 0) -> s(x)

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes