double(0) -> 0

double(s(

double(

+(

+(

+(s(

R

↳Dependency Pair Analysis

DOUBLE(s(x)) -> DOUBLE(x)

DOUBLE(x) -> +'(x,x)

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

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

double(0) -> 0

double(s(x)) -> s(s(double(x)))

double(x) -> +(x,x)

+(x, 0) ->x

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

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

The following dependency pairs can be strictly oriented:

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

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

double(0) -> 0

double(s(x)) -> s(s(double(x)))

double(x) -> +(x,x)

+(x, 0) ->x

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

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

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

**DOUBLE(s( x)) -> DOUBLE(x)**

double(0) -> 0

double(s(x)) -> s(s(double(x)))

double(x) -> +(x,x)

+(x, 0) ->x

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

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

The following dependency pair can be strictly oriented:

DOUBLE(s(x)) -> DOUBLE(x)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(DOUBLE(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

double(0) -> 0

double(s(x)) -> s(s(double(x)))

double(x) -> +(x,x)

+(x, 0) ->x

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

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes