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

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**Dependency Pairs:****+'(s(***x*),*y*) -> +'(*x*,*y*)**+'(***x*, s(*y*)) -> +'(*x*,*y*)**Rules:**

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*))**Dependency Pair:****DOUBLE(s(***x*)) -> DOUBLE(*x*)**Rules:**

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*))

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**Dependency Pairs:****+'(s(***x*),*y*) -> +'(*x*,*y*)**+'(***x*, s(*y*)) -> +'(*x*,*y*)**Rules:**

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*))**Dependency Pair:****DOUBLE(s(***x*)) -> DOUBLE(*x*)**Rules:**

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*))

Duration:

0:00 minutes