sum(0) -> 0

sum(s(

+(

+(

R

↳Dependency Pair Analysis

SUM(s(x)) -> +'(sum(x), s(x))

SUM(s(x)) -> SUM(x)

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

sum(0) -> 0

sum(s(*x*)) -> +(sum(*x*), s(*x*))

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

+(*x*, s(*y*)) -> s(+(*x*,*y*))**Dependency Pair:****SUM(s(***x*)) -> SUM(*x*)**Rules:**

sum(0) -> 0

sum(s(*x*)) -> +(sum(*x*), s(*x*))

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

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

sum(0) -> 0

sum(s(*x*)) -> +(sum(*x*), s(*x*))

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

+(*x*, s(*y*)) -> s(+(*x*,*y*))**Dependency Pair:****SUM(s(***x*)) -> SUM(*x*)**Rules:**

sum(0) -> 0

sum(s(*x*)) -> +(sum(*x*), s(*x*))

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

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

Duration:

0:00 minutes