f(

f(s(

g(0,

R

↳Dependency Pair Analysis

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

G(0,x) -> G(f(x,x),x)

G(0,x) -> F(x,x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

f(*x*, 0) -> s(0)

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

g(0,*x*) -> g(f(*x*,*x*),*x*)**Dependency Pair:****G(0,***x*) -> G(f(*x*,*x*),*x*)**Rules:**

f(*x*, 0) -> s(0)

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

g(0,*x*) -> g(f(*x*,*x*),*x*)

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

f(*x*, 0) -> s(0)

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

g(0,*x*) -> g(f(*x*,*x*),*x*)**Dependency Pair:****G(0,***x*) -> G(f(*x*,*x*),*x*)**Rules:**

f(*x*, 0) -> s(0)

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

g(0,*x*) -> g(f(*x*,*x*),*x*)

Duration:

0:00 minutes