f(1) -> f(g(1))

f(f(

g(0) -> g(f(0))

g(g(

R

↳Dependency Pair Analysis

F(1) -> F(g(1))

F(1) -> G(1)

G(0) -> G(f(0))

G(0) -> F(0)

Furthermore,

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**Dependency Pair:****F(1) -> F(g(1))****Rules:**

f(1) -> f(g(1))

f(f(*x*)) -> f(*x*)

g(0) -> g(f(0))

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

f(1) -> f(g(1))

f(f(*x*)) -> f(*x*)

g(0) -> g(f(0))

g(g(*x*)) -> g(*x*)

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**Dependency Pair:****F(1) -> F(g(1))****Rules:**

f(1) -> f(g(1))

f(f(*x*)) -> f(*x*)

g(0) -> g(f(0))

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

f(1) -> f(g(1))

f(f(*x*)) -> f(*x*)

g(0) -> g(f(0))

g(g(*x*)) -> g(*x*)

Duration:

0:00 minutes