(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(f(x)) → g(f(x))
g(g(x)) → f(x)

Q is empty.

(1) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(2) Obligation:

Q DP problem:
The TRS P consists of the following rules:

F(f(x)) → G(f(x))
G(g(x)) → F(x)

The TRS R consists of the following rules:

f(f(x)) → g(f(x))
g(g(x)) → f(x)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.