(0) Obligation:

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

f(g(x, y), x, z) → f(z, z, z)
g(x, y) → x
g(x, y) → y

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(g(x, y), x, z) → F(z, z, z)

The TRS R consists of the following rules:

f(g(x, y), x, z) → f(z, z, z)
g(x, y) → x
g(x, y) → y

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