(0) Obligation:

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

f(x) → f(g(x))

Q is empty.

(1) AAECC Innermost (EQUIVALENT transformation)

We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none

The TRS R 2 is

f(x) → f(g(x))

The signature Sigma is {f}

(2) Obligation:

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

f(x) → f(g(x))

The set Q consists of the following terms:

f(x0)

(3) DependencyPairsProof (EQUIVALENT transformation)

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

(4) Obligation:

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

F(x) → F(g(x))

The TRS R consists of the following rules:

f(x) → f(g(x))

The set Q consists of the following terms:

f(x0)

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