Termination w.r.t. Q proof of /tmp/tmp4ghMAH/gkg.trs

Termination w.r.t. Q of the following Term Rewriting System could be proven:

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

f(X, g(X)) → f(1, g(X))
g(1) → g(0)

The set Q consists of the following terms:

g(1)
f(x0, g(x0))

↳ QTRS

  ↳ DependencyPairsProof

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

f(X, g(X)) → f(1, g(X))
g(1) → g(0)

The set Q consists of the following terms:

g(1)
f(x0, g(x0))

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

F(X, g(X)) → F(1, g(X))
G(1) → G(0)

The TRS R consists of the following rules:

f(X, g(X)) → f(1, g(X))
g(1) → g(0)

The set Q consists of the following terms:

g(1)
f(x0, g(x0))

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

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

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

F(X, g(X)) → F(1, g(X))
G(1) → G(0)

The TRS R consists of the following rules:

f(X, g(X)) → f(1, g(X))
g(1) → g(0)

The set Q consists of the following terms:

g(1)
f(x0, g(x0))

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 2 less nodes.