Termination w.r.t. Q proof of /tmp/tmp

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(0, 1, x) → f(x, x, x)
f(x, y, z) → 2
0 → 2
1 → 2
g(x, x, y) → y
g(x, y, y) → x

The set Q consists of the following terms:

g(x0, x1, x1)
g(x0, x0, x1)
1
f(x0, x1, x2)
0

↳ QTRS

  ↳ DependencyPairsProof

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

f(0, 1, x) → f(x, x, x)
f(x, y, z) → 2
0 → 2
1 → 2
g(x, x, y) → y
g(x, y, y) → x

The set Q consists of the following terms:

g(x0, x1, x1)
g(x0, x0, x1)
1
f(x0, x1, x2)
0

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(0, 1, x) → F(x, x, x)

The TRS R consists of the following rules:

f(0, 1, x) → f(x, x, x)
f(x, y, z) → 2
0 → 2
1 → 2
g(x, x, y) → y
g(x, y, y) → x

The set Q consists of the following terms:

g(x0, x1, x1)
g(x0, x0, x1)
1
f(x0, x1, x2)
0

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(0, 1, x) → F(x, x, x)

The TRS R consists of the following rules:

f(0, 1, x) → f(x, x, x)
f(x, y, z) → 2
0 → 2
1 → 2
g(x, x, y) → y
g(x, y, y) → x

The set Q consists of the following terms:

g(x0, x1, x1)
g(x0, x0, x1)
1
f(x0, x1, x2)
0

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 1 less node.