Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar3/variousSLASH02.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:

f₃(0, 1, x) -> f₃(x, x, x)
f₃(x, y, z) -> 2
0 -> 2
1 -> 2

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₃(0, 1, x) -> f₃(x, x, x)
f₃(x, y, z) -> 2
0 -> 2
1 -> 2

Q is empty.

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

F₃(0, 1, x) -> F₃(x, x, x)

The TRS R consists of the following rules:

f₃(0, 1, x) -> f₃(x, x, x)
f₃(x, y, z) -> 2
0 -> 2
1 -> 2

Q is empty.
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:

F₃(0, 1, x) -> F₃(x, x, x)

The TRS R consists of the following rules:

f₃(0, 1, x) -> f₃(x, x, x)
f₃(x, y, z) -> 2
0 -> 2
1 -> 2

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