Termination w.r.t. Q proof of TRS/secret06tpa03.trs

Termination w.r.t. Q of the following Term Rewriting System could not be shown:

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

f₂(x, f₂(y, x)) -> f₂(f₂(x, x), f₂(a, y))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₂(x, f₂(y, x)) -> f₂(f₂(x, x), f₂(a, y))

Q is empty.

Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

F₂(x, f₂(y, x)) -> F₂(a, y)
F₂(x, f₂(y, x)) -> F₂(x, x)
F₂(x, f₂(y, x)) -> F₂(f₂(x, x), f₂(a, y))

The TRS R consists of the following rules:

f₂(x, f₂(y, x)) -> f₂(f₂(x, x), f₂(a, y))

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

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

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

F₂(x, f₂(y, x)) -> F₂(a, y)
F₂(x, f₂(y, x)) -> F₂(x, x)
F₂(x, f₂(y, x)) -> F₂(f₂(x, x), f₂(a, y))

The TRS R consists of the following rules:

f₂(x, f₂(y, x)) -> f₂(f₂(x, x), f₂(a, y))

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