Termination w.r.t. Q proof of TRS/HofWald7.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(f₂(f₂(f₂(j, a), b), c), d) -> f₂(f₂(a, b), f₂(f₂(a, d), c))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₂(f₂(f₂(f₂(j, a), b), c), d) -> f₂(f₂(a, b), f₂(f₂(a, d), c))

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(f₂(f₂(f₂(j, a), b), c), d) -> F₂(a, d)
F₂(f₂(f₂(f₂(j, a), b), c), d) -> F₂(f₂(a, b), f₂(f₂(a, d), c))
F₂(f₂(f₂(f₂(j, a), b), c), d) -> F₂(f₂(a, d), c)
F₂(f₂(f₂(f₂(j, a), b), c), d) -> F₂(a, b)

The TRS R consists of the following rules:

f₂(f₂(f₂(f₂(j, a), b), c), d) -> f₂(f₂(a, b), f₂(f₂(a, d), c))

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(f₂(f₂(f₂(j, a), b), c), d) -> F₂(a, d)
F₂(f₂(f₂(f₂(j, a), b), c), d) -> F₂(f₂(a, b), f₂(f₂(a, d), c))
F₂(f₂(f₂(f₂(j, a), b), c), d) -> F₂(f₂(a, d), c)
F₂(f₂(f₂(f₂(j, a), b), c), d) -> F₂(a, b)

The TRS R consists of the following rules:

f₂(f₂(f₂(f₂(j, a), b), c), d) -> f₂(f₂(a, b), f₂(f₂(a, d), c))

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