Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar4/SK90SLASH4.49.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:

f₃(x, y, f₃(z, u, v)) -> f₃(f₃(x, y, z), u, f₃(x, y, v))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₃(x, y, f₃(z, u, v)) -> f₃(f₃(x, y, z), u, f₃(x, y, v))

Q is empty.

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

F₃(x, y, f₃(z, u, v)) -> F₃(x, y, v)
F₃(x, y, f₃(z, u, v)) -> F₃(x, y, z)
F₃(x, y, f₃(z, u, v)) -> F₃(f₃(x, y, z), u, f₃(x, y, v))

The TRS R consists of the following rules:

f₃(x, y, f₃(z, u, v)) -> f₃(f₃(x, y, z), u, f₃(x, y, v))

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:

F₃(x, y, f₃(z, u, v)) -> F₃(x, y, v)
F₃(x, y, f₃(z, u, v)) -> F₃(x, y, z)
F₃(x, y, f₃(z, u, v)) -> F₃(f₃(x, y, z), u, f₃(x, y, v))

The TRS R consists of the following rules:

f₃(x, y, f₃(z, u, v)) -> f₃(f₃(x, y, z), u, f₃(x, y, v))

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