Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar3/secret2005SLASHmb1.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(x, a), y) -> f₂(y, f₂(x, y))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₂(f₂(x, a), y) -> f₂(y, f₂(x, y))

Q is empty.

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

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

The TRS R consists of the following rules:

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

The TRS R consists of the following rules:

f₂(f₂(x, a), y) -> f₂(y, f₂(x, y))

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