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, empty) -> x
f2(empty, cons2(a, k)) -> f2(cons2(a, k), k)
f2(cons2(a, k), y) -> f2(y, k)

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

f2(x, empty) -> x
f2(empty, cons2(a, k)) -> f2(cons2(a, k), k)
f2(cons2(a, k), y) -> f2(y, k)

Q is empty.

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

F2(cons2(a, k), y) -> F2(y, k)
F2(empty, cons2(a, k)) -> F2(cons2(a, k), k)

The TRS R consists of the following rules:

f2(x, empty) -> x
f2(empty, cons2(a, k)) -> f2(cons2(a, k), k)
f2(cons2(a, k), y) -> f2(y, k)

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(cons2(a, k), y) -> F2(y, k)
F2(empty, cons2(a, k)) -> F2(cons2(a, k), k)

The TRS R consists of the following rules:

f2(x, empty) -> x
f2(empty, cons2(a, k)) -> f2(cons2(a, k), k)
f2(cons2(a, k), y) -> f2(y, k)

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