Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar3/AProVESLASHforward

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, z) -> g₃(x, y, z)
g₃(0, 1, x) -> f₃(x, x, x)
a -> b
a -> c

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₃(x, y, z) -> g₃(x, y, z)
g₃(0, 1, x) -> f₃(x, x, x)
a -> b
a -> c

Q is empty.

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

G₃(0, 1, x) -> F₃(x, x, x)
F₃(x, y, z) -> G₃(x, y, z)

The TRS R consists of the following rules:

f₃(x, y, z) -> g₃(x, y, z)
g₃(0, 1, x) -> f₃(x, x, x)
a -> b
a -> 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:

G₃(0, 1, x) -> F₃(x, x, x)
F₃(x, y, z) -> G₃(x, y, z)

The TRS R consists of the following rules:

f₃(x, y, z) -> g₃(x, y, z)
g₃(0, 1, x) -> f₃(x, x, x)
a -> b
a -> c

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