Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar4/nonterminSLASHAG01SLASHHASH4.7.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:

f₁(s₁(x)) -> f₁(g₂(x, x))
g₂(0, 1) -> s₁(0)
0 -> 1

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₁(s₁(x)) -> f₁(g₂(x, x))
g₂(0, 1) -> s₁(0)
0 -> 1

Q is empty.

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

F₁(s₁(x)) -> F₁(g₂(x, x))
F₁(s₁(x)) -> G₂(x, x)

The TRS R consists of the following rules:

f₁(s₁(x)) -> f₁(g₂(x, x))
g₂(0, 1) -> s₁(0)
0 -> 1

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

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

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

F₁(s₁(x)) -> F₁(g₂(x, x))
F₁(s₁(x)) -> G₂(x, x)

The TRS R consists of the following rules:

f₁(s₁(x)) -> f₁(g₂(x, x))
g₂(0, 1) -> s₁(0)
0 -> 1

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph contains 1 SCC with 1 less node.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

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

F₁(s₁(x)) -> F₁(g₂(x, x))

The TRS R consists of the following rules:

f₁(s₁(x)) -> f₁(g₂(x, x))
g₂(0, 1) -> s₁(0)
0 -> 1

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