Termination w.r.t. Q proof of TRS/Zantemaz28.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(0, x), 1) -> f₂(g₁(f₂(x, x)), x)
f₂(g₁(x), y) -> g₁(f₂(x, y))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

f₂(f₂(0, x), 1) -> f₂(g₁(f₂(x, x)), x)
f₂(g₁(x), y) -> g₁(f₂(x, y))

Q is empty.

Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

F₂(g₁(x), y) -> F₂(x, y)
F₂(f₂(0, x), 1) -> F₂(x, x)
F₂(f₂(0, x), 1) -> F₂(g₁(f₂(x, x)), x)

The TRS R consists of the following rules:

f₂(f₂(0, x), 1) -> f₂(g₁(f₂(x, x)), x)
f₂(g₁(x), y) -> g₁(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(g₁(x), y) -> F₂(x, y)
F₂(f₂(0, x), 1) -> F₂(x, x)
F₂(f₂(0, x), 1) -> F₂(g₁(f₂(x, x)), x)

The TRS R consists of the following rules:

f₂(f₂(0, x), 1) -> f₂(g₁(f₂(x, x)), x)
f₂(g₁(x), y) -> g₁(f₂(x, y))

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