Termination w.r.t. Q proof of TRS/Waldmannjwmatchb1.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:

h₁(f₂(x, y)) -> f₂(y, f₂(h₁(h₁(x)), a))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

h₁(f₂(x, y)) -> f₂(y, f₂(h₁(h₁(x)), a))

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:

H₁(f₂(x, y)) -> H₁(h₁(x))
H₁(f₂(x, y)) -> H₁(x)

The TRS R consists of the following rules:

h₁(f₂(x, y)) -> f₂(y, f₂(h₁(h₁(x)), a))

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:

H₁(f₂(x, y)) -> H₁(h₁(x))
H₁(f₂(x, y)) -> H₁(x)

The TRS R consists of the following rules:

h₁(f₂(x, y)) -> f₂(y, f₂(h₁(h₁(x)), a))

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