Termination w.r.t. Q proof of TRS/nontermin/AG01#4.18.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:

a₁(b₁(a₁(b₁(x)))) -> b₁(a₁(b₁(a₁(a₁(b₁(x))))))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

a₁(b₁(a₁(b₁(x)))) -> b₁(a₁(b₁(a₁(a₁(b₁(x))))))

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:

A₁(b₁(a₁(b₁(x)))) -> A₁(a₁(b₁(x)))
A₁(b₁(a₁(b₁(x)))) -> A₁(b₁(a₁(a₁(b₁(x)))))

The TRS R consists of the following rules:

a₁(b₁(a₁(b₁(x)))) -> b₁(a₁(b₁(a₁(a₁(b₁(x))))))

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:

A₁(b₁(a₁(b₁(x)))) -> A₁(a₁(b₁(x)))
A₁(b₁(a₁(b₁(x)))) -> A₁(b₁(a₁(a₁(b₁(x)))))

The TRS R consists of the following rules:

a₁(b₁(a₁(b₁(x)))) -> b₁(a₁(b₁(a₁(a₁(b₁(x))))))

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