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:

h(f(x, y)) → f(y, f(h(h(x)), a))

Q is empty.

↳ QTRS

  ↳ Overlay + Local Confluence

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

h(f(x, y)) → f(y, f(h(h(x)), a))

Q is empty.

The TRS is overlay and locally confluent. By [15] we can switch to innermost.

↳ QTRS

  ↳ Overlay + Local Confluence

    ↳ QTRS

      ↳ DependencyPairsProof

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

h(f(x, y)) → f(y, f(h(h(x)), a))

The set Q consists of the following terms:

h(f(x0, x1))

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

H(f(x, y)) → H(h(x))
H(f(x, y)) → H(x)

The TRS R consists of the following rules:

h(f(x, y)) → f(y, f(h(h(x)), a))

The set Q consists of the following terms:

h(f(x0, x1))

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

↳ QTRS

  ↳ Overlay + Local Confluence

    ↳ QTRS

      ↳ DependencyPairsProof

        ↳ QDP

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

H(f(x, y)) → H(h(x))
H(f(x, y)) → H(x)

The TRS R consists of the following rules:

h(f(x, y)) → f(y, f(h(h(x)), a))

The set Q consists of the following terms:

h(f(x0, x1))

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