Termination w.r.t. Q proof of TRS/higher-order/LifantsevEx2PrimRec.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:

app(app(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, x)))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

app(app(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, 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:

APP(app(rec, h), app(g, app(s, x))) → APP(app(h, x), app(app(rec, h), app(g, x)))
APP(app(rec, h), app(g, app(s, x))) → APP(g, x)
APP(app(rec, h), app(g, app(s, x))) → APP(h, x)
APP(app(rec, h), app(g, app(s, x))) → APP(app(rec, h), app(g, x))

The TRS R consists of the following rules:

app(app(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, 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:

APP(app(rec, h), app(g, app(s, x))) → APP(app(h, x), app(app(rec, h), app(g, x)))
APP(app(rec, h), app(g, app(s, x))) → APP(g, x)
APP(app(rec, h), app(g, app(s, x))) → APP(h, x)
APP(app(rec, h), app(g, app(s, x))) → APP(app(rec, h), app(g, x))

The TRS R consists of the following rules:

app(app(rec, h), app(g, 0)) → g
app(app(rec, h), app(g, app(s, x))) → app(app(h, x), app(app(rec, h), app(g, x)))

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