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

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(app(if, true), x), y) → x
app(app(app(if, true), x), y) → y
app(app(takeWhile, p), nil) → nil
app(app(takeWhile, p), app(app(cons, x), xs)) → app(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil)
app(app(dropWhile, p), nil) → nil
app(app(dropWhile, p), app(app(cons, x), xs)) → app(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs))

Q is empty.

↳ QTRS

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

app(app(app(if, true), x), y) → x
app(app(app(if, true), x), y) → y
app(app(takeWhile, p), nil) → nil
app(app(takeWhile, p), app(app(cons, x), xs)) → app(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil)
app(app(dropWhile, p), nil) → nil
app(app(dropWhile, p), app(app(cons, x), xs)) → app(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs))

Q is empty.