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(not, app(not, x)) → x
app(not, app(app(or, x), y)) → app(app(and, app(not, x)), app(not, y))
app(not, app(app(and, x), y)) → app(app(or, app(not, x)), app(not, y))
app(app(and, x), app(app(or, y), z)) → app(app(or, app(app(and, x), y)), app(app(and, x), z))
app(app(and, app(app(or, y), z)), x) → app(app(or, app(app(and, x), y)), app(app(and, x), z))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)

Q is empty.


QTRS

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

app(not, app(not, x)) → x
app(not, app(app(or, x), y)) → app(app(and, app(not, x)), app(not, y))
app(not, app(app(and, x), y)) → app(app(or, app(not, x)), app(not, y))
app(app(and, x), app(app(or, y), z)) → app(app(or, app(app(and, x), y)), app(app(and, x), z))
app(app(and, app(app(or, y), z)), x) → app(app(or, app(app(and, x), y)), app(app(and, x), z))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)

Q is empty.