(0) Obligation:

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

app(app(app(app(rec, t), u), v), 0) → t
app(app(app(app(rec, t), u), v), app(s, x)) → app(app(u, x), app(app(app(app(rec, t), u), v), x))
app(app(app(app(rec, t), u), v), app(lim, f)) → app(app(v, f), app(app(app(app(rectuv, t), u), v), app(f, n)))
app(app(app(app(rectuv, t), u), v), n) → app(app(app(app(rec, t), u), v), n)

Q is empty.