(**********************************************************************)
(* A few examples showing the current limits of the conversion algorithm *)
(**********************************************************************)
(*** We define (pseudo-)divergence from Ackermann function ***)
Definition ack (n : nat) :=
(fix F (n0 : nat) : nat -> nat :=
match n0 with
| O => S
| S n1 =>
fun m : nat =>
(fix F0 (n2 : nat) : nat :=
match n2 with
| O => F n1 1
| S n3 => F n1 (F0 n3)
end) m
end) n.
Notation OMEGA := (ack 4 4).
Definition f (x:nat) := x.

(* Evaluation in tactics can somehow be controlled *)
Lemma l1 : OMEGA = OMEGA.