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# [Frama-c-discuss] Verifying recursive functions

```Sorry for the unclear answer about this. Pascal is right. Let me
rephrase that in a general setting: if you annotate

//@ decreases V(x1...xk) for R
f(x1,..,xk) {

....
f(e1,...e_k);
...}

then the VC at the recursive call will be
//@ assert V(e1,..,ek) R V(x1...xk)

for the well-founded order R . By default, R is the relation R(x,y) on
integer defined by 0 <= y && x < y. This is the most convenient
well-founded order on ints.

(more details in ACSL ref man in section 2.5

Pascal Cuoq wrote:
>> I don't understand the assert clause in the code below:
>> - "0 <= n" follows from the precondition
>> - "n-1 < n" is a tautology
>> So the assert clause should always evaluate to true, irrespective of
>> what the program does?
>
> The assertion is there to illustrate how decreases clauses will
> work when they are supported.
>
> If the decreases clause had been supported by Jessie, it would
> have been translated into a verification condition very much like
> the property 0 <= n && n-1 < n; to be proved at the point of the assert.
>
> The fact that the property holds means that the decreases clause is a
> valid one,
> and consequently that the termination of the function is guaranteed.
>
> Pascal
>
>
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```