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The first rule of recursion is we do not talk about recursion.

The second rule of recursion is we do not talk about recursion.

The third rule of recursion is without a base case, you have no recursion.

The fourth rule of recursion is it breaks you in two or more pieces.

The fifth rule of recursion is that it is not really recursion if it isn't tail-call optimised.

So a recursive tree search is not really recursive?

Oh no, it is really recursive -- it's just not "real recursion" (TM). ;)