A normalization procedure is presented for a classical natural deduction (
) proof system. This proof system, called
, has a multiple conclusion proof structure where cycles are allowed. With this, we have developed a thorough treatment of cycles, including cycles normalization via an algorithm. We also demonstrate the usefulness of the graphical framework of
, where derivations are seen as digraphs. We use geometric perspective techniques to establish the normalization mechanism, thus giving a direct normalization proof.