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Note that the graphs we are interested in (finite, serial and functional) come with a special shape: each of their connected components contains exactly one cycle, and this cycle forms the ``tail" of the component:  \begin{fact} \label{fact:connected}  Let $G$ be an influence graph and $C$ be a connected component of $G$.   Then $C$ contains exactly one cycle, and cycle.  %and  this cycle is a closed set. \end{fact}  \begin{proof}