a place $p\in {\mathcal{P}}$ is said to be *free choice* if either all the output transitions $q \in p{^{\textrm{out}}}$ satisfy $q{^{\textrm{in}}}= \{p\}$ (*conflict*, see Figure \[fig:configuration\](a)), or $|p{^{\textrm{out}}}| = 1$ (*synchronization*, see Figure \[fig:configuration\](b)). A place is *subject to priority* if its tokens are routed to output transitions according to a priority rule. We refer to Figure \[fig:configuration\](c) for an illustration. For the sake of simplicity, we assume that each place subject to priority has exactly two output transitions, and that any transition has at most one upstream place subject to priority. Given a place $p$ subject to priority, we denote by $q^+(p)$ and $q^-(p)$ its two output transitions, with the convention that $q^+(p)$ has priority over $q^-(p)$. For the sake of readability, we use the notation $q^+$ and $q^-$ when the place $p$ is clear from context.

The set of transitions such that every upstream place $p$ satisfies $|p{^{\textrm{out}}}| = 1$ is referred to as ${\mathcal{Q}_\textsf{sync}}$ and the set of free choice places that have at least two output transitions is referred to as ${\mathcal{P}_\textsf{conflict}}$. We denote by ${\mathcal{P}_\textsf{priority}}$ the set of places subject to priority. The sets $({\mathcal{P}_\textsf{conflict}}){^{\textrm{out}}}$, ${\mathcal{Q}_\textsf{sync}}$ and $({\mathcal{P}_\textsf{priority}}){^{\textrm{out}}}$ form a partition of ${\mathcal{Q}}$. Figure \[fig:configuration\] 