The algorithm can also be shown to be starvation-free, meaning that all processes that enter the loop eventually exit it (assuming they don't stay in the critical section indefinitely). The proof proceeds by induction from downward. A process at is in the critical section, and by assumption will exit it. At all lower levels , it is impossible for a process to wait forever, since either another process will enter the waiting room, setting and "liberating" ; or this never happens, but then all processes that are also in the waiting rooms must be at higher levels and by the inductive hypothesis, they will eventually finish the loop and reset their levels, so that for all , and again exits the loop.