 to reach  .  Figure 00.0 Proof of Lemma 00.0.0: The starting configuration   is shown on the left, where  , and each memory element is initialized to  . Two alternative executions appear at the top and bottom of the figure. The top shows an execution where   writes and reads first, followed by  . The bottom shows an execution where   writes and reads first. In both executions, if we halt the processes in  , then we end up at the same configuration