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The order the commands are run actually doesn't matter and isn't guaranteed. Leaving aside the arcane details of pipe(), fork(), dup() and execve(), the shell first creates the pipe, the conduit for the data that will flow between the processes, and then creates the processes with the ends of the pipe connected to them. The first process that is run may block waiting for input from the second process, or block waiting for the second process to start reading data from the pipe. These waits can be arbitrarily long and don't matter. Whichever order the processes are run, the data eventually gets transferred and everything works.