That's assuming a lot... there are many, many ways to do part of speech tagging. You could imagine a slow implementation that exhaustively considered every possible POS tagging for an input sequence (would be O(k^N) where k is # of parts of speech)
Even a Microsoft Research project has a fairly complex reductions implementation of a POS tagger that is blazingly fast and production ready (learning to search interface). [1]
You could.. if you were crazy. No sane implementation would do that, and POS tagging isn't some brand new thing where people make that kind of mistake.