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Well, if there was a short and simple algorithm running very fast, that provably was correct on all $\phi$ of length at most $2^{2^{2^{1000000}}}$, I guess they would consider awarding the prize...
There is no need to decide whether $M$ runs in polynomial time (which I assume is what you mean by "$M\in P$"); I have put the added detail into an edited version of my answer
