>enumerating all possible algorithms [...] for problem sizes up to n. Please keep in mind that this includes an algorithm that has precomputed all possible sol

>enumerating all possible algorithms [...] for problem sizes up to n. Please keep in mind that this includes an algorithm that has precomputed all possible solutions and retrieves their value from a list. In fact I find it hard to say for certain that you can't for instance assume the existence of an algorithm that calculates the answers to some NP problem in constant time, but which takes an amount of time that can't be proven to be smaller than any other number. This would lead to a situation where P != NP may not be provable.