[adgjlsfhk1]

Sure, but most complicated polynomial time algorithms don't work like this. You either have cases like AKS which are obviously polynomial but not obviously correct, or cases that are obviously correct but not obviously polynomial.

[klyrs]

Algorithms which are obviously polynomial, and non-obviously correct are the only ones I'd entertain from a novice. It's not hard to mine for counterexamples, as long as the code runs.