Representative republic? And I suppose you're against socialistic socialism and for capitalistic capitalism?
The fact is there is no black and white definition of what our government is. Of course, we aren't a direct democracy, but you could call us either a representative democracy or a republic (representative republic is redundant). You could argue minuet differences, but in the end it would just make you a pedant who is purposefully being petty just to try to make someone else look like an idiot when there is no real consequence about what you're arguing.