how did Oedipus become the ruler?

The Oracle prophesized that any son of Laius would eventually kill him and marry his wife. Oedipus finds out he was adopted and consults the same Oracle who tells him the same thing save the part about his real birth parents. Not wanting to kill his dad, Oedipus travels to Thebes. On his way he encounters a travelling caravan. Both claim right of way on the path. There is some major road rage or rather "path rage" and Oedipus kills the man who turns out to be his birth father.