In Star Trek II: The Wrath Of Khan, Enterprise and Reliant face off against each other while both are en route to Regula One. During the conflict both ships are damaged and the scene ends with Joachim insisting that Reliant must withdraw. After that we do not see Reliant again until near the end of the film, at Regula One.

It's not clear to me which of the vessels had working engines, and which got to Regula first. Did Enterprise arrive first, and the next confrontation was when Reliant arrived at Regula and found Enterprise? Or was Reliant able to leave the battle scene and arrive at Regula and hide when Enterprise arrived later? What is the exact sequence of movements of the two vessels between their first meeting and the meeting at Regula?