What prevented Thebes from tracking down thr murderer of Laius at the time murder occured?

The murder of Laius was prevented from being solved immediately due to a sphinx who terrorized the region of Thebes. The sphinx would riddle whoever encountered it, and if any individual couldn't solve its riddles, the sphinx would slay them instantly. Due to their focus on the riddles of the sphinx, the citizens of Thebes and King Laius himself abandoned the immediate investigation on who murdered him. Once Oedipus solved the mystery of the sphinx's riddle, the curse of the creature, as well as their focus on resolving Laius' death returned again.