# Equivalence problem for one-counter automata

I know that the equivalence problem for deterministic one counter automata is decidable, however does anyone know whether it is decidable for all one counter automata or just the deterministic ones?

Any information would be useful, I don't know if this is an open problem or if it has a solution. If there is a known proof (of either decidability or undecidability) then a reference would be greatly appreciated.

I have no time to check the references in detail, but Ibarra states in http://dx.doi.org/10.1007/BF01744294 that, according to Greibachand Baker and Book, the universe problem (is the language $\Sigma^*$?) for non-deterministic one-counter machines with at most one counter reversal is undecidable.