# Is it decidable whether the langauge accepted by a reversal-bounded counter machine is deterministic?

I'm wondering if anyone can point me to either an algorithm or an undecidability proof for the following question:

Given a non-deterministic reversal-bounded multicounter machine $M$, is there some deterministic reversal-bounded multicounter machine $M'$ such that $L(M) = L(M')$?

For anyone interested, reversal-bounded counter machines are described at length in Oscar Ibarra's Paper about them.

Suppose we can decide if $M$ can be determinized, and perform the determinization if it can. Then we can decide if $L(M) = \Sigma^*$ as follows:
If $M$ cannot be determinized, then clearly it is not universal, since there is a deterministic machine accepting $\Sigma^*$. If $M$ can be determinized, then we determinize it and test if it is universal.