# Recurring computations for 2-counter machines

It is known that reachability of 2-counter machines is undecidable. As far as I know, it is semi-decidable though.

Now let's focus instead on the problem of deciding if a 2-counter machine has a computation which passes through the initial state infinitely often.

My understanding is that this problem is non-RE. Is this correct? If so, is there any reference in the literature?