Language Equivalence between Nondeterministic and Deterministic One-Counter Machines

Problem A: Given a deterministic one-counter automaton (a pushdown automaton with one stack alphabet) $A$ and a nondeterministic one-counter net (a one-counter automaton with no zero-tests) $N$, decide if the language recognised by $A$ is the same as the language recognised by $N$. Decidability of A is open. This is related to the open question of decidability for the following problem, which is relatively more well-known. Problem B: Given a deterministic one-counter net $D$ and a nondeterministic one-counter net $N$, decide if the language recognised by $D$ is the same as the language recognised by $N$.