  We evaluate the typical ARA performance of the CDMA multiuser detection by
means of statistical mechanics using the replica method. At first, we consider
the oracle cases where the initial candidate solution is randomly generated
with a fixed fraction of the original signal in the initial state. In the
oracle cases, the first-order phase transition can be avoided or mitigated by
ARA if we prepare for the proper initial candidate solution. We validate our
theoretical analysis with quantum Monte Carlo simulations. The theoretical
results to avoid the first-order phase transition are consistent with the
numerical results. Next, we consider the practical cases where we prepare for
the initial candidate solution obtained by commonly used algorithms. We show
that the practical algorithms can exceed the threshold to avoid the first-order
phase transition. Finally, we test the performance of ARA with the initial
candidate solution obtained by the practical algorithm. In this case, the ARA
can not avoid the first-order phase transition even if the initial candidate
solution exceeds the threshold to avoid the first-order phase transition.
