Computing cycle-free solutions in cyclic AND/OR search spaces is an important AI problem.  Previous work on optimal depth-first search strongly assumes the use of consistent heuristics, the need to keep all examined states in a transposition table, and the existence of solutions.  We give a new theoretical analysis under relaxed assumptions where previous results no longer hold.  We then present a generic approachto proving unsolvability, and apply it to RBFAOO and BLDFS, two state-of-the-art algorithms. We demonstrate the performance in domain-independent nondeterministic planning