We study the recursive path ordering (RPO) in the context of string-rewriting systems. We are interested in finding a symbol ordering in RPO such that for every rule in the rewriting system, the left hand side is higher than the right hand side. We show that this SYMBOL-ORDER problem is NP-complete by a reduction from the 2-3-SAT problem. We also work on the one-rule case and show a polynomial time algorithm for such systems.