An EFS is a kind of logic programs expressing various formal languages. We propose an efficient derivation for EFS’s called an S-derivation, where every possible unifiers are evaluated at one step of the derivation. In the S-derivation, each unifier is partially applied to each goal clause by assigning variables whose values are uniquely determined from the set of all possible unifiers. This contributes to reduce the number of backtracking, and thus the S-derivation works efficiently. In this paper, the S-derivation is shown to be complete for the class of regular EFS’s. We implement an EFS interpreter based on the S-derivation in Prolog programming language, and compare the parsing time with that of DCG provided by the Prolog interpreter. As the results of experiments, we verify the efficiency of the S-derivation for accepting context-free languages.