An Efficient Algorithm for Recognizing the Forward-Branching Class of Term-Rewriting Systems

We present an algorithm for recognizing the forward-branching (FE) [Str89] class of term-rewriting systems. The algorithm is an improvement over a previous algorithm reported in [DS91] and [DS90] with a complexity proof in [Dur94]. The time comple)(ity of the algorithm ln [Dur94) is OC~:::, ln; l) but was reported to be O(('E; ln; l)2), and the space compl€Dty is O(('E; ln,l}2) . We improve on this result by giving an algorithm with both time and space complexity O('E, In;l) . Thus, in the normal case, where the size of each individual left-hand side is relatively small, the new algorithm is much more efficient. Since the quadratic behavior is caused by a set intersection operation that can be implemented with bit vectors, t he algorithm is very efficient in practice.