Simple LPO Constraint Solving Methods

We present simple techniques for deciding the satissability of lexicographic path ordering constraints under two diierent semantics: solutions built over the given signature and solutions in extended signatures. For both cases we give the rst NP algorithms, which is optimal as we prove the problems to be NP-complete. We discuss the eecient applicability of the techniques in practice, where, as far as we know, their simply exponential bound improves upon the existing methods, and describe some optimizations.