MPI-I-93-256

This paper presents a decision procedure for the existential fragment of the theory of simplification oderings, which extends previous work by D. Plaisted. We consider both solvability in the given signature and solvability in an extended signature. The algorithm has cubic complexity for pure conjunctive ordering constraints in the extended signature case. However, we show that some slight extensions of the basic problem are NP-complete, for example, if the ordering is interpreted as a total simplification ordering or a lexicographic path ordering (LPO) with arbitrary precedence.