Orderal Term Rewriting Systems

This article describes a generalization of term rewriting system technique used as a basis for decision algorithm for equational theories. The or-deral term rewriting system technique is presented. The main innovation of the proposed technique is that reductions according to some rules of such a system are performed only if special restrictions are satissed. The restrictions are based on term ordering and guarantee termination of any sequence of reductions. This improvement allows to handle uniformly both permutational and reductional axioms of an equational theory.