Graph-reducible term rewriting systems

Abstract

Term rewriting is commonly implemented by graph reduction in order to improve efficiency. In general, however, graph reduction is not complete: a term may be not normalizable through graph derivations although a normal form exists. Term rewriting systems which permit a complete implementation by graph reduction are called graph-reducible. We show that the following property is sufficient for graph-reducibility: every term having a normal form can be normalized by parallel term rewrite steps in which a rule is applied to all occurrences of some subterm. As a consequence, a broad class of term rewriting systems which includes all terminating and all orthogonal systems can be shown to be graph-reducible.