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Abstract

Orientability of systems of equalities is the following problem: given a system of equalities $s_1 \eql t_1, \ldots, s_n \eql t_n$, does there exist a simplification ordering $\succ$ which orients the system, that is for every $i \in \{1,...,n\}$, either $s_i \succ t_i$ or $t_i \succ s_i$. This problem can be used in rewriting for finding a canonical rewrite system for a system of equalities and in theorem proving for adjusting simplification orderings during completion. We prove that (rather surprisingly) the problem can be solved in polynomial time when we restrict ourselves to the Knuth-Bendix orderings.