Orienting equalities with the Knuth-Bendix order

Orientability of systems of equalities is the following problem: given a system of equalities s₁ ≃ t₁, . . . , s_n ≃ t_n, does there exist a simplification ordering > which orients the system, that is for every i ∈ {1, ..., n}, either s_i > t_i or t_i > 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.