We use our definition of an underlying co-bipartite graph which encodes a given binary relation to propose a new approach to defining a sub-relation or incrementally maintaining a relation which will define only a polynomial number of concepts.

The paper studies the subsequence relation through a notion of an intransitive binary relation on words in traces generated by prefix-rewriting systems. The relation was introduced in 1988 by V.F. Turchin for loop approximation in supercompilation. We study properties of this relation and introduce some refinements of the subsequence relation that inherit the useful features of Turchin’s relation.