Let be a set of alts of a cf-graph that contains and . is immediately embedded in with respect to if and there is no alt such that . is called an internal alt with respect to if there is no alt in immediately embedded in , and an external alt with respect to if there is no alt in , into which is immediately embedded.
A set of nontrivial alts is called a nested set of alts (or hierarchy of embedded alts) of the cf-graph if and, for any pair of alts from , either their intersection is empty or one of them is embedded in the other.
A sequence of cf-graphs is called a representation of the cf-graph in the form of a nested set of alts (-representation of the cf-graph ) if , is a trivial graph and for any , is a factor cf-graph , where is the set of all external alts with respect to and is the set of all internal alts with respect to .