Let K be an annotated minimal edge cover. For an edge 
, if the annotation on e is MOV, CPY, or GLU, let 
denote the cost of that operation. If e is annotated with INS,
DEL, or UPD, then let 
denote the cost of the operation.
Furthermore, let E(m) be the set of edges in K that are incident
on m, that is, 
. Let C(m) be the set
of the children of m. We then define the fair cost of each
edge 
as follows:
Note that this cost depends on K, and thus is not a function of e alone. The following lemma, proved in [&make_named_href('', "node21.html#bbdiffExtended","[CGM97]")], states that the above scheme of distributing the cost of an edge cover over its component edges is a sound one; that is, adding up the cost edge-wise yields the overall cost of the edge cover (i.e., the cost of the corresponding edit script).
