In the mediation approach for data integration, domain rules [2, 3] were previously proposed to deal with access limitations (aka access patterns). For data integration systems (e.g., DaWeS [6, 5]) that use domain rules, we study an upper bound on the possible number of accesses implied by the evaluation of an executable query (expressed with relations having access patterns). Indeed it allows to compare various evaluation algorithms, to schedule API operation calls and meet the service level agreements (SLA) of the service providers.