1. An access control system comprising: a deriving operation request device which transmits a deriving operation request including an information resource identifier of a derivation source information resource, a deriving operation action identifier, and a media type of a derivation destination information resource; a deriving operation control device which controls a deriving operation of information in the derivation source information resource based on the deriving operation request; and an information resource derivation management device which manages derivation control information used for determining whether the deriving operation is possible, wherein the information resource derivation management device comprises: a derivation control information storage unit which stores derivation control information obtained by replicating derivation control source data in which the upper limit number of times enabling derivation of the derivation destination information resource for each media type is previously written in accordance with a generation number and a generation number and a media type of the derivation source information resource; a control reference information storage unit which stores control reference information including an upper limit value of an abundance ratio of a media type and a calculated value of the abundance ratio in accordance with the media type, the calculated value being updatable; a derivation attribute storage unit which stores a derivation attribute for each information resource identifier, the derivation attribute including a media type, a generation number, and an information resource identifier of the derivation source information resource and further including the number of times of previously-performed derivation of the derivation destination information resource for each media type when derived information is present; a unit which replicates the derivation control source data and writes derivation control information in the derivation control information storage unit upon receiving an acquisition request including the information resource identifier of the derivation source information resource and the media type of the derivation destination information resource from the deriving operation control device; a derivation attribute searching unit which searches for a derivation attribute in the derivation attribute storage unit based on the information resource identifier in the acquisition request; a previously-performed derivation number totalizing unit which totalizes the numbers of times of previously-performed derivation for the respective media types in the derivation attribute obtained by the search, thereby acquiring a total value; an abundance ratio calculating unit which calculates an abundance ratio of a media type indicative of a physical medium based on the total value and the number of times of previously-performed derivation of the medial type indicative of the physical medium in the media types in the derivation attribute obtained by search, thereby acquiring a calculated value; an updating unit which updates a calculated value in the control reference information to the calculated value obtained by the calculation; a control reference determination unit which determines whether the calculated value is equal to or above an upper limit value in the control reference information after updating the calculated value; an upper limit number updating unit which updates the upper limit number of times enabling derivation of the derivation control information in the derivation control information storage unit to a zero value when the calculated value is equal to or above the upper limit value as a result of the determination; a transmission unit which transmits the derivation control information in the derivation control information storage unit and the derivation attribute obtained by the search to the deriving operation control device in response to the acquisition request when updated to the zero value or when the result of the determination is negative; a previously-performed derivation number updating unit which updates the number of times of previously-performed derivation based on the information resource identifier of the derivation source information resource and the media type of the derivation destination information resource in a deriving operation result upon receiving the deriving operation result including the information resource identifier of the derivation source information resource, the information resource identifier of the derivation destination information resource, and the media type of the derivation destination information resource from the deriving operation control device after end of the deriving operation; and a derivation attribute writing unit which writes a new derivation attribute including the media type, the generation number, and the information resource identifier of the derivation source information resource into the derivation attribute storage unit in association with the information resource identifier of the derivation destination information resource in the deriving operation result, and the deriving operation control device comprises: an information acquisition unit which acquires information from the derivation source information resource indicated by the information resource identifier based on the information resource identifier of the derivation source information resource in the deriving operation request upon receiving the deriving operation request from the deriving operation request device; a derivation attribute acquisition unit which acquires the derivation control information and the derivation attribute from the information resource derivation management device in response to the acquisition request by transmitting the acquisition request to the information resource derivation management device based on the deriving operation request; a previously-performed derivation number extracting unit which extracts the number of times of previously-performed derivation associated with the media type of the derivation destination information resource in the deriving operation request from the numbers of times of previously-performed derivation of the derivation destination information resource for the respective media types in the acquired derivation attribute; an upper limit number extracting unit which extracts the upper limit number of times enabling derivation associated with both the media type and the generation number in the acquired derivation attribute and the media type of the derivation destination information resource in the deriving operation request from the upper limit numbers of times enabling derivation of the derivation destination information resource for the respective media types associated with the generation number and the media type of the derivation source information resource in the acquired derivation control information; a deriving operation determination unit which determines that the deriving operation for the deriving operation request is possible when the number of times of previously-performed derivation is equal to or below the upper limit number of times enabling derivation based on the extracted number of times of previously-performed derivation and the extracted upper limit number of times enabling derivation; a deriving operation execution unit which executes the deriving operation based on the deriving operation request when the deriving operation determination unit determines that the deriving operation is possible; and a deriving operation result notification unit which notifies the information resource derivation management device of the deriving operation result after end of the deriving operation executed by the deriving operation execution unit.