1. A communication system, comprising: a node(s) that processes a packet received in accordance with a processing rule that stipulates a matching rule and processing for a packet matching to the matching rule; and a controller, the controller including: a removal request history management unit that retains record(s) of past request(s) to the node(s) to remove a processing rule; a processing rule search unit that, in setting a new processing rule for the node(s), references the removal request history management unit to search a processing rule having a matching rule competing with the new processing rule; and a processing rule setting unit that, in case a processing rule having the matching rule competing with the new processing rule exists, re-requests the node(s) to remove the processing rule having the matching rule competing with the new processing rule, wherein the controller further includes a processing rule removal re-request policy management unit that removes the record(s) from the removal request history management unit based on a pre-set policy, wherein the processing rule removal re-request policy management unit removes, in case a number of times of the re-requests for removal of the processing rule(s) competing with the new processing rule as formed by the processing rule setting unit has reached a pre-set threshold value, the record(s) from the removal request history management unit.