1. A processing system including a machine tool, a robot which supplies or ejects a workpiece to or from the machine tool, and a capturing device which is arranged on a movable section of the robot and captures a tool of the machine tool, the processing system comprising: an image processing part which compares a reference image of the tool captured by the capturing device to an image of the tool captured by the capturing device at each time when a predetermined number of processing operations are finished, and detects an amount of abrasion of the tool; a correcting part which corrects a tool position in a processing program of the machine tool based on the amount of abrasion; and an outputting part which calculates a number of remaining possible processing operations until the amount of abrasion reaches a predetermined limit amount of abrasion of the tool, based on an amount of tool abrasion per one processing operation, and externally outputs the calculated number of remaining possible processing operations, wherein, when a difference between an estimated amount of tool abrasion and an actually measured amount of tool abrasion at a predetermined timing of capturing the tool exceeds a predetermined allowable value, the outputting part estimates and outputs a remaining tool life by replacing the estimated amount of tool abrasion with the actually measured amount of tool abrasion, the estimated amount of tool abrasion being obtained by estimating based on the amount of tool abrasion obtained by comparing the reference image of the tool to the image of the tool at the time when the predetermined number of processing operations are finished, and the actually measured amount of tool abrasion being obtained by a captured image at the time when the predetermined number of processing operations are finished.