1. An interference check device comprising: a model-number upper-limit input unit to which an upper limit number of geometric models that is allocated to a modeling target is input, the modeling target being a target of an interference check; a modeling unit that, when a cuboid that is capable of enclosing the modeling target is set as the modeling target as a model for an interference check, uses new geometric models that have a calculation cost per unit distance calculation smaller than the cuboid and that are in number equal to or less than the upper limit number of models to replace the cuboid with the new geometric models and models the modeling target; a model-candidate storage unit that stores, as model candidates, models in which the new geometric models are used; a computation-amount upper-limit setting unit that sets a computation upper-limit amount that is an upper limit of a computation amount in calculation processing of an interference check, on a basis of information relating to a computation processing amount required for each process performed by a controller that controls the modeling target; a volume-model determination unit that extracts, from the model candidates, a model candidate on which a calculation processing of the interference check is capable of being performed with a computation processing amount equal to or less than the computation upper-limit amount, and determines a model candidate having a smallest model enclosure volume as a model for the modeling target from among extracted model candidates; and an interference check unit that performs an interference check between models by using a model determined by the volume-model determination unit, and, if there is a possibility of interference, outputs an operation stop command, and, if there is no possibility of interference, outputs an operation continuation command.