A constraint based system solves a network that includes a first variable node having a first integer domain, a second variable node having a second integer domain, and a constraint for the first variable node and the second variable node. The system retrieves a first integer domain representation of the first integer domain and a second integer domain representation of the second integer domain and determines from the first and second integer domain representations if the first integer domain or second integer domain has at least one excluded value. The system then determines a type of constraint consistency checking based on whether the integer domains have at least one excluded value.