X^{2}-Y^{2}=Z^{2}X+Y+Z<UX+Y5^{ . }Z

X_{1},...,X_{9}are pairwise distinct

A domain constraint (also called basic constraint) takes the form
*x* *D*, where D is a finite domain.

A finite domain problem is a finite set P of quantifier-free constraints such that P contains a domain constraint for every variable occurring in a constraint of P. A variable assignment is a function mapping variables to integers.

A solution of a finite domain problem P is a variable assignment that satisfies every constraint in P.

Notice that a finite domain problem has at most finitely many solutions, provided we consider only variables that occur in the problem (since the problem contains a finite domain constraint for every variable occurring in it).

Andreas Rossberg 2006-08-28