  Motivated by satisfiability of constraints with function symbols, we consider
numerical inequalities on non-negative integers. The constraints we consider
are a conjunction of a linear system Ax = b and a conjunction of (non-)convex
constraints of the form x_i >= x_j^n (x_i <= x_j^n). We show that the
satisfiability of these constraints is NP-complete even if the solution to the
linear part is given explicitly. As a consequence, we obtain NP completeness
for an extension of certain quantifier-free constraints on sets with
cardinalities (QFBAPA) with function images S = f[P^n].
