Let a quantified inequality constraint over the reals be a formula in the
first-order predicate language over the structure of the real numbers, where
the allowed predicate symbols are β€ and <. Solving such constraints is
an undecidable problem when allowing function symbols such sin or cos. In
the paper we give an algorithm that terminates with a solution for all, except
for very special, pathological inputs. We ensure the practical efficiency of
this algorithm by employing constraint programming techniques