If there exist efficient procedures (\emph{canonizers}) for reducing
terms of two first-order theories to canonical form, can one use
them to construct such a procedure for terms of the disjoint union
of the two theories? We prove this is possible whenever the
original theories are convex. As an application, we prove that
algorithms for solving equations in the two theories
(\emph{solvers}) can\emph{not} be combined in a similar
fashion. These results are relevant to the widely used Shostak's
method for combining decision procedures for theories. They provide
the first rigorous answers to the questions about the possibility of
directly combining canonizers and solvers.