 It can be verified that the system of equations (\ref{genrecex}) and the derivation (\ref{genreccal}) exhibited above satisfy the foregoing requirements, thus illustrating how it is possible to mechanically calculate using a system of general recursive equations.  However certain systems—e.g., \(\{\phi(x) = 0, \phi(x) = s(0)\}\)—are inconsistent in the sense of not being satisfied by any function on the natural numbers, while others—e.g., \(\{\phi(x) = \phi(x)\}\)—are not satisfied uniquely. One evident drawback of Gödel’s definition of general recursiveness is thus that there is no apparent means of establishing whether a given system of equations \(\mathcal{E}\) determines a unique function (even if only partially defined).   This is one of the reasons why Gödel’s characterization has been replaced by other extensionally equivalent definitions such as Kleene’s partial recursive functions  (see  Section 2.2)  in the subsequent development of computability theory.