  Recent completeness results on the ZX-Calculus used a third-party language,
namely the ZW-Calculus. As a consequence, these proofs are elegant, but sadly
non-constructive. We address this issue in the following. To do so, we first
describe a generic normal form for ZX-diagrams in any fragment that contains
Clifford+T quantum mechanics. We give sufficient conditions for an
axiomatisation to be complete, and an algorithm to reach the normal form.
Finally, we apply these results to the Clifford+T fragment and the general
ZX-Calculus -- for which we already know the completeness--, but also for any
fragment of rational angles: we show that the axiomatisation for Clifford+T is
also complete for any fragment of dyadic angles, and that a simple new rule
(called cancellation) is necessary and sufficient otherwise.
