  We study the realizability problem for Safety LTL, the syntactic fragment of
Linear Temporal Logic capturing safe formulas. We show that the problem is
EXP-complete, disproving the existing conjecture of 2EXP-completeness. We
achieve this by comparing the complexity of Safety LTL with seemingly weaker
subfragments. In particular, we show that every formula of Safety LTL can be
reduced to an equirealizable formula of the form $\alpha \land \Box \psi$,
where $\alpha$ is a present formula over system variables and $\psi$ contains
Next as the only temporal operator. The realizability problem for this new
fragment, which we call $\mathsf{GX}_{\mathsf{0}}$, is also EXP-complete.
