)$ {#example0} --------------------------------------------------------  To check whether $(M,X),s_0\models AG (s_0\rightarrow AXA[\neg s_0 U s_0])$, is equivalent to checking whether $$(M,X)\models \neg E[true~U (s_0\wedge EX(E[\neg s_0 U (s_0\wedge\neg s_0)]\vee EG\neg s_0))]