$\{\}$
$\{a,b,c\}$
$\{a\}$
$\{b\}$
$\{c\}$
$\{a,c\}$
$\{a,b\}$
$\{b,c\}$
$write(\{a\})$:
$\sqsupseteq \{a\} \to$ OK
$\sqsupseteq \{a\} \to$ OK
$\sqsupseteq \{a\}$
return OK
$write(\{b\})$:
$\not\sqsupseteq \{b\}$
$\not\sqsupseteq \{b\}$
$\sqsupseteq \{b\} \to$ OK