Shit, I was half sleep when a read this and thought "so, Nagi's mom looks just like Erika... what's wrong with Japan and the Oedipus complex", totally forgot the main plot XD
Like many arcs in this manga, I don't get the purpose of these two last chapters, makes me think the mangaka was angry at something and just wanted to rant about something...
Actually, "compulsory execution" is a legal term meaning that, having proved the right of yor claim in front of a judge (in this case there was no jugdment as everyone saw the crime), the state has the obligation to retribute you by taking any necessary measure against the lossing party (like...