$($c$)$ Give a WHILE$-$program that terminates for all input and that is not in WHILE ${?}^{\text{l}\text{i}\text{n}\text{t}\text{i}\text{m}\text{e}}.$

You can use extended WHILE if you want but make sure your program is using

correct syntax.

$($d$)$ Consider the following Family Reunion Drama Problem, short FRD$.$ For a family

reunion, $m$ family members travel together to a resort. A binary relation dislike

is given, which defines which of those $m$ family members cannnot stand each

other. Now, given $m,$ dislike, and a positive integer $k,$ the question is: can all

$m$ family members stay in $k$ different hotels $($in the same resort$)$ such that no

two family members that dislike each other have to stay in the same hotel? We

assume that all hotels have more than $m$ available rooms. FRD is a decision

problem. Show that it is NP$-$hard.