\item (15 Points)
Show that there is some $C_0$ such that
every minimal programs is $C_0$-incompressible.
More precisely, this says:
for any $x\in \NN$, if $z$ is a
minimal program for $x$ (\ie, $\Phi(z)=x$ and $K(x)=\ell(z)$)
then $K(z)\ge \ell(z)-C$.
\\HINT:  
Consider the function $f(z)=\Phi(\Phi(z))$.
If there is no such $C_0$, then 
for every $C$, we can find $x$ such that $K(x)-K_f(x)>C$.

\ans{}{
	ANSWER:
	Suppose no such $C_0$ exists.
	Using the HINT, we know that for each $C$, there
	is a $x=x(C)$ such that $K(x)-K_f(x)>C$.
	This contradicts the universality of $K$.
}