for $($i$=0$; i$<100$; i$=$i$+1)\{$

X$[$i$]=$ X$[$i$]+$ c; $//$ S$1$

Y$[$i$]=$ X$[$i$]+$ c; $//$ S$2$

Z$[$i$]=$ Y$[$i$]+$ c; $//$ S$3$

Y$[$i$]=$ c $-$ Y$[$i$]$; $//$ S$4$

$\}$

The tasks are as follows:

$($a$)$ Find all the true dependencies, output dependencies, and anti$-$dependencies $(10$ points$)$

$($b$)$ Eliminate the output dependencies and anti$-$dependencies by renaming $(10$ points$)$