This task refers to compiler optimizations $($see Lecture slides $6-$ Optimizations in Fasto$),$ and specifically dead$-$binding elimination $($DBE$).$

Consider the following Fasto expression, with labeled subexpressions:

$(11)$let x $=(1)$u in $(10)$let y $=(2)$x$+$x in $(9)$let y $=(5)($let x $=(3)$foo$($x$)$ in $(4)7)$ in $(8)$let t $=(6)$x$+$u in $(7)$y$*$x

Each subexpression extends from its label and as far to the right as syntactically possible. For example, subexpression $(2)$ is x$+$x$,$ and $(5)$ is let x $=$ foo$($x$)$ in $7,$ while $(11)$ is the whole expression. foo is some user$-$defined function, about which you should assume nothing $($in particular, it might contain I$/$O$).$