Suppose S $$ N is recursively enumerable but not computable. Let f : N $->$ N $\backslash$cup $\{\}$ be a $($partial$)$ computable function such that n in S if and only if f $($n$)=($i$.$e$.,$ f terminates on input n$).$ Show that there does not exists a total computable function g : N $->$ N with the following property: for those n such that f terminates on input n$,$ it terminates after at most g$($n$)$ steps.