Does removal of unit production from the grammar may increase number of total production? There are m variable in a grammar. The number of productions after removal of unit productions in the worst case is ,(Assume there are no null productions)

(a) O(m)
(b) O($m^2$)

(c) O($k^m$)

(d) O($2^m$)



My attempt:

He asked about number of total production remains in the minimized grammar ,
 so , if the there is no null production , it is advantage , as you know when we convert a grammar without null production , generally , removal of all production introduces new production in the resultant grammar (it can be upto set of all subset of given max RHS number of variable , so exponetial ) .

But , in given grammar , you don't have null production , so you are removing only unit production (i.e. A--->B type productions ) , resultant grammar maximum 'm' production , where m is number of variable . 
example :-
S---->A
A---->B
B---->a/b/c
resultant grammar ,
S---->a/b/c
So , it is O(m) time .


  Can you explain in formal way, please?
Hint: Consider the grammar
$$S \to \overbrace{X\cdots X}^{\text{$n$ times}} \\ X\to a|b$$
What happens when you remove unit productions?