Consider the following context free grammar:
$S \rightarrow ASA | aB$
$A \rightarrow B | S$
$B \rightarrow b | \epsilon$
How many productions will be there in the modified grammar if we remove null-productions and unit-productions from this grammar?
My Solution:
Step 1: Remove epsilon transitions
Nullable variables = $ \big\{A,B\big\} $
Modified grammar after removal of null productions:
$S \rightarrow ASA | aB | a | AS | SA | S$
$A \rightarrow B | S $
$B \rightarrow b$
Step 2: Remove Unit Productions
$S \rightarrow ASA |aB |a | AS | SA | \mathbf{S}$
$A \rightarrow \mathbf {B} | \mathbf{S}$
$B \rightarrow b$
Modified grammar after the removal of the unit productions:
$S \rightarrow ASA |aB |a | AS | SA$
$A \rightarrow b | ASA |aB |a | AS | SA$
$B \rightarrow b$
I am getting 12 productions. can someone please confirm if it's correct?