Suppose a CFG has unit productions
A -> B and
C -> D among other productions, possibly involving
A,B,C,D and possibly other symbols too. The method of eliminating these unit productions, to get a CNF, which I've learned in class, I can describe for
A -> B. I'm supposed to look at every production rule in the grammar, and find every permutation of substituting
B or not.
For instance, if the rule includes
X -> AAB then to eliminate
A -> B for this rule, I should find the permutations
X -> AAB|BAB|BBB|ABB which are added to the grammar, and the rule
A -> B is then eliminated.
My question is, does it ever matter if you eliminate
A -> B first and then
C -> D, versus doing them in reverse order?