avoiding left recursion in a grammar with the production S->€

hi all men, i'm back here to ask you a question. let G be a left-
recursive context-free grammar where i eliminated the unit and epsilon
productions, maintaining S->€ because € belongs to the language
generated by G. if i eliminate the left recursive production, i can't
avoid the unit productions getting back.

let's made a simple example, to avoid left recursion i have to
consider all the productions for a given nonterminal S for which there
is at least a left recursive production. let S -> Sa1 | Sa2 | ... |
San the left recursive productions for S, and let S -> b1 | b2 | ... |
bm be the non left-recursive prodcutions for A. Then, i should add a
new nonterminal B, and replace the productions for A with these
productions:

S-> b1 | ... | bn
S-> b1B | ... | bnB
B -> a1 | ... | an
B -> a1B | ... | anB

that is ok if i don't have the production S->€, because if i have it,
then i'll get the unit production S->B back. how can i avoid this? re-
eliminating unit productions could be useless, because i could get
again left recursive productions if the grammar is *also* indirectly
left recursive, like:

S -> Ab | SAb | €
A -> Sa | ASa | a

how can i solve this problem?

thank you

regards, Stefano

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