# Removing left factoring from Context-Free Grammar

I know that, removing left factoring is a simple task.
And i understand following procedure:

$$S→aA | aB$$
Becomes:
$$S→aS'$$
$$S'→A|B$$

Yet I'm running into problems with this particular grammar:

$$S→AD|bbS|bScS|BS$$
$$A→aAbb | abb$$
$$B→aB|ba|b$$
$$D→cDd|cccd$$

How to remove left factoring from it, I'm trying to convert it into LL(1) grammar

• What do you mean by "removing left factoring"? Left factoring is a technique that removes left recursion: stackoverflow.com/questions/15194142/… Commented Jul 19, 2020 at 15:40
• @BearAqua The post you link to establishes a difference between left factoring and left recursion, not a connection. Commented Jul 20, 2020 at 3:05

$$S \rightarrow a^{m}b^{2m}c^{n+2}d^{n}\;|\;(a^{*}(ba|b)|bb)S\;|\;bScS; \; m,n \ge 1$$
You can't factor out, for instance, the subexpressions generating the sequences of $$a$$'s that appear on the left. The language is not even LL($$k$$), let alone LL($$1$$).
$$S \rightarrow aS\;|\;T\; \\ T \rightarrow aTb\;|\;\varepsilon$$