Further suppose L is infinite, hence there is no upper bound on the length of strings belonging to L. L does not contain .
G has no unit productions or productions.
There are only a finite number of variables in a grammar, and the productions for each variable have finite lengths. The only way that a grammar can generate arbitrarily long strings is if one or more variables is both useful and recursive. If a variable is not useful, it does not occur in the derivation of any string of the language. Useless variables can always be eliminated from a grammar. Suppose that no variable in the grammar is recursive.