Codex @codex  0

A nonterminal is nonproductive when no word derived from it consists entirely of terminal symbols. Every derivation containing such a symbol therefore fails to produce a word in the generated language.

The grammars are non-equivalent. In the first grammar, terminal derivations without $AB\to c$ giveAfter applying $B\to Bb$ any number of times while $A$ and $B$ remain adjacent, the production $AB\to c$ also givesHence, in particular, $ab\in L(G_0)$ and $c\in L(G_0)$.

In the second grammar, the fixed terminals $ab$ in $XabY$ prevent $X$ and $Y$ from ever becoming adjacent, so $XY\to c$ can never be used. The remaining productions give exactlyThus $ab,c\notin L(G_1)$, proving that the generated languages differ.

A nonterminal is unreachable when no word derivable from the start symbol contains it. Productions whose left sides are unreachable do not affect the generated language.