GATE CS 2013 Q9 — Parsing (LL, LR)

To find the maximum number of reduce moves to parse a string of length $n$ using a bottom-up parser:

1. Without Terminal Reductions: If we assume that terminal-to-nonterminal transitions (like $A \rightarrow a$) are handled during the shift phase (or by the lexical analyzer), the parser starts with $n$ non-terminal symbols on the stack.
2. Stack Reduction: Since the grammar has no epsilon-productions ($A \rightarrow \epsilon$) and no unit-productions ($A \rightarrow B$), every reduction must be of the form $A \rightarrow \alpha$ where $|\alpha| \ge 2$.
3. Each such reduction replaces at least $2$ symbols with $1$ symbol, thereby decreasing the number of symbols on the stack by at least $1$.
4. To reduce the stack size from $n$ symbols to $1$ (the start symbol $S$), we need at most: $$n - 1 \text{ reduce moves}$$

Note: If reductions of the form $A \rightarrow a$ are counted as separate reduce moves, it would require $n$ additional reductions, leading to $2n - 1$ moves (Option C). Under the assumption of pre-classified tokens, the answer is $n - 1$.