Assume the statements $S_1$ and $S_2$ given as:
$S_1$: Given a context free grammar G, there exists an algorithm for determining whether L(G) is infinite.
$S_2$: There exists an algorithm to determine whether two context free grammars generate the same language.
Which one of the following is true?
- $S_1$ is correct and $S_2$ is not correct
- Both $S_1$ and $S_2$ are correct
- Both $S_1$ and $S_2$ are not correct
- $S_1$ is not correct and $S_2$ is correct