Determine if two grammars for the same language are ambiguous
Consider this a hint.  As I write in my comment, what is the syntax tree of ()()()?  Does the first two pairs belong to the leftmost of the &lt;string&gt;&lt;string&gt;-part, or does the two latter pairs belong to the rightmost?

$$ \left(
 \overbrace{  \overbrace{ () }^\text{string} \quad
 \overbrace{ () }^\text{string}}^\text{string}
\quad \overbrace{ () }^\text{string} \right)
\text{ vs }
\left(
 \overbrace{ () }^\text{string}\quad
 \overbrace{  \overbrace{ () }^\text{string}\quad
 \overbrace{ () }^\text{string}}^\text{string} \right)
$$