I thought that in regular expressions, the "greediness" applies to quantifiers rather than matches as a whole. However, I observe that
grep -E --color=auto 'a+(ab)?' <(printf "aab")
returns aab rather than aab.
The same applies to sed. On the other hand, in pcregrep and other tools, it is really the quantifier that is greedy. Is this a specific behaviour of grep?
N.B. I checked both grep (BSD grep) 2.5.1-FreeBSD and grep (GNU grep) 3.1