Cygwin creates a subdirectory /cygdrive where it stores phisical drives e.g. C: as c, F: as f, etc. Hence /cygdrive/f/CygWin/usr is a valid long name pointing to /usr directory in Cygwin
When used with Cygwin, MinGW gcc and ld do not follow paths given as "/cygdrive/f/CygWin/usr" when given as include or lib parths using -I or -L respectively though it does not complain either. But MinGW requires
-I'F:/CygWin/usr'
and similar for the -L option.
Hence...