GNU make reports "process_begin: CreateProcess(NULL, pwd, ...) failed." on Cygwin

I very rarely build anything on Windows.  My day job doesn't call for it much, and I certainly wouldn't want to do that for "fun."  So, when I do, I often run into problems that (a) I don't understand and (b) nobody else seems to have seen before.  This is one of those sorts of problems.

My build on a new machine failed almost immediately after typing "make" with this error:

process_begin: CreateProcess(NULL, pwd, ...) failed.

I have no idea what that means.  The "pwd" command, of course, works just fine for me at the command line, and "whence" tells me it comes from /usr/bin.  Everything looks fine there.

After a lot of debugging and comparisons with others who had working configurations, I found this: near the front of my PATH, I had an entry like this:

/cygdrive/c/this/does/../not/exist

That's not the actual path, of course, but it gives the idea.  The bug I encountered is this: if you have a path that includes "/.." and if the previous directory in that path doesn't physically exist on that machine, then the path search function stops right there.  It doesn't look at the rest of the path entries at all.  So, if you have something like this before "/usr/bin", you're sunk.  That works fine on all UNIX and Unix-like systems, and it even works fine for the Cygwin shells.  But, for some reason, it doesn't work within GNU make's code that deals with path searches.

Changing that path so that it didn't have "/.." in it fixed the problem.