To find out, I wrote a Perl script (titled mino.pl) to solve it.
The script used global variables to manage its data.
It used a procedurally-recursive Depth-First Search scan to
solve the board.
It worked!
A Google search for "theseus minotaur" revealed that there was an
entire site - www.logicmazes.com
filled with other interesting puzzles with different rules. One of them
that caught my attention was Alice Mazes.
I took my mino.pl script and gradually converted it to solve Alice Mazes,
this time using CVS to manage the code.