+-------------------------------------------------------------------------------+                                                                  
         |                                                                               |
         v                                                                               |
(0,x,y) -+-> (1,x,y) -+- ( x != y ) -> (2,x,y) -+- ( x >  y ) -> (3,x-y,y) -+-> (5,x,y) -+
                      |                         |                           |
                      |                         +- ( x <= y ) -> (4,x,y-x) -+
                      |
                      +- ( x == y ) -> (6,x,y)