turtle(Program,ShortProgram):-
	Coordinate = (0,0),
	Orientation = (1,0),
	canonical_drawing(Program,Coordinate,Orientation,Drawing),
	length(ShortProgram,_),
	canonical_drawing(ShortProgram,Coordinate,Orientation,Drawing),
	!.

canonical_drawing(Program,Coordinate,Orientation,Drawing) :-
	generate(Program,Coordinate,Orientation,ADrawing),
	sort(ADrawing,Drawing).

generate([],_,_,[]).
generate([rotate|Program],Coordinate,(DX,DY),O) :-
	generate(Program,Coordinate,(DY,-DX),O).
generate([step|Program],(X,Y),(DX,DY),Drawing) :-
	X1 is X + DX,
	Y1 is Y + DY,
	Drawing = [(X,Y)-(X1,Y1),(X1,Y1)-(X,Y)|RestDrawing],
	generate(Program,(X1,Y1),(DX,DY),RestDrawing).