Untangling Rope
The Ashley Book of Knots gives the following procedure:

To untangle a snarl, loosen all jams or knots and open a hole through the mass at the point where the longest end leaves the snarl.  Then proceed to roll or wind the end out through the center exactly as a stocking is rolled.  Keep the snarl open and loose at all times and do not pull on the end; permit it to unfold itself.  As the process is continued the end gradually emerges.  No snarl is too complicated to be solved by this method; only patience is required.

But what if you find a jammed knot in the tangle?