Let say that we have four straight strings called RED, GREEN, BLUE and YELLOW. These strings are tied up randomly. We know the current state of strings (like starting point, where we should start untying from here) and the final state (where current string must be look like after untying them).

Here is a very simple example of the problem:

At every move, we are allowed to replace only two nearby strings. For example, to solve the shown example of the problem, we should do the following replacements:

1) replace GREEN and YELLOW

2) replace BLUE and GREEN

But in a programmable environment, how can I calculate the movements even on a complex state?