I conjecture (i.) a stochastic “mechanical algorithm” that untangles untanglable strings in finite iterations, (ii.) a class of heuristics that reliably reduce stochasticity and increase efficiency of this algorithm, and furthermore (iii.) a subclass of such heuristics that renders the algorithm superior in average- and worst-case time-complexity to any algorithm that must analyze a topological relationship between two points on the string.
Let there exist a function, pull(a, b, F), where a and b represent points on a string (say, as scalar displacements from a common origin on the string) and F represents a force, that simultaneously pulls an untanglable string by force F at a and -F at b, until there is no movement. I conjecture that for any untanglable string there exists a scalar f such that invoking pull on a random a, random b, and F > f untangles the string in a finite number of iterations.