I know many of you don't favor "foreign" interference. There were several attempts from misc " outside teams" to resolve the Cyprob but failed to do so.
Taking a closer look & evaluating the given facts:
1. 36 years of endless talks - total failure.
2. New talks under way - not very promising - failure is imminent
3. "Distance" between both sides - too great
4. Willingness to resolve - low
5. More time needed - estimation impossible
Binding arbitration may be the only way to resolve the problem. The synthesis of the arbitrating team must be accepted from both sides. Final decision is binding but subject to modifications in the years to come and with/without pending approval from the arbitrator/s.
Implementation is immediate with terms based on a gradual removal of all foreign and domestic troops from the island. Security to increase proportionally to troop withdrawal, assigned by the arbitrator/s.
History example link http://en.wikipedia.org/wiki/Jay_Treaty
The Jay Treaty of 1794 between Britain and the United States sent unresolved issues regarding debts and boundaries to arbitration, which took 7 years and proved successful.