Can it be proven that Collatz numbers cannot repeat?

One potential counterexample of the Collatz conjecture would be if there was a number that looped back to itself. Of course, this would still not prove the conjecture because some sequences could still potentially diverge to infinity. Has it been proven that Collatz sequences cannot repeat?

• Regarding your first sentence: have you seen this? – J. M. is a poor mathematician May 16 '16 at 19:08
• I suppose that the cycle $1 \to 4 \to 2 \to 1$ does not count. – Rodrigo de Azevedo May 16 '16 at 19:17
• @thecat It is widely known that proof of the two facts a) there is no non-trivial loop, and b) no sequence ascends to infinity, is sufficient to prove the Collatz conjecture. Since these are the only two ways some linear sequence might not ultimately reach 1. – samerivertwice May 25 '16 at 18:59