Looking for cycles in an alternative representation of the Collatz sequences

Would it be possible to define a procedure capable to find all the existing cycles within the Collatz sequences? In this article we address this question in two stages: in the first one, we propose an equivalent and reversible set of actions to represent any Hailstone sequence. In the second one, we show a condition which any loop satisfies within this new definition, ultimately revealing that the problem 3n + 1 generates just a single cycle for any value of n, being moreover, always reached.