Absolute, mathematical proof that a hypothesised 2nd loop cannot exist in the Collatz Conjecture.

This proof shows that the necessary requirements for a 2nd loop in the Collatz cannot be met, ever. For a loop to exist all rises and falls in values between each value of x leaving and returning to itself must cancel to a net rise of 0. However I prove using simple algebra and elementary logic that if the lowest odd value of x has a net rise of 0 the 2nd lowest odd value of x cannot have a net rise of 0 so such a 2nd loop can never exist.