Collatz/Bařina a$n$+b conjecture proofs by 16/64: Cayley a$n$+b tree not Cantor-Gödel-Conway-Wolfram undecidable

Lothar Collatz considered biperiodic iterations, and conjectured that picturing $n\mathrm{\to3}n\mathrm{+1}$ iterations for odd numbers and $n\mathrm{\to}n/2$ for even numbers, and proving that all natural numbers have a root path to the `trivial' cyclic root $(c=4)\to2\to1\to c\to\dots$, would conn