The Collatz Problem in the Light of an Infinite Free Semigroup

Table 1

Logic of the re-scale procedure.

Case	𝐴	𝐵	Action	Result
1	Even	Even	Divide by 2	any case
2	Even	Odd	None	Ok
3	Odd	Even	𝑘→𝑘−1	Case  4
4	Odd	Odd	𝑘→2𝑘	Case  2