The modulo-10 Collatz conjecture

For a positive integer $n\geq1$, if $n$ is a multiple of $10$, replace it by $n/10$; otherwise, let $r$ be its last digit, replace it by $(12n+8r)/10$, and iterate this process. Modulo-10 Collatz conjecture. For every starting integer $n\geq1$, the process eventually reaches $4$ after finitely many iterations. This is the paper's first generalized Collatz example and is presented as a conjecture supported by preliminary computational verification; no proof is supplied.