Bouncer
1RB0LB_1LA0RA (bbch) with 2 states, the smallest number of states for which a bouncer can appear.A bouncer is a Turing machine whose tape head, roughly speaking, alternates back and forth between the two edges of the tape in a linear fasion, growing the tape along one or both edges with each iteration. A bouncer is a possible classification of non-halting Turing machines.
See Section 7 of bbchallenge's deciders write-up.