Register Automaton is a simple esolang invented by User:A which only has 1 instruction:
Flip cell x. If that content is equal to the content of cell y, go to line Lx.
It is an infinite loop, changing cells 0 and 1 forever.
Since a program can only access the cells mentioned in it, which are bit valued, there is no unbounded memory. Register Automaton is therefore at most a finite-state automaton.