There's apparently a whole field about this: https://en.wikipedia.org/wiki/One-instruction_set_computer https://en.wikipedia.org/wiki/One-instruction_set_compu

There's apparently a whole field about this: https://en.wikipedia.org/wiki/One-instruction_set_computer https://en.wikipedia.org/wiki/One-instruction_set_computer (I don't know what's known about how to tell whether or not a particular instruction will be Turing complete. Maybe, as in many other parts of computer science, you can do it by reductions: FOO is Turing complete if you can implement BAR with it, where BAR is already known to be Turing complete; BAZ is not Turing complete if you can implement it with QUX, where QUX is already known not to be Turing complete?)