I’ve just recently started looking into implementing a minimal ALU, and I’ve been having trouble finding good resources to answer the question “other than a one-instruction computer, what is the smallest number of instructions needed in a Turing-complete RISC?”

I’m guessing it would be NAND, ADD, increment, and some sort of branch?

NAND covers all of the bitwise ops. If you have ADD, NOT and increment, you can get SUB. If you have ADD and SUB, you can get MUL and DIV.

Am I missing anything?