Yes, it's a bit wasteful. But importantly, it's straightforward, and it's what efficient universal Turing Machines would use in their input, so it makes sense f

Yes, it's a bit wasteful. But importantly, it's straightforward, and it's what efficient universal Turing Machines would use in their input, so it makes sense for a comparison. Even the binary lambda coding allows for some optimization, like coding for variable 2 at depth 2 as 111 rather than 1110 since an occurrence of variable >= 3 would not make the term closed. > so we can simply treat that as an alternative to encoding a transition That's fine for the shift number but a lot of BB research concerns the number of 1s written rather than the number of steps taken, and there it matters. They prefer to use a single model for all variants.