[neilkk]

I think the point here is that it was not known whether all 3,3 halting problems are reducible to trivial Collatz-like problems. Unless someone is able to observe that sligicko's is actually trivial, then this provides a counterexample.

[FartyMcFarter]

> I think the point here is that it was not known whether all 3,3 halting problems are reducible to trivial Collatz-like problems.

True, but it still isn't known either way. Nothing changed in that regard.

[neilkk]

'trivial' isn't a mathematical concept. If no one has shown why this problem is trivial, it isn't trivial.

[FartyMcFarter]

This problem isn't trivial, but neither are the ones we could already reduce BB(3, 3) to (via Conway's construction).

[neilkk]

Some reductions via Conway's method give non-trivial Collatz problems even though other simple techniques show the halting question for those machines to be trivial; the Conway reduction sometimes reduces trivial Turing machines to non-trivial Collatz problems.