That's what I was getting at - that the problem as stated in the headline was harder than, and different from, what he really needed. But I suspect what you just described may be harder still than what he was describing in his headline. You don't always need a completely general solution, as even one that clears away a few more special cases would help. After all, the real case I outlined is non-recursive, and you don't need an oracle machine to show it. PML.