If I remember correctly, that's the chief reason Ackermann came up with the function. Have a look at <URL: http://mathworld.wolfram.com/AckermannFunction.html > and the links on that page for computable and primitive recursive, and see if that helps. The site also has a definition of recursive.
OK. Then isn't there an answer to the original question? I couldn't find a machine model that satisfies Cagdas's operational requirements. Any thoughts? Maybe it's a very easy answer but I can't see it, and I can't say I know the proof of every theorem in Cindrella book.
Cheers,
Indeed, I am still looking for a theorem of some sort that either equates stongly normalizing systems to primitive recursive functions (if this is the case), or a theorem that demonstrates some sort of limitation to strongly normalizing systems when compared to a turing machine, or a system that can decide recursive class but unable to recognize recursively enumerable class.