Is instantiabilty of templated types decidable?

[Nick Sabalausky]

On Sun, 11 Nov 2012 19:37:45 +0100
Timon Gehr <timon.gehr at gmx.ch> wrote:

> On 11/11/2012 03:45 PM, Peter Alexander wrote:
> >
> > Collatz sequence.
> >
> > struct Collatz(int n)
> > {
> >      enum next = n % 2 == 0 ? n / 2 : 3 * n + 1;
> >      Collatz!(next)* foo;
> > }
> >
> > It's an unsolved problem in mathematics whether or not this
> > instantiates an infinite number of templates.
> 
> The possible inputs are finite, so the property is decidable.

Technically, yea, but I think upwards of ~4 billion template
instantiations is quite unrealistic, to the point of being effectively
undecidable.