A simple example that is hard to determine if it halts is to iterate through a,b,c,n and see if a^n+b^n=c^n. I.e. solve Fermat's last theorem by brute force. (I won't spell out the iteration details.) If your software could determine if this halts or not, it would prove Fermat's last theorem. (Obviously since FLT has been proven, this particular case is known not to halt.)