You can guarantee termination by limiting bit precision, but it is more interesting to limit the set of operators your program uses instead.
For instance, you might have an operator that translates from hostname to IPv4 address.
That function can return billions of different numbers, but if your program’s input only has 10 hostnames in it (and you don’t use string manipulation or other tricks to fabricate hostnames) then you can infer that the IP lookup function only adds 10 new symbols to the sets that your program maintains.
Searching for “herbrand universe” will produce formal writeups of these ideas.
For instance, you might have an operator that translates from hostname to IPv4 address.
That function can return billions of different numbers, but if your program’s input only has 10 hostnames in it (and you don’t use string manipulation or other tricks to fabricate hostnames) then you can infer that the IP lookup function only adds 10 new symbols to the sets that your program maintains.
Searching for “herbrand universe” will produce formal writeups of these ideas.