Anal Turing was wrong

There are at most 2^n different programs of length n (in binary).

Those that terminate go on forever, those that don't terminate stop after x steps.

let f(n) = the largest x.

Now write the program:

halts?(program) {
 int maxsteps = f(length(program));
 for(int i = 0; i < maxsteps; i++) { step(program); }
 if(halted?(program)) return HALTS;
 else return LOOPS;
}

any questions Turing?

see wiki:busy%20beaver