Okay. So you acknowledge that your approach will never solve the hard part of the halt/loop/paradox problem that your code hopes to solve. But instead of recognizing this as a fundamental limitation to your approach, you've gone on to create a new class of algorithm: lame. Do you suppose you can come up an algorithm to classify programs as halt/loop/paradox/lame in finite time?

Or, how about this one:

  def foo(n):
    if n <= 1:
      return
    elif n & 1:
      return foo(n//3)
    else:
      return foo(n//2)

I can trivially prove this halts for all n. Can your code?