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Consider US Patent #5533051:
To my best understanding, what the patented algorithm says is that it can guarantee a lossless one-bit compression on any input. Clearly this is totally impossible (recursivly apply the algorithm to reach a one-bit representation of any input).
Am I understanding this algorithm the wrong way?
Your understanding is correct. The algorithm as described will loop forever for some inputs (since the answer to “is the output file at or below required size?” will always be “no”).
See the comp.compression FAQ for an in-depth discussion of claims of being able to compress any input and compression of random input.