Sorry, but I think you may have misunderstood the problem. Or perhaps I am misunderstanding your code.

What you appear to be doing is searching the stream for a known 5-value sequence, using a FSM that uses 24,664 bytes of memory to represent those 5 characters and an extra 1056 bytes of memory for every extra byte; and takes (on my machine) 202 seconds to locate those 5 bytes 4,312,277 bytes into the stream.

The actual problem is that the sequence I am looking for is in the stream, and can be huge; as in greater than memory. eg 100GB.

For the 'simple' version of the problem, the sequence to find starts at the beginning of the stream, but extends to a size greater than memory, and once complete, will repeat immediately, (and obviously extend as far again). The problem is how to retain enough information about a huge, and ever growing sequence to recognise when you have seen it twice.

It is only once you have see it twice that it is possible to know how long the sought after sequence is.

The more complex version can have additional just existing between occurrences of the repetition(s) and you don't know whether the first characters you see constitute a part of the repetition, or junk. (But that's for another day :) ).