Exact reconstruction of the published shuffle failure

Exact statement

For $((ab)^*)\amalg((bc)^*)$ , exact reconstruction gives a 9-state, 18-transition location automaton, a 9-state marked prefix automaton, and an 8-state, 16-transition unmarked prefix automaton; exhaustive partition search finds no quotient.

StatusIndependently reproduced with an exact structural checker

External reviewNo documented external or specialist review of these FPRD results is recorded.

Context

The source example is the benchmark that shows shuffle prefix automata need not be quotients of location automata.

Proof or evidence

A structural recursion rebuilds both automata, unmarks syntactically equal prefix states, and tests every compatible state partition.

Published example reconstruction →

Verification notes

The computed state and transition counts match the source construction; exhaustive quotient search returns none.

Limitations

This finite reproduction does not explain every possible shuffle failure.

Open work

Use the incoming-spectrum witness from FPRD-SH-T04 as the direct explanation of this example.