The input automaton is a classical automaton. Stamina will compute its star height.
It first finds an upper bound using the Loop Complexity heuristics, and then proceeds with the star height computation.
************LOOP COMPLEXITY******************
According to the Loop Complexity heuristics, the star-height is at most 2.
A regular expression for the language (omitting epsilon) is: (bb*aa*b+(a+bb*aa*b)((a+bb*aa*b))*(a+bb*aa*b))
The Loop Complexity suggests the following unboundedness witness: bb#aa#b(bb#aa#b)^#bb#aa#b
************STAR HEIGHT COMPUTATION**********
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Testing star height 0
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Testing star height 1
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Processing product: 876 elements and 520 rules and 1865 vectors and 593500 expressions to process.
Processing product: 925 elements and 539 rules and 1865 vectors and 569223 expressions to process.
Processing product: 925 elements and 546 rules and 1865 vectors and 469223 expressions to process.
Processing product: 925 elements and 553 rules and 1865 vectors and 369223 expressions to process.
Processing product: 925 elements and 556 rules and 1865 vectors and 269223 expressions to process.
Processing product: 925 elements and 556 rules and 1865 vectors and 169223 expressions to process.
Processing product: 925 elements and 556 rules and 1865 vectors and 69223 expressions to process.
RESULTS: the star height is 2, as predicted by the Loop Complexity heuristics, and a regular expression witnessing it is (bb*aa*b+(a+bb*aa*b)((a+bb*aa*b))*(a+bb*aa*b)).