Bouziane’s transformation of the Petri net reachability problem and incorrectness This paper seems to point out that Bouziane’s solution is incorrect.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.143.9009&amp;rep=rep1&amp;type=pdf

In the conclusion: 


  This false claim served for deriving a bound on the number of states
  of the constructed automaton – which in reality can have infinitely
  many states.


I think I understand this point as it relates to the general reachibility problem, However The Petri-Net used as an illustration contains 'loops' at transitions: t3 and t1 - transitions that have both incoming and outgoing arcs.

If Petri-Net being examined were composed of only elementary paths, the resulting witness sequence / state machine language would not be susceptible to the pumping lemma.

Does this seem accurate? why or why not?
Found another article that helped me understand:

COMPEXITY OF SOME PROBLEMS IN PETRI NETS* 

http://www.sciencedirect.com/science/article/pii/0304397577900147

This paper does a good job of explaining the difference between a k-bounded Petri-Net and an unbounded one.

A Petri net is bounded if and only if it has a finite reachability set. 

Bouziane’s solution applies only to bounded Petri-Nets.