If we let G n be the DAG that uses t 2 exactly n times, then the language L defined by this automaton is n∈N G n .
since w(G n ) = w(t 1 )w(t 2 ) n w(t 3 ) and w(t 1 ), w(t 2 ) and w(t 3 ) are positive, w satisfies R1 and: w also satisfies R2 and the weighted automaton in Example 3 is probabilistic.