This means that each time that the model now chooses a grammar (based on repeated sampling of the updated dirichlet distribution), it will try to use that grammar and all subsequent choices dependent on that grammar to generate both the original first token of input and the second token as output.
when the model encounters n > 1 tokens of input, the model will (a) take the sums of successes per grammar with (n -1) tokens of input and use these sums to update the pseudo-counts of the dirichlet distribution; then (b) generate the entire corpus of n tokens of input 500 times using posterior probabilities from the updated dirichlet distribution.