We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions. A stream definition is called `productive' if it can be evaluated continuously in such a way that a uniquely determined stream is obtained as the limit. Whereas productivity is undecidable for stream definitions in general, we show that it can be decided for `pure' stream definitions. For every pure stream definition ess of its evaluation can be modelled by the dataflow of abstract stream elements, called `pebbles', in a finite `pebbleflow net(work)'. And the production of a pebbleflow net associated with a pure stream definition, that is, the amount of pebbles the net is able to produce at its output port, can be calculated by reducing nets to trivial nets.