We present the data analysis pipeline , commissioning observations and initial results from the GREENBURST fast radio burst ( FRB ) detection system on the Robert C. Byrd Green Bank Telescope ( GBT ) previously described by Surnis et al . which uses the 21 cm receiver observing commensally with other projects . The pipeline makes use of a state-of-the-art deep learning classifier to winnow down the very large number of false positive single-pulse candidates that mostly result from radio frequency interference . In our observations totalling 156.5 days so far , we have detected individual pulses from 20 known radio pulsars which provide an excellent verification of the system performance . We also demonstrate , through blind injection analyses , that our pipeline is complete down to a signal-to-noise threshold of 12 . Depending on the observing mode , this translates to peak flux sensitivities in the range 0.14–0.89 Jy . Although no FRBs have been detected to date , we have used our results to update the analysis of Lawrence et al . to constrain the FRB all-sky rate to be 1140 ^ { +200 } _ { -180 } per day above a peak flux density of 1 Jy . We also constrain the source count index \alpha = 0.83 \pm 0.06 which indicates that the source count distribution is substantially flatter than expected from a Euclidean distribution of standard candles ( where \alpha = 1.5 ) . We discuss this result in the context of the FRB redshift and luminosity distributions . Finally , we make predictions for detection rates with GREENBURST , as well as other ongoing and planned FRB experiments .