  We present a demonstration version of a commensal pipeline for Fast Radio
Burst (FRB) searches using a real-time incoherent beam from the Murchison
Widefield Array (MWA). The main science target of the pipeline are bright
nearby FRBs from the local Universe which are the best candidates to probe FRB
progenitors and understand physical mechanisms powering these extremely
energetic events. The new MWA beamformer, known as the "MWAX multibeam
beamformer", can form multiple incoherent and coherent beams commensally to any
on-going MWA observations. One of the beams is currently used for FRB searches
(tested in 10 kHz frequency resolution and time resolutions between 0.1 and 100
ms). A second beam is used for a Search for Extraterrestrial Intelligence
(SETI). This paper focuses on the FRB search pipeline and its verification on
selected known bright pulsars. The pipeline uses the FREDDA implementation of
the Fast Dispersion Measure Transform algorithm (FDMT) for single pulse
searches. Initially, it was tested during standard MWA observations, and more
recently using dedicated observations of selected 11 bright pulsars. The pulsar
PSR J0835-4510 (aka Vela) has been routinely used as the primary probe of the
data quality because its folded profile was always detected in the frequency
band 200 - 230 MHz with typical SNR >10. Similarly, the low DM pulsar PSR
B0950+08 was always detected in folded profile in the frequency band 140 - 170
MHz, and so far has been the only object for which single pulses were detected.
We present the estimated sensitivity of the search in the currently limited
observing bandwidth of a single MWA coarse channel (1.28 MHz) and for the
upgraded, future system with 12.8 MHz (10 channels) of bandwidth. Based on
expected sensitivity and existing FRB rate measurements, we estimate an
expected number of FRB detections to be between a few and a few tens per year.
