  The Double Pulsar (PSR J0737-3039) is the only neutron star-neutron star
(NS-NS) binary in which both NSs have been detectable as radio pulsars. The
Double Pulsar has been assumed to dominate the Galactic NS-NS binary merger
rate R_g among all known systems, solely based on the properties of the
first-born, recycled pulsar (PSR J0737-3039A, or A) with an assumption for the
beaming correction factor of 6. In this work, we carefully correct
observational biases for the second-born, non-recycled pulsar (PSR J0737-0737B,
or B) and estimate the contribution from the Double Pulsar on R_g using
constraints available from both A and B. Observational constraints from the B
pulsar favour a small beaming correction factor for A (~2), which is consistent
with a bipolar model. Considering known NS-NS binaries with the best
observational constraints, including both A and B, we obtain R_g=21_{-14}^{+28}
per Myr at 95 per cent confidence from our reference model. We expect the
detection rate of gravitational waves from NS-NS inspirals for the advanced
ground-based gravitational-wave detectors is to be 8^{+10}_{-5} per yr at 95
per cent confidence. Within several years, gravitational-wave detections
relevant to NS-NS inspirals will provide us useful information to improve
pulsar population models.
