Except as otherwise provided in a co-operative agreement, production in paying quantities upon any part of the acreage included in any state oil and gas lease continues the lease upon every subdivision thereof (whether the same remains in the original lease or is assigned before or after production is had) subject, however, to the continued payment of rentals at the rate in effect at the time of production, and further subject to the implied covenants of development contained in any such lease.
N.M. Admin. Code § 19.2.100.38