All leases issued under the provisions of Sections 19-8-14 through 19-8-33 N.M. Stat. Ann. shall be for a primary term of three years and as long thereafter as any mineral or minerals in paying quantities be produced or mined from the lands, subject to the continued payment of annual rentals.

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If lessee shall fail to discover and produce minerals in paying quantities during the primary term of the lease, the lessee may continue the lease in full force and effect for an additional or secondary term of two years and as long thereafter as any mineral or minerals in paying quantities be produced or mined from the leased land, by paying each year in advance ten times the rental provided in the primary term.

Provided, however, if the lessee shall fail to discover and produce minerals in paying quantities during the secondary term of the lease, the lessee of record or the record owner of an approved assignment may continue the lease, as to the portion held by him, in full force and effect for an additional or tertiary term of five years and so long thereafter as any mineral or minerals in paying quantities by [be] produced or mined from the leased land, by paying each year in advance three dollars ($3.00) per acre per year as rental.

If the lessee shall fail to discover and produce minerals in paying quantities during the tertiary term of the lease, the lessee of record or the record owner of an approved assignment may continue the lease, as to the portion held by him, in full force and effect for an additional or quarternary [quaternary] term of five years and so long thereafter as any mineral or minerals in paying quantities be produced or mined from the leased land, by paying each year in advance of the lease anniversary date ten dollars ($10.00) per acre per year as rental, plus a sum as advance royalty computed as follows:

for the 11th year, ten dollars ($10.00) per acre per year;

for the 12th year, twenty dollars ($20.00) per acre per year;

for the 13th year, thirty dollars ($30.00) per acre per year;

for the 14th year, forty dollars ($40.00) per acre per year; and

for the 15th year, fifty dollars ($50.00) per acre per year. Provided, however, upon the commencing of the production of minerals in paying quantities, the principal sum so paid as advance royalty for the lease year in which the mineral is produced and the advance royalty paid for the two previous years shall be credited against the royalty payable hereunder to the lessor.