A Type II CRISPR-Cas9-associated split-nexus polynucleotide composition comprising: a first Type II CRISPR-Cas9-associated split-nexus polynucleotide comprising a 5' end and a 3' end (sn1-casPN) comprising, in the 5' to 3' direction, a nucleic acid target binding sequence, a first stem element nucleotide sequence II, a loop element nucleotide sequence, a first stem element nucleotide sequence I and a nexus stem element nucleotide sequence I, wherein the first stem element nucleotide sequence I and the first stem element nucleotide sequence II are capable of forming a first stem element by base-pair hydrogen bonding between the first stem element nucleotide sequence I and the first stem element nucleotide sequence II; and a second Type II CRISPR-Cas9-associated split-nexus polynucleotide comprising a 5' end and a 3' end (sn2-casPN) comprising, in the 5' to 3' direction, a nexus stem element nucleotide sequence II, wherein the nexus stem element nucleotide sequence I of the sn1-casPN and the nexus stem element nucleotide sequence II of the sn2-casPN are capable of forming a nexus stem element by base-pair hydrogen bonding between the nexus stem element nucleotide sequence I and the nexus stem element nucleotide sequence II, optionally wherein the first stem element nucleotide sequence I further comprises, in the 5' to 3' direction, an upper stem element nucleotide sequence I, a bulge element nucleotide sequence I, and a lower stem element nucleotide sequence I, and the first stem element nucleotide sequence II further comprises, in the 5' to 3' direction, a lower stem element nucleotide sequence II, a bulge element nucleotide sequence II, and an upper stem element nucleotide sequence II, wherein the upper stem element nucleotide sequence I and the upper stem element nucleotide sequence II are capable of forming an upper stem element by base-pair hydrogen bonding between the upper stem element nucleotide sequence I and the upper stem element nucleotide sequence II, and the lower stem element nucleotide sequence I and the lower stem element nucleotide sequence II are capable of forming a lower stem element by base-pair hydrogen bonding between the lower stem element nucleotide sequence I and the lower stem element nucleotide sequence II. a first Type II CRISPR-Cas9-associated split-nexus polynucleotide comprising a 5' end and a 3' end (sn1-casPN) comprising, in the 5' to 3' direction, a nucleic acid target binding sequence, a first stem element nucleotide sequence II, a loop element nucleotide sequence, a first stem element nucleotide sequence I and a nexus stem element nucleotide sequence I, wherein the first stem element nucleotide sequence I and the first stem element nucleotide sequence II are capable of forming a first stem element by base-pair hydrogen bonding between the first stem element nucleotide sequence I and the first stem element nucleotide sequence II; and a second Type II CRISPR-Cas9-associated split-nexus polynucleotide comprising a 5' end and a 3' end (sn2-casPN) comprising, in the 5' to 3' direction, a nexus stem element nucleotide sequence II, wherein the nexus stem element nucleotide sequence I of the sn1-casPN and the nexus stem element nucleotide sequence II of the sn2-casPN are capable of forming a nexus stem element by base-pair hydrogen bonding between the nexus stem element nucleotide sequence I and the nexus stem element nucleotide sequence II, optionally wherein the first stem element nucleotide sequence I further comprises, in the 5' to 3' direction, an upper stem element nucleotide sequence I, a bulge element nucleotide sequence I, and a lower stem element nucleotide sequence I, and the first stem element nucleotide sequence II further comprises, in the 5' to 3' direction, a lower stem element nucleotide sequence II, a bulge element nucleotide sequence II, and an upper stem element nucleotide sequence II, wherein the upper stem element nucleotide sequence I and the upper stem element nucleotide sequence II are capable of forming an upper stem element by base-pair hydrogen bonding between the upper stem element nucleotide sequence I and the upper stem element nucleotide sequence II, and the lower stem element nucleotide sequence I and the lower stem element nucleotide sequence II are capable of forming a lower stem element by base-pair hydrogen bonding between the lower stem element nucleotide sequence I and the lower stem element nucleotide sequence II.