$(25pts)$ For two RNA strings $s_1{s}_{2}dots{s}_m$ and $t_1{t}_2$dots.$t_n,$ two inter$-$RNA base pairs $(s_i,t_j)$ and $(s_k,t_l)$ are called crossing if $(1)j>li>k(A,U),(U,A),(G,U),(U,G),(G,C)j.$ Devise $an$ algorithm $to$ compute the maximal number $of$ non$-$crossing inter$-$RNA base pairs between two RNA strings $(25pts).$

Note that $An$ RNA string $is$ a string that represents the order $of$ nucleobases along a strand $of$ RNA. For this reason, RNA strings are constructed from the alphabet $\{A,C,G,U\},$ whose symbols represent the bases adenine, cytosine, guanine, and uracil. For example, "AAGAUGCCGU" $isan$ RNA string $of$ length $10.$ RNA bases can pair with each other $to$ form a base pairs: $(A,U),(U,A),(G,U),(U,G),(G,C),or(C,G).$ Each RNA base cannot pair more than once.

For this problem, there $isno$ intra$-$RNA base pairs. Note that the trace$-$back $is$ not needed for this problem. Please write down the recursive functions and describe the notations you use.i and $j>l$; $or(2)i>k$ and $j.$ Devise $an$ algorithm $to$ compute the maximal number $of$ non$-$crossing inter$-$RNA base pairs between two RNA strings $(25pts).$

Note that $An$ RNA string $is$ a string that represents the order $of$ nucleobases along a strand $of$ RNA. For this reason, RNA strings are constructed from the alphabet $\{A,C,G,U\},$ whose symbols represent the bases adenine, cytosine, guanine, and uracil. For example, "AAGAUGCCGU" $isan$ RNA string $of$ length $10.$ RNA bases can pair with each other $to$ form a base pairs: $(A,U),(U,A),(G,U),(U,G),(G,C),or(C,G).$ Each RNA base cannot pair more than once.

For this problem, there $isno$ intra$-$RNA base pairs. Note that the trace$-$back $is$ not needed for this problem. Please write down the recursive functions and describe the notations you use.