Apply CYK algorithm to check whether word $01001011$ is generated by the following grammar or not. You need to show the detail of constructing table as each rows are filled as we did with another example in the class. Fill in the corresponding row in each table. Show your work in detail for each step.

S $$ AB $|$ BA

A $$ XC $|0$

B $$ XD$|1$

C $$ AX

D $$ BX

X $0|1$

Note: I understand up to Row $3,$ but Row $4$ and above are what's confusing me$.$

I understand that a substring can be split $($to have $2$ and $2,1$ and $3,$ & $3$ and $1).$

I may be incorrect but for Row $4$ Column $1,$ I got C and S as the non$-$terminals.