Derive the state equation of the sequential circuit shown below: $*$

$A(t+1)=A^{\text{'}}{B}^{\text{'}}+A^{\text{'}}{x}^{\text{'}}+$ABx,$B(t+1)=B{x}^{\text{'}}+B^{\text{'}}x$

$A(t+1)=A{B}^{\text{'}}+A{x}^{\text{'}}+A^{\text{'}}Bx,B(t+1)=B{x}^{\text{'}}+B^{\text{'}}x$

$A(t+1)=A{B}^{\text{'}}+A{x}^{\text{'}},B(t+1)=B{x}^{\text{'}}+B^{\text{'}}x$