Solution of one system of equations in boolean variables having style like x1 => x2 => … =>x6=1 && y1 => y2 => … =>y6 =1 && x1 => y1 via Mapping method

Original system looks like :-
x1 => x2 => x3 => x4 => x5 => x6 =1
y1 => y2 => y3 => y4 => y5 => y6 =1
x1 => y1 =1

Down here we follow approach originally developed in
http://www.loiro.ru/files/news/news_943_etodotobrajeniya-mea-2013-10.pdf
Build basic diagram and define function F( ) to apply Mapping method
suggested  by E. Mironchick

Now calculate number of solutions of equation
x1 => x2 => x2 => x3 => x4 => x5 => x6 =1 starting with x1=1

Calculate  number of solutions of equation
y1 => y2 => y3 => y4 => y5 => y6 =1  starting with y1=0

So, we intend to calculate number  of {x},{y} corteges breaking
third equation and afterwards deduct amount, been obtained,  from 43^2

Keeping in mind

Thus final answer is : – Count = 43^2 – 21*22 = 1387