select count(*)
  from theTable A
  inner join theTable B
 where (A.col_1 = x and B.col_1 = y and A.col_2 = B.col_2);

should become

SELECT COUNT(*)
  FROM theTable A JOIN theTable B ON (A.col_2 = B.col_2)
 WHERE A.col_1 = x
   AND B.col_1 = y