union X empty X union empty X X 0 z z and tt X X mult z X z mult 0 X Y 0 mult X Y mult 1 X Y plus 0 mult X Y Y plus z X X plus 0 X 0 Y 0 plus X Y plus 0 X 1 Y 1 plus X Y plus 1 X 1 Y 0 plus plus X Y 1 z prod empty 1 z prod singl X X prod union A B mult prod A prod B sum empty 0 z sum singl X X sum union A B plus sum A sum B plus union mult plus union mult 2.2 mult x y mult y x union x union y z union union x y z mult x mult y z mult mult x y z plus x y plus y x union x y union y x plus x plus y z plus plus x y z union x union y z union x y union x y union y x plus x y plus y x union x union y z union union x y z plus x plus y z plus x y mult x mult y z mult x y plus x plus y z plus plus x y z mult x y mult y x mult x mult y z mult mult x y z mult 0 X Y mult X Y plus 1 X 1 Y plus plus X Y 1 z prod union A B mult prod A prod B prod union A B prod B mult 1 X Y plus 0 mult X Y Y sum empty 0 z sum union A B plus sum A sum B plus 1 X 1 Y plus X Y prod union A B prod A plus 1 X 1 Y 0 plus plus X Y 1 z sum union A B sum B plus 0 X 1 Y plus X Y sum union A B sum A mult 1 X Y mult X Y plus 0 X 0 Y 0 plus X Y mult 0 X Y 0 mult X Y mult 1 X Y 0 mult X Y plus 0 X 0 Y plus X Y union union empty X _1 union X _1 mult mult 0 X Y _1 mult 0 mult X Y _1 plus plus 0 X 0 Y _1 plus 0 plus X Y _1 plus plus 1 X 1 Y _1 plus 0 plus plus X Y 1 z _1 mult mult 1 X Y _1 mult plus 0 mult X Y Y _1 plus plus 0 X 1 Y _1 plus 1 plus X Y _1 mult mult z X _1 mult z _1 union union X empty _1 union X _1 plus plus z X _1 plus X _1 union x union y z union union x y z union x y union y x union x union y z union x y true sum union A B sum A sum union A B sum B true 0 1 0 1 1 0 prod 1 0 z 0 0 prod 1 0 and 2 0 plus 2 0 sum 1 0 mult 2 0 0 1 0 union 2 1 2 1 singl 1 0 plus 2 0 empty 0 0 tt 0 0 sum 1 1 0 and 2 0 union 2 0 mult 2 0 sum union A B sum B sum union A B sum A sum empty 0 z false prod union A B prod B prod union A B prod A true 0 1 0 1 1 0 prod 1 0 z 0 0 prod 1 1 0 and 2 0 plus 2 0 sum 1 0 mult 2 0 0 1 0 union 2 1 2 1 singl 1 0 plus 2 0 empty 0 0 tt 0 0 sum 1 0 and 2 0 union 2 0 mult 2 0 prod union A B prod A prod union A B prod B prod union A B mult prod A prod B false mult x mult y z mult mult x y z mult x y mult y x mult 1 X Y mult X Y mult x mult y z mult x y mult 0 X Y mult X Y true 0 1 0 1 1 1 0 prod 1 0 z 0 0 prod 1 0 and 2 0 plus 2 0 sum 1 0 mult 2 1 2 39 0 1 1 0 union 2 0 singl 1 0 plus 2 1 0 2 0 0 empty 0 0 tt 0 0 sum 1 0 and 2 0 union 2 0 mult 2 1 2 0 mult x mult y z mult x y plus x plus y z plus plus x y z plus z X X 0 z z plus x y plus y x mult x mult y z mult mult x y z mult z X z plus 0 X 1 Y 1 plus X Y mult 1 X Y plus 0 mult X Y Y mult x y mult y x plus 1 X 1 Y 0 plus plus X Y 1 z plus 0 X 0 Y 0 plus X Y mult 0 X Y 0 mult X Y mult x mult y z mult mult x y z mult 1 X Y mult X Y mult x y mult y x mult 0 X Y mult X Y true Failed! NaTT certifiable-1.6