Recall the simple statement grammar we discussed in class:

::=

::= |

::= if then | if then else

::= :=

::= = 0

::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

::= a | b | c | . . . | z

The above grammar has ambiguity for parsing the following compound statement:

if x = 0 then if y = 0 then z := 1 else z := 2

Is it possible to change the grammar without changing the language to parse the above statement unambiguously? If not, please give an infor- mal argument. If yes, please provide your solution. Note that you are not supposed to change the language by adding new terminals (tokens), i.e., de- limiters.