4 Fix the grammar for dangling if-then-else statement

Recall the simple statement grammar we discussed in class:

::=

::= | <>assgn>

::= if then | if then else

::= :=

::= = 0

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

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

The above grammar will cause 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 informal argument. If yes, please provide your solution. Note that you are not supposed to add new terminals (tokens), i.e., delimiters, as it will change the language.