# Find equivalent LL(1) grammar

There is sample question to calculate equivalent LL(1) grammar for below grammar:

$$S \rightarrow S b$$

$$S \rightarrow S d$$

$$S \rightarrow c S$$

$$S \rightarrow c c a$$

At first step, it has left recursion so I remove it and convert it to bellow grammar:

$$S \rightarrow F M$$

$$F \rightarrow c S$$ (same as $$F \rightarrow c F M$$)

$$F \rightarrow c c a$$

$$M \rightarrow \epsilon$$

$$M \rightarrow b M$$

$$M \rightarrow d M$$

We can remove first collision of second and third part too:

$$S \rightarrow F M$$

$$F \rightarrow c D$$

$$D \rightarrow F M$$ (same as $$D \rightarrow c D M$$)

$$D \rightarrow c a$$

$$M \rightarrow \epsilon$$

$$M \rightarrow b M$$

$$M \rightarrow d M$$

One more time remove first collision:

$$S \rightarrow F M$$ (predict: c)

$$F \rightarrow c D$$ (predict: c)

$$D \rightarrow c G$$ (predict: c)

$$G \rightarrow D M$$ (predict: c)

$$G \rightarrow a$$ (predict: a)

$$M \rightarrow \epsilon$$ (predict: b, d, \$ )

$$M \rightarrow b M$$ (predict: b)

$$M \rightarrow d M$$ (predict: d)

Everything is solved except last part of grammar. I tried to solve it but I think there is no LL(1) grammar for this. Is it true? If not, Is it possible to help me? Thanks.