breaking transitive dependencies in third normal form (case)

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Suppose we are second normal form with:

R(a,b,c,d,e)
FD: (a->bcde, c->de, d->e)

And we remove transitive dependencies:

R1(a,b,c)
R2(c,d,e)
R3(d,e)

Is this a correct decomposition?

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