'Context-sensitive Grammar for a^nb^nc^n

Is the following CSG for a^nb^nc^n correct?

S->aSbC|abc
Cb->bC
C->c

If not please explain why?



Solution 1:[1]

Productions:
S -> abc | aAbc
Ab -> bA
Ac -> Bbcc
bB -> Bb
aB -> aa | aaA

Solution:

S ? aAbc
? abAc
? abBbcc
? aBbbcc
? aaAbbcc
? aabAbcc
? aabbAcc
? aabbBbccc
? aabBbbccc
? aaBbbbccc
? aaabbbccc

Sources

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Source: Stack Overflow

Solution Source
Solution 1 Parth Sarathi Pathak