Chomsky or Greibach Normal Form? I tried to solve this exercise:

Discuss the normal forms (CNF or GNF) of a grammar with productions:

$S\rightarrow BC | CB$

$B\rightarrow cB | c$

$C\rightarrow cC | \epsilon$

Same request with the following grammar:

$S\rightarrow BC | CB$

$B\rightarrow cB | c$

$C\rightarrow cC | c$



I applied the rules to convert a grammar into its normal form and I think that both are CNFs. 

For the first grammar:

$S\rightarrow BC | CB|C'B|c$

$B\rightarrow C'B | c$

$C\rightarrow C'C | c$

$C'\rightarrow c$

For the second grammar:

$S\rightarrow BC | CB|TB|c$

$B\rightarrow TB | c$

$C\rightarrow TC | c$

$T\rightarrow c$

Is that correct?
A context-free grammar is in Chomsky normal form if all productions are of the form $A \to BC$ (where $B,C$ are not the starting symbol), $A \to a$, or $S \to \epsilon$, where $S$ is the starting symbol. A context-free grammar is in Greibach normal form if all productions are of the form $A \to a\alpha$, where $\alpha$ consists only of non-terminals (but not the starting symbol), or $S \to \epsilon$, where $S$ is the starting symbol.

Every context-free grammar has an equivalent context-free grammar in Chomsky normal form, and another one in Greibach normal form; there could be several equivalent context-free grammars in either normal form.

When you applied the rules to convert your grammars into normal form, you got Chomsky normal form because the rules were designed for converting a given context-free grammar to Chomsky normal form. You could follow other rules and get Greibach normal form.