# Can a context-senstive gramma contains production rule $cB\rightarrow Bc$?

Some textbook show that the grammar $$G=(N,T,P,S)$$ below belongs to context-senstive grammars:

1. S->aSBC
2. S->abc
3. cB->Bc
4. bG->bb

where N={S,B}, T={a,b,c}.

I am confused by the fact that the production rule cB->Bc cannot satisfy the definition of a CSG. So, why is the above grammar belongs to CSG?

Some definitions of a context-sensitive grammar only require that for any production rule of the form $$u \to v$$, the length of $$u$$ shall be less than or equal to the length of $$v$$. This seemingly weaker requirement is in fact weakly equivalent, see Noncontracting grammar#Transforming into context-sensitive grammar.