Is $L = \{ W_1W_2 \mid W_1,W_2 \in (a+b)^* , N_a(W_1) = N_b(W_2)\}$ context free? Can we construct an NPDA for the language?

There is a book here that claims $L$ is not CF (without any elaboration), but I think we can construct a NPDA that accepts the language.

Is $L = \{ W_1W_2 \mid W_1,W_2 \in (a+b)^* , N_a(W_1) = N_b(W_2)\}$ context free? Can we construct an NPDA for the language?

There is a book here that claims $L$ is not CF (without any elaboration), but I think we can construct a NPDA that accepts the language. My guess is we can construct the language with an NPDA where after reading some $a$ and $b$ and pushing $A$ for each $a$ into the stack, makes a guess to jump to a new state and consumes the pushed $A$ with each $b$.

I have a simple question. A student in computer science asked me the question. This is not her homework (This is the starting semester point in our country!). If $W_1W_2 | W_1,W_2 \in (a+b)^* , N_a(W_1)=N_b(W_2)$ is context free? If NPDA can construct the language? There is a book here that claimed this is not CF (without any description :( ), but I think we can construct a NPDA to build the language.

Is $L = \{ W_1W_2 \mid W_1,W_2 \in (a+b)^* , N_a(W_1) = N_b(W_2)\}$ context free? Can we construct an NPDA for the language? 

There is a book here that claims $L$ is not CF (without any elaboration), but I think we can construct a NPDA that accepts the language.

I have a simple question. If $W_1W_2 | W_1,W_2 \in (a+b)^* , N_a(W_1)=N_b(W_2)$ is context free? If NPDA can construct the language?

I have a simple question. A student in computer science asked me the question. This is not her homework (This is the starting semester point in our country!). If $W_1W_2 | W_1,W_2 \in (a+b)^* , N_a(W_1)=N_b(W_2)$ is context free? If NPDA can construct the language? There is a book here that claimed this is not CF (without any description :( ), but I think we can construct a NPDA to build the language.