Common wall

Being common wall your neighbour is well within his right to reconstruct his house, you cannot stop. However, find out amicable settlement roping in other neighbours/ elderly/ respectable persons of locality.

Don't take legal recourse. 

common wall cannot remain common for ever. If your neighbor desires to demolish and reconstruct your house, he has every rights to do so, since this common wall is an obstruction, he has given a prior notice to you to take care of your house if the demolition  of common wall will bring down your roof depending on it.  as advised by Dr. Vashista, better settle the scores amicably instead of taking a legal recourse which will remain a bitter experience and a permanent scar in the neighborhood relationship. Experience that counts and not ego.

Sir, you and your neighbour have equal right in the common wall (Based on your signed agreement saying that the wall is common to you both).

If your neighbour reconstruct his house and break the common wall, then you ask your neighbour for compensation of your half share only, by calculating the market value of the entire wall (in that you will get 1/2 amount).