We cannot give a full solution to this exercise without knowing the actual way the pulleys, block A and wedge are connected and the angle of incline.

The important principles to solve this are :  the string may have probably (?) the same tension all along the length.  The tension will be related to the weight of the block A.    All parts of the string will have the same speed and magnitude of acceleration.   

As we look at the acceleration of the block A wrt  wedge B, we can add a pseudo force on the block in the left side direction.  OR, equivalently, add an acceleration of  "-a" towards left.

1) With respect to the wedge, the acceleration of block will be the resultant of its acceleration along the incline and that of "-a".
        If it happens that if Wedge moves by distance x, the block also moves x horizontally , then their relative acceleration is 0.

2) Wrt Earth, the acceleration could probably be that the block is moving towards right.  The normal reaction force from the wedge is to be considered.  If they are moving together due to the constraint of string, then the acceleration of the wedge will be that of the block wrt Earth.