That would depend upon exactly what it is you are trying to prove. I would be inclined to usetwoseparate inductions:

1) prove, by induction on y, that (x+ y)+ 1= x+ (y+ 1) for all x.

2) prove, by induction on z, that (x+ y)+ z= x+ (y+ z) for all x and z using (1) as your base case.