initHalf(Nil)       = Nil
initHalf(Cons(a,x)) = Cons(a,initHalfWork(x,x))

initHalfWork(xs, Nil)         = Nil
initHalfWork(xs, Cons(x,Nil)) = Nil
initHalfWork(Cons(a,x), Cons(b,Cons(c,y)))
    = Cons(a,initHalfWork(x,y))