-- Like dupdouble, fib is another typical example that 
-- current method does not handle well.
-- The current method fails to construct a correct inverse for the function.

fib(Z) = S(Z)
fib(S(n)) = fib2(n)

fib2(Z) = S(S(Z))
fib2(S(m)) = add(fib(S(m)), fib(m))

add(Z,y) = y
add(S(x),y) = S(add(x,y))