Problem with stems, voices, etc.

[Sami Amiris]

Please excuse anewbie question. This example is supposed to get me two distinct 
voices going from staff to staff on autopilot, when they pass by middle C. Here 
is the code:

\version "2.14.2"
\score
        {
        \new PianoStaff
        <<
                \new Staff = "up"{
                \clef treble
                \new Voice = "upper"{
                \autochange {
                \relative c'' %If this becomes c' or lower, everything ok.
                              %as it is, it puts everything in the voice of     
       
                              %"down".
                        {
                        \stemUp{        
                        \bar "|:" bes4 c bes' c \bar ":|" d1 \bar "|."
                }}}}}
                                
                \new Staff = "down"{
                \clef bass
                \new Voice = "lower"{
                \autochange {
                \relative c' %this is of no consequence, really
                        {
                        \stemDown{      
                         bes4 c bes' c | d1 
                }}}}}
        >>
        }

If that "relative c''" was "relative c'" on "up", then everything would be 
fine. 
But as soon as the "up" staff goes relative to c'' or higher, the two voices 
coalesce into the voice of the "down" part. It is as if I wrote just one voice 
with octaves! Try the example, and then change " relative c'' " to " relative 
c' 
" in "up" and " relative c' " to " relative c " in "down", and you'll see how I 
would like it to be. Any ideas?