You should not have the <%= %> round Processing order as that is not ruby, so
<% if cart.processing == 'true'%>Processing order<% end %>
but possibly better
<%= "Processing order" if cart.processing == 'true' %>
That is assuming that cart.processing is a string not a boolean.
I suspect your original code would have shown an error in the console
and development.log, in which case it is always a good idea to post
the error when asking for help.
Also, why is cart.processing returning a string? (Or why are you testing the value is 'true'?) It would be more natural to have cart.processing? be truthy.