diff --git a/complexity b/complexity
index d6cec86..48fadab 100644
--- a/complexity
+++ b/complexity
@@ -15,6 +15,10 @@ Notation
 
    Single letters will be used to indicate relations and letters between
    | will indicate the cardinality (number of tuples) of the relation.
+   
+   Then after evaluating the big O notation, an attempt to find more
+   precise results will be done, since it will be important to know
+   with a certain precision the weight of the operation.
 
 1.  UNARY OPERATORS
 
@@ -41,8 +45,24 @@ Notation
    
    In the end we have O(|n|) as complexity for a selection on the
    relation n.
+   
+   The assumption made of considering constant the number of fields is
+   a bit strong. For example a relation could have hundreds of fields
+   and two tuples.
+   
+   So in general, the complexity is something more like O(|n| * f) where
+   f is the number of the fields.
 
 1.2  Rename
 
-xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-1.3  Projection
\ No newline at end of file
+   The rename operation itself is very simple, just modify the list
+   containing the name of the fields.
+   The big issue is to copy the content of the relation into a new
+   relation object, so the new one can be modified.
+   
+   So the operation depends on the size of the relation: O(|n| * f).
+   
+1.3  Projection
+
+
+xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
\ No newline at end of file