diff --git a/debugging_notes.txt b/debugging_notes.txt
index bc53307ad5b7296bc91988d88b4cb3dccd167b1a..89f22ad806355d1fa7da2c899e4b763a9d5c4ec9 100644
--- a/debugging_notes.txt
+++ b/debugging_notes.txt
@@ -5,7 +5,6 @@ Gurobi cannot express < , >  (strickly less than or strickly greater than)
 
 Current problem:
 
-
 >> the teacher is not deterministic(i.e., gurobi) and requires further
 constraint to make it determinic. ---> maybe not sure sure? 
 
@@ -50,7 +49,23 @@ in gurobi
 can you find a negative example(perceived state)
 in this shape?
 
-a negative example is a concrete state and perceived state si <var1,... ,var5>
-such that V(si) > V(sii) where sii is the next state after si.
+a negative example is a concrete state and perceived state (xi,zi) 
+such that V(xi) > V(f(xi, g(zi))) where f(xi, g(zi)) == xii which is the next state.
+xi and zi must be in current learn shape. 
+
+trans(xi, zi) check if in tree.
+
+
+
+xi=<var1, va2 ,v3>
+zi=<var4,var5>
+xii = f(xi, g(zi))
+
+
+check V(xi) <= V(xii)
+Equivalent to
+V(xi) <= V(f(xi, g(zi))
+and xi zi are in current learnt shape.
+