
diff -r d9d2da923b7f -r 788f4aa28bc5 etnms/etnms.tex
--- a/etnms/etnms.tex	Thu Feb 06 10:49:23 2020 +0000
+++ b/etnms/etnms.tex	Sat Feb 08 21:34:50 2020 +0000
@@ -1376,10 +1376,42 @@
 
 \noindent
 $\rup\backslash_{simp} \, s$ is equal to 
-$ _1(_{11}a^* +  _0\ONE)  $
-$\rup\backslash_{simp} \, s \neq \simp(\rup\backslash s)$,
- whereas this does not happen for the old
+$ _1(_{011}a^* +  _1\ONE)  $ whereas
+$ \simp(\rup\backslash s) = (_{1011}a^* +  _{11}\ONE)$.
+This discrepancy does not appear for the old
 version of $\simp$.
+
+Why?
+
+During the first derivative operation, 
+\begin{center}
+$\rup\backslash a=(    _0[ \ONE\cdot {\bf b}] + _1( _0[ _1\ONE \cdot {\bf a}^*] + [ \ONE \cdot {\bf a}])      )$,
+\end{center}
+\noindent
+ the second derivative gives us
+ \begin{center}
+$\rup\backslash a=(_0( [\ZERO\cdot {\bf b}] + 0) + _1( _0( [\ZERO\cdot {\bf a}^*] + _1[ _1\ONE \cdot {\bf a}^*]) + _1( [\ZERO \cdot {\bf a}] + \ONE)  ))$,
+\end{center}
+
+\noindent
+and this simplifies to
+\begin{center}
+$ _1(_{011}{\bf a}^* +  _1\ONE)  $ 
+\end{center}
+
+If, after the first derivative we apply simplification we get
+$(_0{\bf b}  + _{101}{\bf  a}^* + _{11}{\bf a}  )$,
+and we do another derivative, getting
+$(\ZERO  + (_{101}(\ONE \cdot _1{\bf a}^*)+_{11}\ONE)$,
+which simplifies to 
+\begin{center}
+$ (_{1011}a^* +  _{11}\ONE)  $ 
+\end{center}
+
+
+
+
+
 We have changed the algorithm to suppress the old
 counterexample, but this gives rise to new counterexamples.
 This dilemma causes this amendment not a successful 




