diff --git a/submission_thesis/CH6_Evaluation/Makefile b/submission_thesis/CH6_Evaluation/Makefile
index 5743eec..a1e839a 100644
--- a/submission_thesis/CH6_Evaluation/Makefile
+++ b/submission_thesis/CH6_Evaluation/Makefile
@@ -3,7 +3,7 @@
 #
 # Place all .dia files here as .png targets
 #
-DIA =
+DIA = components_81_euler.png
 
 
 doc: $(DIA)
diff --git a/submission_thesis/CH6_Evaluation/components_81_euler.dia b/submission_thesis/CH6_Evaluation/components_81_euler.dia
new file mode 100644
index 0000000..e8b7d98
Binary files /dev/null and b/submission_thesis/CH6_Evaluation/components_81_euler.dia differ
diff --git a/submission_thesis/CH6_Evaluation/copy.tex b/submission_thesis/CH6_Evaluation/copy.tex
index c1c8cca..c14b66d 100644
--- a/submission_thesis/CH6_Evaluation/copy.tex
+++ b/submission_thesis/CH6_Evaluation/copy.tex
@@ -123,11 +123,11 @@ The function $fm$ has a component as its domain and the components failure modes
 We can represent the number of potential failure modes of a component $c$, to be  $ | fm(c) | .$
 
 \paragraph{Indexing components with the group $G$.}
-If we index all the components in the system under investigation $ c_1, c_2 \ldots c_{|\FG|} $ we can express 
+If we index all the components in the system under investigation $ c_1, c_2 \ldots c_{|G|} $ we can express 
 the number of checks required to rigorously examine every
 failure mode against all the other components in the system.
 
-We can define this as a function, Comparison Complexity, can be represented by a function $CC$, with its domain as $G$, and
+Comparison Complexity can be represented by a function $CC$, with its domain as $G$, and
 its range as the number of checks---or reasoning stages---to perform to satisfy a rigorous FMEA inspection.
 
 Where $\mathcal{G}$ represents the set of all {\fgs}, and $ \mathbb{N} $ any natural integer, $CC$ is defined by,
@@ -174,10 +174,10 @@ to identify the hierarchy level.
 % \end{equation}
 \subsection{A general formula for counting Comparison Complexity in an FMMD hierarchy}
 
-An FMMD Hierarchy will have reducing numbers of functional groups as we progress up the hierarchy.
+An FMMD Hierarchy will have reducing numbers of {\fgs} as we progress up the hierarchy.
 In order to calculate its comparison~complexity we need to apply equation~\ref{eqn:CC} to
 all {\fgs} on each level.
-
+We can define an FMMD hierarchy as a set of {\fgs}, $H$.
 We define a helper function $g$ with a domain of the level $i$ in an FMMD hierarchy $H$, and a co-domain of a set of {\fgs} (specifically all the {\fgs} on the given level),
 defined by 
 
@@ -188,7 +188,7 @@ g(H, i) \rightarrow \forall {\FG}^{\xi} \;where\; ({\xi} = {i}) \wedge ({\FG}^{\
 \end{equation}
 
 Where $L$ represents the number of levels in the FMMD hierarchy,
-$|g(\xi)|$ represents the number of functional groups on the level
+$|g(\xi)|$ represents the number of {\fgs} on the level
 and $H$ represents an FMMD hierarchy,
 we overload the comparison complexity thus:
 %$$
@@ -202,10 +202,11 @@ we overload the comparison complexity thus:
 \pagebreak[4]
 \subsection{Complexity Comparison Examples}
 
-The potential divider discussed in section~\ref{potdivfmmd} has  four failure modes and two components and therefore has   $CC$ of 4.
+The potential divider discussed in section~\ref{subsec:potdiv} has  four failure modes and two components and therefore has   $CC$ of 4.
 $$CC(potdiv) = \sum_{n=1}^{2} |2|.(|1|) = 4 $$
 
-Even considering  a $example$ system with just 81 components (with these components
+%Even considering  a $example$ 
+A system, $example$, with just 81 components (with these components
 having 3 failure modes each) we would have an $CC$ of 
 
 $$CC(example) = \sum_{n=1}^{81} |3|.(|80|) = 19440 .$$
@@ -228,16 +229,23 @@ rigorous checking feasible.
 \pagebreak[4]
 %\subsection{Using the concept of Complexity Comparison to compare RFMEA with FMMD}
 
-\begin{figure}
+% \begin{figure}
+%  \centering
+%  \includegraphics[width=400pt,keepaspectratio=true]{CH5_Examples/three_tree.png}
+%  % three_tree.png: 851x385 pixel, 72dpi, 30.02x13.58 cm, bb=0 0 851 385
+%  \caption{FMMD Hierarchy with number of components in {\fg} fixed to 3 $(|G| = 3)$ } % \wedge (|fm(c)| = 3)$}
+%  \label{fig:three_tree}
+% \end{figure}
+
+\begin{figure}[h]
  \centering
- \includegraphics[width=400pt,keepaspectratio=true]{CH5_Examples/three_tree.png}
- % three_tree.png: 851x385 pixel, 72dpi, 30.02x13.58 cm, bb=0 0 851 385
- \caption{FMMD Hierarchy with number of components in {\fg} fixed to 3 $(|G| = 3)$ } % \wedge (|fm(c)| = 3)$}
+ \includegraphics[width=400pt]{./CH6_Evaluation/components_81_euler.png}
+ % components_81_euler.png: 3056x2532 pixel, 72dpi, 107.81x89.32 cm, bb=0 0 3056 2532
+ \caption{FMMD Hierarchy with number of compnents in each $FG$ fixed to three ($|FG|=3$)}
  \label{fig:three_tree}
 \end{figure}
 
 
-
 \subsection{Comparing FMMD and RFMEA comparison complexity}
 
 Because components have variable numbers of failure modes,