diff --git a/ReversalModel/make_plots.py b/ReversalModel/make_plots.py
index beaa7ba..6ccbec3 100755
--- a/ReversalModel/make_plots.py
+++ b/ReversalModel/make_plots.py
@@ -35,8 +35,10 @@ del df_timeout['cpu']
 def timeout_by(name: str) -> pd.DataFrame:
     df_return = df_timeout.loc[:, [name, 'timeout']] \
         .groupby(name) \
-        .sum() \
+        .mean() \
         .reset_index()
+
+    df_return['timeout'] = df_return['timeout'] * 100
     df_return[name] = df_return[name].astype(str)
     return df_return
 
diff --git a/bibliography.bib b/bibliography.bib
new file mode 100644
index 0000000..6cfe1a7
--- /dev/null
+++ b/bibliography.bib
@@ -0,0 +1,27 @@
+@software{tange_2023_7855617,
+  author       = {Tange, Ole},
+  title        = {GNU Parallel 20230422 ('Grand Jury')},
+  month        = Apr,
+  year         = 2023,
+  note         = {{GNU Parallel is a general parallelizer to run
+    multiple serial command line programs in parallel
+      without changing them.}},
+  publisher    = {Zenodo},
+  doi          = {10.5281/zenodo.7855617},
+  url          = {https://doi.org/10.5281/zenodo.7855617}
+}
+@software{m4,
+  author = {{Free Software Foundation}},
+  title = {GNU M4 - GNU macro processor},
+  url = {https://www.gnu.org/software/m4/manual/index.html},
+  version = {1.4.6},
+  date = {2021-05-29},
+}
+@software{spin,
+  author = {{Gerard J. Holzmann}},
+  title = {Spin model checker},
+  url = {https://spinroot.com/spin/whatispin.html},
+  version = {6.5.2},
+  date = {2019-12-06},
+}
+
diff --git a/build.sh b/build.sh
new file mode 100755
index 0000000..d57b41e
--- /dev/null
+++ b/build.sh
@@ -0,0 +1,11 @@
+#!/bin/bash
+
+set -e
+
+SCRIPT_DIR=$(cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd)
+
+cd "$SCRIPT_DIR"
+
+pdflatex --shell-escape report
+biber report
+pdflatex --shell-escape report
diff --git a/plots/length.pgf b/plots/length.pgf
index 9d83341..70cad71 100644
--- a/plots/length.pgf
+++ b/plots/length.pgf
@@ -475,323 +475,323 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000470in}{3.307922in}%
+\pgfsys@transformshift{1.000470in}{3.317255in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000564in}{3.290417in}%
+\pgfsys@transformshift{1.000564in}{3.360704in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000564in}{3.320961in}%
+\pgfsys@transformshift{1.000564in}{3.333775in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000752in}{3.354562in}%
+\pgfsys@transformshift{1.000752in}{3.356616in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000752in}{3.363893in}%
+\pgfsys@transformshift{1.000752in}{3.317596in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000845in}{3.322967in}%
+\pgfsys@transformshift{1.000845in}{3.332231in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001127in}{3.348219in}%
+\pgfsys@transformshift{1.001127in}{3.318300in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001033in}{3.364783in}%
+\pgfsys@transformshift{1.001033in}{3.300866in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001221in}{3.353524in}%
+\pgfsys@transformshift{1.001221in}{3.319815in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001409in}{3.343237in}%
+\pgfsys@transformshift{1.001409in}{3.345909in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001879in}{3.329608in}%
+\pgfsys@transformshift{1.001879in}{3.344235in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002161in}{3.343058in}%
+\pgfsys@transformshift{1.002161in}{3.342595in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002724in}{3.335763in}%
+\pgfsys@transformshift{1.002724in}{3.310107in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.003570in}{3.346129in}%
+\pgfsys@transformshift{1.003570in}{3.325463in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001033in}{3.330872in}%
+\pgfsys@transformshift{1.001033in}{3.363335in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001409in}{3.297851in}%
+\pgfsys@transformshift{1.001409in}{3.362228in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001409in}{3.356661in}%
+\pgfsys@transformshift{1.001409in}{3.347798in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001973in}{3.322464in}%
+\pgfsys@transformshift{1.001973in}{3.329999in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002724in}{3.350803in}%
+\pgfsys@transformshift{1.002724in}{3.290574in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004039in}{3.314956in}%
+\pgfsys@transformshift{1.004039in}{3.297620in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004415in}{3.293000in}%
+\pgfsys@transformshift{1.004415in}{3.321152in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001315in}{3.296758in}%
+\pgfsys@transformshift{1.001315in}{3.360282in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001879in}{3.290717in}%
+\pgfsys@transformshift{1.001879in}{3.338664in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002630in}{3.294034in}%
+\pgfsys@transformshift{1.002630in}{3.292493in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.003664in}{3.323408in}%
+\pgfsys@transformshift{1.003664in}{3.322294in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004603in}{3.316086in}%
+\pgfsys@transformshift{1.004603in}{3.318138in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.006200in}{3.300924in}%
+\pgfsys@transformshift{1.006200in}{3.296194in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.009488in}{3.359245in}%
+\pgfsys@transformshift{1.009488in}{3.357903in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001785in}{3.315733in}%
+\pgfsys@transformshift{1.001785in}{3.319435in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002912in}{3.345423in}%
+\pgfsys@transformshift{1.002912in}{3.333930in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004415in}{3.299198in}%
+\pgfsys@transformshift{1.004415in}{3.354814in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.007421in}{3.363272in}%
+\pgfsys@transformshift{1.007421in}{3.298735in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.011930in}{3.365878in}%
+\pgfsys@transformshift{1.011930in}{3.332197in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.016158in}{3.305151in}%
+\pgfsys@transformshift{1.016158in}{3.362213in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.022452in}{3.304953in}%
+\pgfsys@transformshift{1.022452in}{3.309512in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002630in}{3.319410in}%
+\pgfsys@transformshift{1.002630in}{3.355066in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.005355in}{3.300710in}%
+\pgfsys@transformshift{1.005355in}{3.345042in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.009488in}{3.328723in}%
+\pgfsys@transformshift{1.009488in}{3.328897in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.015782in}{3.299176in}%
+\pgfsys@transformshift{1.015782in}{3.361006in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.023955in}{3.309205in}%
+\pgfsys@transformshift{1.023955in}{3.350265in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.036730in}{3.308088in}%
+\pgfsys@transformshift{1.036730in}{3.358790in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.055048in}{3.365288in}%
+\pgfsys@transformshift{1.055048in}{3.332340in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004885in}{3.355980in}%
+\pgfsys@transformshift{1.004885in}{3.352516in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.011179in}{3.341564in}%
+\pgfsys@transformshift{1.011179in}{3.308220in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.019539in}{3.289209in}%
+\pgfsys@transformshift{1.019539in}{3.289338in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.034664in}{3.312754in}%
+\pgfsys@transformshift{1.034664in}{3.304672in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.056833in}{3.357412in}%
+\pgfsys@transformshift{1.056833in}{3.332391in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.093939in}{3.291394in}%
+\pgfsys@transformshift{1.093939in}{3.321627in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.154530in}{3.324549in}%
+\pgfsys@transformshift{1.154530in}{3.362772in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001221in}{3.304888in}%
+\pgfsys@transformshift{1.001221in}{3.350460in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001691in}{3.345124in}%
+\pgfsys@transformshift{1.001691in}{3.298798in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.003382in}{3.345913in}%
+\pgfsys@transformshift{1.003382in}{3.301564in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004039in}{3.352908in}%
+\pgfsys@transformshift{1.004039in}{3.298673in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.005261in}{3.337705in}%
+\pgfsys@transformshift{1.005261in}{3.358107in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.006858in}{3.292002in}%
+\pgfsys@transformshift{1.006858in}{3.361473in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.010615in}{3.326905in}%
+\pgfsys@transformshift{1.010615in}{3.341180in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.014467in}{3.347511in}%
+\pgfsys@transformshift{1.014467in}{3.334343in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.022639in}{3.333674in}%
+\pgfsys@transformshift{1.022639in}{3.307109in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.031282in}{3.320954in}%
+\pgfsys@transformshift{1.031282in}{3.295386in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.058148in}{3.318199in}%
+\pgfsys@transformshift{1.058148in}{3.313275in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.081164in}{3.333917in}%
+\pgfsys@transformshift{1.081164in}{3.352141in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.167118in}{3.323102in}%
+\pgfsys@transformshift{1.167118in}{3.362184in}%
 \pgfsys@useobject{currentmarker}{}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.247155in}{3.363531in}%
+\pgfsys@transformshift{1.247155in}{3.289417in}%
 \pgfsys@useobject{currentmarker}{}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.006952in}{3.359145in}%
+\pgfsys@transformshift{1.006952in}{3.295050in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.016064in}{3.304517in}%
+\pgfsys@transformshift{1.016064in}{3.343432in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.030342in}{3.302167in}%
+\pgfsys@transformshift{1.030342in}{3.318276in}%
 \pgfsys@useobject{currentmarker}{}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.052606in}{3.356712in}%
+\pgfsys@transformshift{1.052606in}{3.299740in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.083324in}{3.354225in}%
+\pgfsys@transformshift{1.083324in}{3.295644in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.124470in}{3.350413in}%
+\pgfsys@transformshift{1.124470in}{3.346282in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.178391in}{3.356175in}%
+\pgfsys@transformshift{1.178391in}{3.310952in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.245933in}{3.337380in}%
+\pgfsys@transformshift{1.245933in}{3.340419in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.342879in}{3.347109in}%
+\pgfsys@transformshift{1.342879in}{3.324498in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.022639in}{3.291740in}%
+\pgfsys@transformshift{1.022639in}{3.341398in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.045748in}{3.323964in}%
+\pgfsys@transformshift{1.045748in}{3.316048in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.086518in}{3.364068in}%
+\pgfsys@transformshift{1.086518in}{3.340525in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.148894in}{3.363809in}%
+\pgfsys@transformshift{1.148894in}{3.289974in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.277779in}{3.318591in}%
+\pgfsys@transformshift{1.277779in}{3.338862in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.526906in}{3.327263in}%
+\pgfsys@transformshift{1.526906in}{3.305181in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.891203in}{3.318465in}%
+\pgfsys@transformshift{1.891203in}{3.346951in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.575176in}{3.341913in}%
+\pgfsys@transformshift{2.575176in}{3.321122in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -821,263 +821,263 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000564in}{2.965311in}%
+\pgfsys@transformshift{1.000564in}{2.977867in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000752in}{2.913594in}%
+\pgfsys@transformshift{1.000752in}{2.973477in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001221in}{2.922659in}%
+\pgfsys@transformshift{1.001221in}{2.924421in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001879in}{2.907032in}%
+\pgfsys@transformshift{1.001879in}{2.980666in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002912in}{2.976936in}%
+\pgfsys@transformshift{1.002912in}{2.977025in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004885in}{2.973425in}%
+\pgfsys@transformshift{1.004885in}{2.956676in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.007139in}{2.946743in}%
+\pgfsys@transformshift{1.007139in}{2.933356in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001409in}{2.954902in}%
+\pgfsys@transformshift{1.001409in}{2.933434in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002255in}{2.933792in}%
+\pgfsys@transformshift{1.002255in}{2.936017in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.003852in}{2.933626in}%
+\pgfsys@transformshift{1.003852in}{2.979384in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.006952in}{2.921986in}%
+\pgfsys@transformshift{1.006952in}{2.922470in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.013621in}{2.934328in}%
+\pgfsys@transformshift{1.013621in}{2.952004in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.022733in}{2.977550in}%
+\pgfsys@transformshift{1.022733in}{2.979315in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
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 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.043306in}{2.192993in}%
+\pgfsys@transformshift{1.043306in}{2.150229in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.399900in}{2.142798in}%
+\pgfsys@transformshift{1.399900in}{2.206838in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.162327in}{2.207293in}%
+\pgfsys@transformshift{1.162327in}{2.166882in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.080036in}{2.141768in}%
+\pgfsys@transformshift{1.080036in}{2.183312in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.578573in}{2.172591in}%
+\pgfsys@transformshift{1.578573in}{2.194766in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.204694in}{2.159698in}%
+\pgfsys@transformshift{1.204694in}{2.147365in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.646773in}{2.199131in}%
+\pgfsys@transformshift{1.646773in}{2.145940in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1395,43 +1395,43 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.005261in}{1.769475in}%
+\pgfsys@transformshift{1.005261in}{1.807681in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.046782in}{1.815361in}%
+\pgfsys@transformshift{1.046782in}{1.751482in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.232594in}{1.768197in}%
+\pgfsys@transformshift{1.232594in}{1.757885in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.948600in}{1.806131in}%
+\pgfsys@transformshift{1.948600in}{1.787280in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.019445in}{1.794169in}%
+\pgfsys@transformshift{1.019445in}{1.761426in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.154530in}{1.804808in}%
+\pgfsys@transformshift{1.154530in}{1.751623in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.055424in}{1.773466in}%
+\pgfsys@transformshift{1.055424in}{1.754709in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.376964in}{1.817546in}%
+\pgfsys@transformshift{2.376964in}{1.809006in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.296191in}{1.821988in}%
+\pgfsys@transformshift{1.296191in}{1.785482in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.835294in}{1.768268in}%
+\pgfsys@transformshift{2.835294in}{1.778731in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1461,19 +1461,19 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.017473in}{1.418972in}%
+\pgfsys@transformshift{1.017473in}{1.380840in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.182055in}{1.414837in}%
+\pgfsys@transformshift{1.182055in}{1.400466in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.072239in}{1.406898in}%
+\pgfsys@transformshift{1.072239in}{1.438304in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.560161in}{1.411230in}%
+\pgfsys@transformshift{1.560161in}{1.410650in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1503,11 +1503,11 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.069609in}{1.001152in}%
+\pgfsys@transformshift{1.069609in}{0.997294in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.429585in}{0.999731in}%
+\pgfsys@transformshift{1.429585in}{1.038497in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1572,8 +1572,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{3.471875in}}%
-\pgfpathlineto{\pgfqpoint{4.410000in}{3.471875in}}%
-\pgfpathlineto{\pgfqpoint{4.410000in}{3.183125in}}%
+\pgfpathlineto{\pgfqpoint{4.416611in}{3.471875in}}%
+\pgfpathlineto{\pgfqpoint{4.416611in}{3.183125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{3.183125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{3.471875in}}%
 \pgfpathclose%
@@ -1592,8 +1592,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{3.086875in}}%
-\pgfpathlineto{\pgfqpoint{4.832727in}{3.086875in}}%
-\pgfpathlineto{\pgfqpoint{4.832727in}{2.798125in}}%
+\pgfpathlineto{\pgfqpoint{4.938496in}{3.086875in}}%
+\pgfpathlineto{\pgfqpoint{4.938496in}{2.798125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.798125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{3.086875in}}%
 \pgfpathclose%
@@ -1612,8 +1612,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{2.701875in}}%
-\pgfpathlineto{\pgfqpoint{5.593636in}{2.701875in}}%
-\pgfpathlineto{\pgfqpoint{5.593636in}{2.413125in}}%
+\pgfpathlineto{\pgfqpoint{5.877890in}{2.701875in}}%
+\pgfpathlineto{\pgfqpoint{5.877890in}{2.413125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.413125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.701875in}}%
 \pgfpathclose%
@@ -1632,8 +1632,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{2.316875in}}%
-\pgfpathlineto{\pgfqpoint{6.072727in}{2.316875in}}%
-\pgfpathlineto{\pgfqpoint{6.072727in}{2.028125in}}%
+\pgfpathlineto{\pgfqpoint{6.469360in}{2.316875in}}%
+\pgfpathlineto{\pgfqpoint{6.469360in}{2.028125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.028125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.316875in}}%
 \pgfpathclose%
@@ -1652,8 +1652,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{1.931875in}}%
-\pgfpathlineto{\pgfqpoint{6.382727in}{1.931875in}}%
-\pgfpathlineto{\pgfqpoint{6.382727in}{1.643125in}}%
+\pgfpathlineto{\pgfqpoint{6.852076in}{1.931875in}}%
+\pgfpathlineto{\pgfqpoint{6.852076in}{1.643125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.643125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.931875in}}%
 \pgfpathclose%
@@ -1672,8 +1672,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{1.546875in}}%
-\pgfpathlineto{\pgfqpoint{6.551818in}{1.546875in}}%
-\pgfpathlineto{\pgfqpoint{6.551818in}{1.258125in}}%
+\pgfpathlineto{\pgfqpoint{7.060831in}{1.546875in}}%
+\pgfpathlineto{\pgfqpoint{7.060831in}{1.258125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.258125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.546875in}}%
 \pgfpathclose%
@@ -1692,8 +1692,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{1.161875in}}%
-\pgfpathlineto{\pgfqpoint{6.608182in}{1.161875in}}%
-\pgfpathlineto{\pgfqpoint{6.608182in}{0.873125in}}%
+\pgfpathlineto{\pgfqpoint{7.130415in}{1.161875in}}%
+\pgfpathlineto{\pgfqpoint{7.130415in}{0.873125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{0.873125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.161875in}}%
 \pgfpathclose%
@@ -1712,8 +1712,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{0.776875in}}%
-\pgfpathlineto{\pgfqpoint{6.636364in}{0.776875in}}%
-\pgfpathlineto{\pgfqpoint{6.636364in}{0.488125in}}%
+\pgfpathlineto{\pgfqpoint{7.165208in}{0.776875in}}%
+\pgfpathlineto{\pgfqpoint{7.165208in}{0.488125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{0.488125in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{0.776875in}}%
 \pgfpathclose%
diff --git a/plots/n.pgf b/plots/n.pgf
index 488b426..9d73872 100644
--- a/plots/n.pgf
+++ b/plots/n.pgf
@@ -500,171 +500,171 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000470in}{3.366199in}%
+\pgfsys@transformshift{1.000470in}{3.376768in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000564in}{3.317706in}%
+\pgfsys@transformshift{1.000564in}{3.375998in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000564in}{3.336226in}%
+\pgfsys@transformshift{1.000564in}{3.378878in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000752in}{3.327328in}%
+\pgfsys@transformshift{1.000752in}{3.314960in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000752in}{3.336432in}%
+\pgfsys@transformshift{1.000752in}{3.366983in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000845in}{3.356652in}%
+\pgfsys@transformshift{1.000845in}{3.357611in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001127in}{3.371855in}%
+\pgfsys@transformshift{1.001127in}{3.356896in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000564in}{3.335357in}%
+\pgfsys@transformshift{1.000564in}{3.318451in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000752in}{3.376057in}%
+\pgfsys@transformshift{1.000752in}{3.331133in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001221in}{3.315733in}%
+\pgfsys@transformshift{1.001221in}{3.355854in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001879in}{3.351777in}%
+\pgfsys@transformshift{1.001879in}{3.335307in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002912in}{3.368038in}%
+\pgfsys@transformshift{1.002912in}{3.373598in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.004885in}{3.344332in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.007139in}{3.355579in}%
+\pgfsys@transformshift{1.007139in}{3.332472in}%
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 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000845in}{3.370859in}%
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 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004603in}{3.378073in}%
+\pgfsys@transformshift{1.004603in}{3.328812in}%
 \pgfsys@useobject{currentmarker}{}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.010803in}{3.341200in}%
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 \begin{pgfscope}%
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 \begin{pgfscope}%
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 \begin{pgfscope}%
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 \begin{pgfscope}%
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 \begin{pgfscope}%
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 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.017191in}{3.314824in}%
+\pgfsys@transformshift{1.017191in}{3.331410in}%
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 \begin{pgfscope}%
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+\pgfsys@transformshift{1.157067in}{3.379046in}%
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 \end{pgfscope}%
 \begin{pgfscope}%
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+\pgfsys@transformshift{1.276464in}{3.329470in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.069609in}{3.371526in}%
+\pgfsys@transformshift{1.069609in}{3.323463in}%
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 \end{pgfscope}%
 \begin{pgfscope}%
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+\pgfsys@transformshift{1.288770in}{3.364637in}%
 \pgfsys@useobject{currentmarker}{}%
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@@ -694,135 +694,135 @@
 \pgfusepath{fill}%
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 \begin{pgfscope}%
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 \begin{pgfscope}%
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 \begin{pgfscope}%
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+\pgfsys@transformshift{1.019445in}{3.026472in}%
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+\pgfsys@transformshift{1.154530in}{3.037958in}%
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+\pgfsys@transformshift{1.429585in}{3.022636in}%
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@@ -852,119 +852,119 @@
 \pgfusepath{fill}%
 }%
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-\pgfsys@transformshift{1.001033in}{2.682008in}%
+\pgfsys@transformshift{1.001033in}{2.654535in}%
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+\pgfsys@transformshift{1.001409in}{2.656830in}%
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+\pgfsys@transformshift{1.001973in}{2.661470in}%
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@@ -994,103 +994,103 @@
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@@ -1120,95 +1120,95 @@
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@@ -1238,87 +1238,87 @@
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 \begin{pgfscope}%
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+\pgfsys@transformshift{1.023955in}{1.661666in}%
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 \end{pgfscope}%
 \begin{pgfscope}%
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 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.055048in}{1.612756in}%
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 \begin{pgfscope}%
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 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.023391in}{1.622805in}%
+\pgfsys@transformshift{1.023391in}{1.636670in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.061530in}{1.650857in}%
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 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.153309in}{1.652008in}%
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 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.444052in}{1.641596in}%
+\pgfsys@transformshift{1.444052in}{1.614311in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.264330in}{1.614844in}%
+\pgfsys@transformshift{2.264330in}{1.628650in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.520691in}{1.643074in}%
+\pgfsys@transformshift{2.520691in}{1.668385in}%
 \pgfsys@useobject{currentmarker}{}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.026397in}{1.641598in}%
+\pgfsys@transformshift{1.026397in}{1.651292in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.137715in}{1.610510in}%
+\pgfsys@transformshift{1.137715in}{1.603945in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.310658in}{1.664231in}%
+\pgfsys@transformshift{1.310658in}{1.671492in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.080036in}{1.618130in}%
+\pgfsys@transformshift{1.080036in}{1.612802in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.578573in}{1.656587in}%
+\pgfsys@transformshift{1.578573in}{1.622854in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.058148in}{1.668178in}%
+\pgfsys@transformshift{1.058148in}{1.669001in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.081164in}{1.662267in}%
+\pgfsys@transformshift{1.081164in}{1.645700in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1348,83 +1348,83 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.004885in}{1.325718in}%
+\pgfsys@transformshift{1.004885in}{1.305690in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.011179in}{1.263832in}%
+\pgfsys@transformshift{1.011179in}{1.306798in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.019539in}{1.302872in}%
+\pgfsys@transformshift{1.019539in}{1.324977in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.034664in}{1.302774in}%
+\pgfsys@transformshift{1.034664in}{1.322752in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.056833in}{1.315591in}%
+\pgfsys@transformshift{1.056833in}{1.281311in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.093939in}{1.302726in}%
+\pgfsys@transformshift{1.093939in}{1.271371in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.154530in}{1.288222in}%
+\pgfsys@transformshift{1.154530in}{1.292748in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.015218in}{1.313040in}%
+\pgfsys@transformshift{1.015218in}{1.265008in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.054955in}{1.319289in}%
+\pgfsys@transformshift{1.054955in}{1.308625in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.182148in}{1.307968in}%
+\pgfsys@transformshift{1.182148in}{1.305143in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.635688in}{1.297849in}%
+\pgfsys@transformshift{1.635688in}{1.277784in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.167118in}{1.271259in}%
+\pgfsys@transformshift{1.167118in}{1.276754in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.247155in}{1.297241in}%
+\pgfsys@transformshift{1.247155in}{1.283319in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.733573in}{1.315594in}%
+\pgfsys@transformshift{1.733573in}{1.323905in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{3.181085in}{1.329330in}%
+\pgfsys@transformshift{3.181085in}{1.328889in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.054203in}{1.266578in}%
+\pgfsys@transformshift{1.054203in}{1.314234in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.313758in}{1.293092in}%
+\pgfsys@transformshift{1.313758in}{1.287160in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.782218in}{1.290025in}%
+\pgfsys@transformshift{2.782218in}{1.304474in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.204694in}{1.306349in}%
+\pgfsys@transformshift{1.204694in}{1.298491in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.835294in}{1.305101in}%
+\pgfsys@transformshift{2.835294in}{1.263417in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1454,67 +1454,67 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.006952in}{0.987346in}%
+\pgfsys@transformshift{1.006952in}{0.971402in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.016064in}{0.972388in}%
+\pgfsys@transformshift{1.016064in}{0.972611in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.030342in}{0.920241in}%
+\pgfsys@transformshift{1.030342in}{0.963300in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.052606in}{0.973851in}%
+\pgfsys@transformshift{1.052606in}{0.943841in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.083324in}{0.961552in}%
+\pgfsys@transformshift{1.083324in}{0.986765in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.124470in}{0.982714in}%
+\pgfsys@transformshift{1.124470in}{0.933533in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.024612in}{0.943463in}%
+\pgfsys@transformshift{1.024612in}{0.947704in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.178391in}{0.941793in}%
+\pgfsys@transformshift{1.178391in}{0.933673in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.079567in}{0.943956in}%
+\pgfsys@transformshift{1.079567in}{0.949885in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.245933in}{0.933186in}%
+\pgfsys@transformshift{1.245933in}{0.930366in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.198306in}{0.925570in}%
+\pgfsys@transformshift{1.198306in}{0.976525in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.342879in}{0.935545in}%
+\pgfsys@transformshift{1.342879in}{0.928876in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.525591in}{0.942113in}%
+\pgfsys@transformshift{1.525591in}{0.921732in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.115358in}{0.961174in}%
+\pgfsys@transformshift{1.115358in}{0.971447in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.637661in}{0.963778in}%
+\pgfsys@transformshift{1.637661in}{0.983501in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.646773in}{0.965989in}%
+\pgfsys@transformshift{1.646773in}{0.960676in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1544,51 +1544,51 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.022639in}{0.640678in}%
+\pgfsys@transformshift{1.022639in}{0.607685in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.045748in}{0.605714in}%
+\pgfsys@transformshift{1.045748in}{0.600952in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.086518in}{0.603010in}%
+\pgfsys@transformshift{1.086518in}{0.601131in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.148894in}{0.624959in}%
+\pgfsys@transformshift{1.148894in}{0.626163in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.277779in}{0.602279in}%
+\pgfsys@transformshift{1.277779in}{0.577741in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.526906in}{0.629771in}%
+\pgfsys@transformshift{1.526906in}{0.638946in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.891203in}{0.595002in}%
+\pgfsys@transformshift{1.891203in}{0.609915in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.080412in}{0.593341in}%
+\pgfsys@transformshift{1.080412in}{0.590648in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.575176in}{0.615930in}%
+\pgfsys@transformshift{2.575176in}{0.624636in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.251100in}{0.620517in}%
+\pgfsys@transformshift{1.251100in}{0.608509in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.845361in}{0.638181in}%
+\pgfsys@transformshift{1.845361in}{0.590000in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.395297in}{0.633568in}%
+\pgfsys@transformshift{1.395297in}{0.616443in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \end{pgfscope}%
@@ -1623,8 +1623,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{3.477222in}}%
-\pgfpathlineto{\pgfqpoint{5.227273in}{3.477222in}}%
-\pgfpathlineto{\pgfqpoint{5.227273in}{3.220556in}}%
+\pgfpathlineto{\pgfqpoint{5.556061in}{3.477222in}}%
+\pgfpathlineto{\pgfqpoint{5.556061in}{3.220556in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{3.220556in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{3.477222in}}%
 \pgfpathclose%
@@ -1643,8 +1643,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{3.135000in}}%
-\pgfpathlineto{\pgfqpoint{5.480909in}{3.135000in}}%
-\pgfpathlineto{\pgfqpoint{5.480909in}{2.878333in}}%
+\pgfpathlineto{\pgfqpoint{5.908333in}{3.135000in}}%
+\pgfpathlineto{\pgfqpoint{5.908333in}{2.878333in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.878333in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{3.135000in}}%
 \pgfpathclose%
@@ -1663,8 +1663,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{2.792778in}}%
-\pgfpathlineto{\pgfqpoint{5.593636in}{2.792778in}}%
-\pgfpathlineto{\pgfqpoint{5.593636in}{2.536111in}}%
+\pgfpathlineto{\pgfqpoint{6.064899in}{2.792778in}}%
+\pgfpathlineto{\pgfqpoint{6.064899in}{2.536111in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.536111in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.792778in}}%
 \pgfpathclose%
@@ -1683,8 +1683,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{2.450556in}}%
-\pgfpathlineto{\pgfqpoint{5.706364in}{2.450556in}}%
-\pgfpathlineto{\pgfqpoint{5.706364in}{2.193889in}}%
+\pgfpathlineto{\pgfqpoint{6.221465in}{2.450556in}}%
+\pgfpathlineto{\pgfqpoint{6.221465in}{2.193889in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.193889in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.450556in}}%
 \pgfpathclose%
@@ -1703,8 +1703,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{2.108333in}}%
-\pgfpathlineto{\pgfqpoint{5.762727in}{2.108333in}}%
-\pgfpathlineto{\pgfqpoint{5.762727in}{1.851667in}}%
+\pgfpathlineto{\pgfqpoint{6.299747in}{2.108333in}}%
+\pgfpathlineto{\pgfqpoint{6.299747in}{1.851667in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.851667in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{2.108333in}}%
 \pgfpathclose%
@@ -1723,8 +1723,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{1.766111in}}%
-\pgfpathlineto{\pgfqpoint{5.819091in}{1.766111in}}%
-\pgfpathlineto{\pgfqpoint{5.819091in}{1.509444in}}%
+\pgfpathlineto{\pgfqpoint{6.378030in}{1.766111in}}%
+\pgfpathlineto{\pgfqpoint{6.378030in}{1.509444in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.509444in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.766111in}}%
 \pgfpathclose%
@@ -1743,8 +1743,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{1.423889in}}%
-\pgfpathlineto{\pgfqpoint{5.847273in}{1.423889in}}%
-\pgfpathlineto{\pgfqpoint{5.847273in}{1.167222in}}%
+\pgfpathlineto{\pgfqpoint{6.417172in}{1.423889in}}%
+\pgfpathlineto{\pgfqpoint{6.417172in}{1.167222in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.167222in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.423889in}}%
 \pgfpathclose%
@@ -1763,8 +1763,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{1.081667in}}%
-\pgfpathlineto{\pgfqpoint{5.960000in}{1.081667in}}%
-\pgfpathlineto{\pgfqpoint{5.960000in}{0.825000in}}%
+\pgfpathlineto{\pgfqpoint{6.573737in}{1.081667in}}%
+\pgfpathlineto{\pgfqpoint{6.573737in}{0.825000in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{0.825000in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{1.081667in}}%
 \pgfpathclose%
@@ -1783,8 +1783,8 @@
 \pgfsetstrokeopacity{0.000000}%
 \pgfsetdash{}{0pt}%
 \pgfpathmoveto{\pgfqpoint{4.381818in}{0.739444in}}%
-\pgfpathlineto{\pgfqpoint{6.072727in}{0.739444in}}%
-\pgfpathlineto{\pgfqpoint{6.072727in}{0.482778in}}%
+\pgfpathlineto{\pgfqpoint{6.730303in}{0.739444in}}%
+\pgfpathlineto{\pgfqpoint{6.730303in}{0.482778in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{0.482778in}}%
 \pgfpathlineto{\pgfqpoint{4.381818in}{0.739444in}}%
 \pgfpathclose%
diff --git a/plots/r.pgf b/plots/r.pgf
index 488f778..2f83b75 100644
--- a/plots/r.pgf
+++ b/plots/r.pgf
@@ -500,187 +500,187 @@
 \pgfusepath{fill}%
 }%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000470in}{3.329266in}%
+\pgfsys@transformshift{1.000470in}{3.357446in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000564in}{3.338044in}%
+\pgfsys@transformshift{1.000564in}{3.365568in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.000845in}{3.336892in}%
+\pgfsys@transformshift{1.000845in}{3.360325in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001785in}{3.358697in}%
+\pgfsys@transformshift{1.001785in}{3.333708in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.005261in}{3.368774in}%
+\pgfsys@transformshift{1.005261in}{3.317575in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.017473in}{3.329115in}%
+\pgfsys@transformshift{1.017473in}{3.325593in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001033in}{3.367692in}%
+\pgfsys@transformshift{1.001033in}{3.319021in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.001409in}{3.364617in}%
+\pgfsys@transformshift{1.001409in}{3.353781in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.002536in}{3.329091in}%
+\pgfsys@transformshift{1.002536in}{3.373665in}%
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@@ -710,143 +710,143 @@
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-\pgfsys@transformshift{1.000564in}{3.022041in}%
+\pgfsys@transformshift{1.000564in}{3.010191in}%
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@@ -876,119 +876,119 @@
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@@ -1018,103 +1018,103 @@
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 \begin{pgfscope}%
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+\pgfsys@transformshift{1.428364in}{2.351670in}%
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-\pgfsys@transformshift{1.052606in}{2.306176in}%
+\pgfsys@transformshift{1.052606in}{2.340957in}%
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+\pgfsys@transformshift{1.525591in}{2.353408in}%
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+\pgfsys@transformshift{1.148894in}{2.355098in}%
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@@ -1144,83 +1144,83 @@
 \pgfusepath{fill}%
 }%
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-\pgfsys@transformshift{1.000752in}{1.952862in}%
+\pgfsys@transformshift{1.000752in}{1.958268in}%
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-\pgfsys@transformshift{1.002912in}{1.984589in}%
+\pgfsys@transformshift{1.002912in}{1.958859in}%
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-\pgfsys@transformshift{1.024518in}{2.002257in}%
+\pgfsys@transformshift{1.024518in}{1.982620in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.232312in}{2.002667in}%
+\pgfsys@transformshift{1.232312in}{1.953750in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.002161in}{2.011748in}%
+\pgfsys@transformshift{1.002161in}{1.975899in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.013621in}{1.961759in}%
+\pgfsys@transformshift{1.013621in}{2.011094in}%
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-\pgfsys@transformshift{1.293279in}{1.995959in}%
+\pgfsys@transformshift{1.293279in}{2.006527in}%
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-\pgfsys@transformshift{1.002724in}{1.957404in}%
+\pgfsys@transformshift{1.002724in}{1.954164in}%
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+\pgfsys@transformshift{1.004603in}{2.007172in}%
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 \begin{pgfscope}%
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+\pgfsys@transformshift{1.444052in}{2.010168in}%
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 \begin{pgfscope}%
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+\pgfsys@transformshift{1.056833in}{1.994234in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.733573in}{1.956098in}%
+\pgfsys@transformshift{1.733573in}{1.998045in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.083324in}{1.970000in}%
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+\pgfsys@transformshift{1.277779in}{2.007627in}%
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@@ -1250,79 +1250,79 @@
 \pgfusepath{fill}%
 }%
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-\pgfsys@transformshift{1.000845in}{1.653090in}%
+\pgfsys@transformshift{1.000845in}{1.667403in}%
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 \begin{pgfscope}%
-\pgfsys@transformshift{1.048848in}{1.637070in}%
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+\pgfsys@transformshift{1.002724in}{1.636703in}%
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 \begin{pgfscope}%
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@@ -1352,75 +1352,75 @@
 \pgfusepath{fill}%
 }%
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-\pgfsys@transformshift{1.001127in}{1.282679in}%
+\pgfsys@transformshift{1.001127in}{1.286223in}%
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@@ -1450,63 +1450,63 @@
 \pgfusepath{fill}%
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 \begin{pgfscope}%
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@@ -1536,59 +1536,59 @@
 \pgfusepath{fill}%
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 \begin{pgfscope}%
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 \begin{pgfscope}%
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+\pgfsys@transformshift{1.363076in}{0.607680in}%
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 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.031282in}{0.644949in}%
+\pgfsys@transformshift{1.031282in}{0.636522in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{2.034273in}{0.641476in}%
+\pgfsys@transformshift{2.034273in}{0.588842in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.081164in}{0.606595in}%
+\pgfsys@transformshift{1.081164in}{0.586869in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.247155in}{0.604900in}%
+\pgfsys@transformshift{1.247155in}{0.614393in}%
 \pgfsys@useobject{currentmarker}{}%
 \end{pgfscope}%
 \begin{pgfscope}%
-\pgfsys@transformshift{1.342879in}{0.607097in}%
+\pgfsys@transformshift{1.342879in}{0.594853in}%
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@@ -1623,8 +1623,8 @@
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@@ -1643,8 +1643,8 @@
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-\pgfpathlineto{\pgfqpoint{5.424545in}{2.878333in}}%
+\pgfpathlineto{\pgfqpoint{5.830051in}{3.135000in}}%
+\pgfpathlineto{\pgfqpoint{5.830051in}{2.878333in}}%
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 \pgfpathlineto{\pgfqpoint{4.381818in}{3.135000in}}%
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@@ -1663,8 +1663,8 @@
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diff --git a/report.pdf b/report.pdf
index 0adf2ee..0a3acaf 100644
Binary files a/report.pdf and b/report.pdf differ
diff --git a/report.tex b/report.tex
index 95717b8..3b2b7c3 100644
--- a/report.tex
+++ b/report.tex
@@ -2,6 +2,7 @@
 \usepackage{algorithm}
 \usepackage{algpseudocode}
 \usepackage[utf8]{inputenc}
+\usepackage[english]{babel}
 \usepackage[margin=2.25cm]{geometry}
 \usepackage{hyperref}
 \usepackage{listings}
@@ -25,6 +26,10 @@
 \DeclareMathOperator*{\argmax}{arg\,max}
 \DeclareMathOperator*{\argmin}{arg\,min}
 \usepackage{minted}
+\usepackage[style=numeric,backend=biber]{biblatex}
+
+% bibliography
+\addbibresource{bibliography.bib}
 
 \definecolor{codegreen}{rgb}{0,0.6,0}
 \definecolor{codegray}{rgb}{0.5,0.5,0.5}
@@ -67,6 +72,99 @@ Assignment 4 -- Software Analysis \\\vspace{0.5cm}
 \begin{document}
 \maketitle
 
+\section{Introduction}
+
+This assignment consists in using model checking tecniques to verify
+the correctness of the algorithm implemented in an existing program. In
+particular, a sequential and a multi-threaded implementation of a
+array-reversing Java utility class implementation are verified to check
+correctness of both reversal procedures, consistency between the results they
+produce and for absence of race conditions.
+
+To achieve this I use the Spin model checker \cite{spin} to write an equivalent
+finite state automaton implementation of the algorithm using the
+\textit{ProMeLa} specification and define linear temporal logic (LTL) properties
+to be automatically verified.
+
+This report covers the definition of the model to check and the necessary LTL
+properties to verify correctness of the implementation, and additionally
+presents a brief analysis on the performance of the automated model checker.
+
+\section{Model definition}
+
+In this section I define the \textit{ProMeLa} code which implements a FSA model
+of the Java implementation. The model I define does not match the exact provided
+Java implementation, but aims to replicate the salient algorithmic and
+concurrent behaviour of the program.
+
+Due to the way I implement the LTL properties in the following section, I decide
+to implement the model as a GNU M4 macro processor \cite{m4} template file.
+Therefore, the complete model can be found in the path
+\texttt{ReverseModel/reversal.pml.m4} in the assignment repository
+
+\begin{center}
+\href{https://gitlab.com/usi-si-teaching/msde/2022-2023/software-analysis/maggioni/assignment-4}{\textit{usi-si-teaching/msde/2022-2023/software-analysis/maggioni/assignment-4}}
+\end{center}
+
+on \textit{gitlab.com}.
+
+As suggested by the assignment description, I define some preprocessor constants
+to allow for altering some parameters. As mentioned above, I use GNU M4 instead
+of the regular \textit{ProMeLa} preprocessor to implement these definitions.
+Specifically, I define the following properties:
+
+\begin{description}
+\item[N,] which represents the number of parallel threads spawned by the
+    parallel reverser;
+\item[LENGTH,] which represents the length of the array to reverse;
+\item[R,] which represents the upper bound for the random values used to fill
+    the array to reverse, the lower bound of them being 0.
+\end{description}
+
+The variable values are injected as parameters of the \texttt{m4} command, so no
+definition is required in the model code.
+
+Then by using these values the model specification declares the following global
+variables:
+
+\begin{minted}{c}
+int to_reverse[LENGTH];
+int reversed_seq[LENGTH]; 
+int reversed_par[LENGTH];
+bool done[N + 1];
+bool seq_eq_to_parallel = true;
+\end{minted}
+
+\texttt{to\_reverse} is the array to reverse, and \texttt{reverse\_seq} and
+\texttt{reverse\_par} are respectively where the sequential and parallel
+reverser store the reversed array. The \texttt{done} array stores an array of
+boolean values: \mintinline{c}{done[0]} stores whether the sequential reverser
+has terminated, and each \mintinline{c}{done[i]} for $1 \leq i \leq N$ stores
+whether the i-th spawned thread of the parallel reverser has terminated
+(consequently, since threads are joined in order, when \mintinline{c}{done[N] == true} the parallel reverser terminates). Finally 
+\texttt{seq\_eq\_to\_parallel} is set to \mintinline{c}{false} when an
+incongruence between \texttt{reversed\_seq} and \texttt{reversed\_par} is found
+after termination of both reversers.
+
+The body of the model is structured in the following way: 
+
+\begin{minted}{c}
+init {
+    { /* array initialization */ }
+    { /* sequential reverser algorithm */ }
+    { /* parallel reverser algorithm */ }
+    { /* congruence check between reversers */ }
+}
+\end{minted}
+
+Each of the enumerated sections is surrounded by curly braces to emulate the
+effect of locally scoped variables in procedures, which do not exist in
+\textit{ProMeLa} aside the cuncurrency-like \texttt{proctype} construct.
+
+        The citation \cite{tange_2023_7855617}.
+The citation \cite{spin}.
+
+
 \begin{figure}
 \begin{subfigure}[t]{\linewidth}
 \centering
@@ -83,13 +181,14 @@ Assignment 4 -- Software Analysis \\\vspace{0.5cm}
 \resizebox{0.85\textwidth}{!}{\input{plots/r.pgf}}
 \caption{Variable \texttt{R}}
 \end{subfigure}
-
-    \caption{Distribution of CPU time and percentage of timeouts (i.e.\
-    executions with a real execution time greater than 5 minutes, discarded for
-    sake of time) for different executions of the model checker for different
-    parameters of \texttt{N}, \texttt{LENGTH} and \texttt{R}.}
+\caption{Distribution of CPU time and percentage of timeouts (i.e.\
+executions with a real execution time greater than 5 minutes, discarded for
+sake of time) for different executions of the model checker for different
+parameters of \texttt{N}, \texttt{LENGTH} and \texttt{R}.}
 \label{fig:bigplot}
 \end{figure}
 
+\printbibliography
+
 \end{document}