diff --git a/analysisII.pdf b/analysisII.pdf
index bf8d10f..382dafc 100644
Binary files a/analysisII.pdf and b/analysisII.pdf differ
diff --git a/analysisII.tex b/analysisII.tex
index dfac4d1..31bc8fd 100644
--- a/analysisII.tex
+++ b/analysisII.tex
@@ -35,5 +35,6 @@ Rui Yang (\href{mailto:rui.yang@stud.uni-heidelberg.de}{rui.yang@stud.uni-heidel
 \input{ana10.tex}
 \input{ana11.tex}
 \input{ana12.tex}
+\input{ana13.tex}
 
 \end{document}