\documentstyle[rep10,leqno]{report}
\voffset = -1in
\evensidemargin 0.1in
\oddsidemargin 0.1in
\textheight 9in
\textwidth 6in
\begin{document}
\normalsize
\baselineskip=12pt
\noindent
Input = 
$
\\-1 + k_{1}\,
 u_{5} + k_{2}\,
 k_{10} + u_{1}\,
 k_{8}\\
k_{1}\,
 k_{6} + k_{2}\,
 u_{7} + u_{1}\,
 k_{9}\\
k_{1}\,
 k_{7} + k_{2}\,
 k_{11} + u_{1}\,
 u_{6}\\
k_{3}\,
 u_{5} + k_{4}\,
 k_{10} + u_{2}\,
 k_{8}\\
-1 + k_{3}\,
 k_{6} + k_{4}\,
 u_{7} + u_{2}\,
 k_{9}\\
k_{3}\,
 k_{7} + k_{4}\,
 k_{11} + u_{2}\,
 u_{6}\\
k_{5}\,
 k_{8} + u_{3}\,
 u_{5} + u_{4}\,
 k_{10}\\
k_{5}\,
 k_{9} + u_{3}\,
 k_{6} + u_{4}\,
 u_{7}\\
-1 + k_{5}\,
 u_{6} + u_{3}\,
 k_{7} + u_{4}\,
 k_{11}\\
-1 + k_{6}\,
 k_{3} + k_{7}\,
 u_{3} + u_{5}\,
 k_{1}\\
k_{6}\,
 u_{2} + k_{7}\,
 k_{5} + u_{5}\,
 u_{1}\\
k_{6}\,
 k_{4} + k_{7}\,
 u_{4} + u_{5}\,
 k_{2}\\
k_{8}\,
 k_{1} + k_{9}\,
 k_{3} + u_{6}\,
 u_{3}\\
-1 + k_{8}\,
 u_{1} + k_{9}\,
 u_{2} + u_{6}\,
 k_{5}\\
k_{8}\,
 k_{2} + k_{9}\,
 k_{4} + u_{6}\,
 u_{4}\\
k_{10}\,
 k_{1} + k_{11}\,
 u_{3} + u_{7}\,
 k_{3}\\
k_{10}\,
 u_{1} + k_{11}\,
 k_{5} + u_{7}\,
 u_{2}\\
-1 + k_{10}\,
 k_{2} + k_{11}\,
 u_{4} + u_{7}\,
 k_{4}\\
k_{1}\,
 k_{1}^{ -1 } == 1\\
k_{1}^{ -1 }\,
 k_{1} == 1\\
k_{2}\,
 k_{2}^{ -1 } == 1\\
k_{2}^{ -1 }\,
 k_{2} == 1\\
k_{3}\,
 k_{3}^{ -1 } == 1\\
k_{3}^{ -1 }\,
 k_{3} == 1\\
k_{4}\,
 k_{4}^{ -1 } == 1\\
k_{4}^{ -1 }\,
 k_{4} == 1\\
k_{5}\,
 k_{5}^{ -1 } == 1\\
k_{5}^{ -1 }\,
 k_{5} == 1\\
k_{6}\,
 k_{6}^{ -1 } == 1\\
k_{6}^{ -1 }\,
 k_{6} == 1\\
k_{7}\,
 k_{7}^{ -1 } == 1\\
k_{7}^{ -1 }\,
 k_{7} == 1\\
k_{8}\,
 k_{8}^{ -1 } == 1\\
k_{8}^{ -1 }\,
 k_{8} == 1\\
k_{9}\,
 k_{9}^{ -1 } == 1\\
k_{9}^{ -1 }\,
 k_{9} == 1\\
k_{10}\,
 k_{10}^{ -1 } == 1\\
k_{10}^{ -1 }\,
 k_{10} == 1\\
k_{11}\,
 k_{11}^{ -1 } == 1\\
k_{11}^{ -1 }\,
 k_{11} == 1\\
$
File Name = thms/WoerdOutput-13805\\
NCMakeGB Iterations = 2\\
NCMakeGB on Digested Iterations = 2\\
SmallBasis Iterations = 1\\
SmallBasis on Knowns Iterations = 1\\
Deselect$\rightarrow \{\}$\\
UserSelect$\rightarrow \{\}$\\
UserUnknowns$\rightarrow \{\}$\\
NCShortFormulas$\rightarrow$-1\\
RR$\rightarrow $True\\
RRByCat$\rightarrow $False\\
SB$\rightarrow $True\\
SBByCat$\rightarrow $False\\
DegreeCap$\rightarrow $18\\
DegreeSumCap$\rightarrow $26\\
DegreeCapSB$\rightarrow $19\\
DegreeSumCapSB$\rightarrow $27\\
NCCV$\rightarrow $False\\
THE ORDER IS NOW THE FOLLOWING:\hfil\break
$
k_{1}<k_{1}^{ -1 }<k_{2}<k_{2}^{ -1 }<k_{3}<k_{3}^{ -1 }<k_{4}<k_{4}^{ -1 }<k_{5}<k_{5}^{ -1 }<k_{6}<k_{6}^{ -1 }<k_{7}<k_{7}^{ -1 }<k_{8}<k_{8}^{ -1 }<k_{9}<k_{9}^{ -1 }<k_{10}<k_{10}^{ -1 }<k_{11}<k_{11}^{ -1 }\ll
u_{1}\ll
u_{2}\ll
u_{3}\ll
u_{4}\ll
u_{5}\ll
u_{6}\ll
u_{7}\\
$
\rule[2pt]{6in}{4pt}\hfil\break
\rule[2pt]{1.879in}{4pt}
\ YOUR SESSION HAS DIGESTED\ 
\rule[2pt]{1.879in}{4pt}\hfil\break
\rule[2pt]{1.923in}{4pt}
\ THE FOLLOWING RELATIONS\ 
\rule[2pt]{1.923in}{4pt}\hfil\break
\rule[2pt]{6in}{4pt}\hfil\break
THE FOLLOWING VARIABLES HAVE BEEN SOLVED FOR:\hfil\break
$\{u_{2},
$ $
u_{3},
$ $
u_{4},
$ $
u_{5},
$ $
u_{6},
$ $
u_{7}\}$
\smallskip\\
The corresponding rules are the following:\smallskip\\
\begin{minipage}{6in}
$
u_{2}\rightarrow k_{3}\,
 k_{1}^{ -1 }\,
 u_{1} - k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 } - k_{4}\,
 k_{10}\,
 k_{8}^{ -1 } + k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }
$
\end{minipage}\medskip\\
\begin{minipage}{6in}
$
u_{3}\rightarrow -1\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}
$
\end{minipage}\medskip\\
\begin{minipage}{6in}
$
u_{4}\rightarrow -1\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{4} - k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{2} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{2}
$
\end{minipage}\medskip\\
\begin{minipage}{6in}
$
u_{5}\rightarrow k_{1}^{ -1 } - k_{1}^{ -1 }\,
 k_{2}\,
 k_{10} - k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}
$
\end{minipage}\medskip\\
\begin{minipage}{6in}
$
u_{6}\rightarrow k_{5}^{ -1 } - k_{8}\,
 u_{1}\,
 k_{5}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 } + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 } + k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }
$
\end{minipage}\medskip\\
\begin{minipage}{6in}
$
u_{7}\rightarrow -1\,
 k_{2}^{ -1 }\,
 k_{1}\,
 k_{6} - k_{2}^{ -1 }\,
 u_{1}\,
 k_{9}
$
\end{minipage}\medskip\\
\rule[3pt]{6in}{.7pt}\\
The expressions with unknown variables $\{\}$\\
and knowns $\{k_{1},
$ $
k_{10},
$ $
k_{11},
$ $
k_{2},
$ $
k_{3},
$ $
k_{4},
$ $
k_{5},
$ $
k_{6},
$ $
k_{7},
$ $
k_{8},
$ $
k_{9},
$ $
k_{1}^{ -1 },
$ $
k_{10}^{ -1 },
$ $
k_{11}^{ -1 },
$ $
k_{2}^{ -1 },
$ $
k_{3}^{ -1 },
$ $
k_{4}^{ -1 },
$ $
k_{5}^{ -1 },
$ $
k_{6}^{ -1 },
$ $
k_{7}^{ -1 },
$ $
k_{8}^{ -1 },
$ $
k_{9}^{ -1 }\}$\smallskip\\
\begin{minipage}{6in}
$
k_{1}\,
 k_{1}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{10}\,
 k_{10}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{11}\,
 k_{11}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{2}\,
 k_{2}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{3}\,
 k_{3}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{4}\,
 k_{4}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{5}\,
 k_{5}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{6}\,
 k_{6}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{7}\,
 k_{7}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{8}\,
 k_{8}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{9}\,
 k_{9}^{ -1 }\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{1}^{ -1 }\,
 k_{1}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{10}^{ -1 }\,
 k_{10}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{11}^{ -1 }\,
 k_{11}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{2}^{ -1 }\,
 k_{2}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{3}^{ -1 }\,
 k_{3}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{4}^{ -1 }\,
 k_{4}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{5}^{ -1 }\,
 k_{5}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{6}^{ -1 }\,
 k_{6}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{7}^{ -1 }\,
 k_{7}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{8}^{ -1 }\,
 k_{8}\rightarrow 1
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{9}^{ -1 }\,
 k_{9}\rightarrow 1
$
\end{minipage}\\
\rule[2pt]{6in}{1pt}\hfil\break
\rule[2.5pt]{1.701in}{1pt}
\ USER CREATIONS APPEAR BELOW\ 
\rule[2.5pt]{1.701in}{1pt}\hfil\break
\rule[2pt]{6in}{1pt}\hfil\break
\rule[2pt]{6in}{4pt}\hfil\break
\rule[2pt]{1.45in}{4pt}
\ SOME RELATIONS WHICH APPEAR BELOW\ 
\rule[2pt]{1.45in}{4pt}\hfil\break
\rule[2pt]{2.18in}{4pt}
\ MAY BE UNDIGESTED\ 
\rule[2pt]{2.18in}{4pt}\hfil\break
\rule[2pt]{6in}{4pt}\hfil\break
THE FOLLOWING VARIABLES HAVE NOT BEEN SOLVED FOR:\hfil\break
$\{k_{1},
$ $
k_{10},
$ $
k_{11},
$ $
k_{2},
$ $
k_{3},
$ $
k_{4},
$ $
k_{5},
$ $
k_{6},
$ $
k_{7},
$ $
k_{8},
$ $
k_{9},
$ $
u_{1},
$ $
k_{1}^{ -1 },
$ $
k_{10}^{ -1 },
$ $
k_{11}^{ -1 },
$ $
k_{2}^{ -1 },
$ $
k_{3}^{ -1 },
$ $
k_{4}^{ -1 },
$ $
k_{5}^{ -1 },
$ $
k_{6}^{ -1 },
$ $
k_{7}^{ -1 },
$ $
k_{8}^{ -1 },
$ $
k_{9}^{ -1 }\}$
\smallskip\\
\rule[3pt]{6in}{.7pt}\\
The expressions with unknown variables $\{u_{1}\}$\\
and knowns $\{k_{1},
$ $
k_{10},
$ $
k_{11},
$ $
k_{2},
$ $
k_{3},
$ $
k_{4},
$ $
k_{5},
$ $
k_{6},
$ $
k_{7},
$ $
k_{8},
$ $
k_{9},
$ $
k_{1}^{ -1 },
$ $
k_{11}^{ -1 },
$ $
k_{2}^{ -1 },
$ $
k_{5}^{ -1 },
$ $
k_{7}^{ -1 },
$ $
k_{8}^{ -1 },
$ $
k_{9}^{ -1 }\}$\smallskip\\
\begin{minipage}{6in}
$
k_{4}\,
 k_{2}^{ -1 }\,
 u_{1}\rightarrow -1\,
 k_{9}^{ -1 } + k_{3}\,
 k_{6}\,
 k_{9}^{ -1 } + k_{3}\,
 k_{1}^{ -1 }\,
 u_{1} - k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 } - k_{4}\,
 k_{10}\,
 k_{8}^{ -1 } + k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 } - k_{4}\,
 k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{9}^{ -1 }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 u_{1}\rightarrow k_{7}\,
 k_{5} + k_{1}^{ -1 }\,
 u_{1} + k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1} - k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 } - k_{6}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 } - k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 u_{1} + k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
u_{1}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\rightarrow u_{1} + k_{1}\,
 k_{7}\,
 k_{5} + k_{2}\,
 k_{11}\,
 k_{5} - u_{1}\,
 k_{8}\,
 u_{1} + u_{1}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 } + u_{1}\,
 k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 } - u_{1}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{11}^{ -1 }\,
 k_{2}^{ -1 }\,
 u_{1}\,
 k_{9}\,
 k_{3}\rightarrow k_{11}^{ -1 }\,
 k_{10}\,
 k_{1} - k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} - k_{11}^{ -1 }\,
 k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{11}^{ -1 }\,
 k_{2}^{ -1 }\,
 u_{1}\,
 k_{9}\,
 k_{4}\rightarrow -1\,
 k_{11}^{ -1 } + k_{11}^{ -1 }\,
 k_{10}\,
 k_{2} - k_{7}^{ -1 }\,
 k_{6}\,
 k_{4} - k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2} - k_{11}^{ -1 }\,
 k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{4} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{2} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{2}
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{2}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 u_{1}\,
 k_{8}\rightarrow -1\,
 k_{10}\,
 u_{1}\,
 k_{8} + k_{2}^{ -1 }\,
 u_{1}\,
 k_{8} - k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3}\,
 k_{1}^{ -1 } - k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{4}\,
 k_{10} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{7}\,
 k_{5}\,
 k_{8} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{2}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 u_{1}\,
 k_{9}\rightarrow -1\,
 k_{10}\,
 u_{1}\,
 k_{9} + k_{2}^{ -1 }\,
 u_{1}\,
 k_{9} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{7}\,
 k_{5}\,
 k_{9} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{9} - k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{9} - k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{11}\,
 k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\rightarrow k_{11}\,
 k_{5} - k_{10}\,
 k_{1}\,
 k_{7}\,
 k_{5} - k_{10}\,
 k_{2}\,
 k_{11}\,
 k_{5} - k_{11}\,
 k_{5}\,
 k_{8}\,
 u_{1} + k_{11}\,
 k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 } + k_{11}\,
 k_{5}\,
 k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 } + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3}\,
 k_{7}\,
 k_{5} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{4}\,
 k_{11}\,
 k_{5} + k_{2}^{ -1 }\,
 u_{1}\,
 k_{9}\,
 k_{3}\,
 k_{7}\,
 k_{5} + k_{2}^{ -1 }\,
 u_{1}\,
 k_{9}\,
 k_{4}\,
 k_{11}\,
 k_{5} - k_{11}\,
 k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{11}\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}\rightarrow -1\,
 k_{10}\,
 k_{1} + k_{11}\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{3} + k_{2}^{ -1 }\,
 u_{1}\,
 k_{9}\,
 k_{3} - k_{11}\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1}
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{11}\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{2}\rightarrow 1 - k_{10}\,
 k_{2} + k_{11}\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{4} + k_{11}\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2} + k_{2}^{ -1 }\,
 k_{1}\,
 k_{6}\,
 k_{4} + k_{2}^{ -1 }\,
 u_{1}\,
 k_{9}\,
 k_{4} - k_{11}\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{2}
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{7}\,
 k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\rightarrow -1\,
 k_{6}\,
 k_{3}\,
 k_{7}\,
 k_{5} - k_{6}\,
 k_{4}\,
 k_{11}\,
 k_{5} - k_{7}\,
 k_{5}\,
 k_{8}\,
 u_{1} - k_{1}^{ -1 }\,
 k_{2}\,
 k_{11}\,
 k_{5} + k_{7}\,
 k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 } + k_{7}\,
 k_{5}\,
 k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 } + k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1}\,
 k_{7}\,
 k_{5} + k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{2}\,
 k_{11}\,
 k_{5} + k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}\,
 k_{7}\,
 k_{5} + k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{2}\,
 k_{11}\,
 k_{5} - k_{7}\,
 k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{2}\,
 k_{11}\rightarrow k_{5}\,
 k_{8}\,
 u_{1}\,
 k_{5}^{ -1 } + k_{7}^{ -1 }\,
 k_{6}\,
 k_{3}\,
 k_{7} + k_{7}^{ -1 }\,
 k_{6}\,
 k_{4}\,
 k_{11} + k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{11} + k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 } - k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 } - k_{5}\,
 k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 } - k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1}\,
 k_{7} - k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{2}\,
 k_{11} - k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}\,
 k_{7} + k_{5}\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}\,
 k_{7}\,
 k_{11}^{ -1 }\rightarrow k_{8}\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{4} + k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2} + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3}\,
 k_{7}\,
 k_{11}^{ -1 } - k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{2} - k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{2} + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1}\,
 k_{7}\,
 k_{11}^{ -1 }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}\rightarrow k_{8}\,
 k_{1} + k_{9}\,
 k_{3} - k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} + k_{8}\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} + k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} + k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1} - k_{8}\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} - k_{8}\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1} + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} - k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{6}\,
 k_{3} - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1} + k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} + k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1} - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{1} - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{7}^{ -1 }\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{8}\,
 k_{1}
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 }\rightarrow k_{9}\,
 k_{4} - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2} + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{4}\,
 k_{10}\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 u_{1}\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } + k_{9}\,
 k_{4}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 } - k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{9}\,
 k_{3}\,
 k_{1}^{ -1 }\,
 k_{2}\,
 k_{10}\,
 k_{8}^{ -1 }\,
 k_{5}^{ -1 }\,
 k_{11}^{ -1 }
$
\end{minipage}\\
\vspace{10pt}

\noindent
The time for preliminaries was 0:00:00\\
The time for NCMakeGB 1 was 0:00:00\\
The time for Remove Redundant 1 was 0:00:00\\
The time for the main NCMakeGB was 0:00:01\\
The time for Remove Redundant 2 was 0:00:00\\
The time for reducing unknowns was 0:00:00\\
The time for clean up basis was 0:00:00\\
The time for SmallBasis was 0:00:05\\
The time for CreateCategories was 0:00:08\\
The time for NCCV was 0:00:00\\
The time for RegularOutput was 0:00:06\\
The time for everything so far was 0:00:22\\
\end{document}
\end