\documentclass[rep10,leqno]{report}
\voffset = -1in
\evensidemargin 0.1in
\oddsidemargin 0.1in
\textheight 9in
\textwidth 6in
\begin{document}
\normalsize
\baselineskip=12pt
\noindent
Input = 
$
\\A\,
 Pinv[A]\,
 A == A\\
Pinv[A]\,
 A\,
 Pinv[A] == Pinv[A]\\
A{}^{ T }\,
 \left(Pinv[A]\right){}^{ T } == Pinv[A]\,
 A\\
\left(Pinv[A]\right){}^{ T }\,
 A{}^{ T } == A\,
 Pinv[A]\\
\left(Pinv[A]\right){}^{ T } == Pinv[A{}^{ T }]\\
A{}^{ T }\,
 A\,
 Pinv[A] == A{}^{ T }\\
A\,
 Pinv[A]\,
 Pinv[A{}^{ T }] == Pinv[A{}^{ T }]\\
B\,
 Pinv[B]\,
 B == B\\
Pinv[B]\,
 B\,
 Pinv[B] == Pinv[B]\\
B{}^{ T }\,
 \left(Pinv[B]\right){}^{ T } == Pinv[B]\,
 B\\
\left(Pinv[B]\right){}^{ T }\,
 B{}^{ T } == B\,
 Pinv[B]\\
\left(Pinv[B]\right){}^{ T } == Pinv[B{}^{ T }]\\
B{}^{ T }\,
 B\,
 Pinv[B] == B{}^{ T }\\
B\,
 Pinv[B]\,
 Pinv[B{}^{ T }] == Pinv[B{}^{ T }]\\
A\,
 B\,
 Pinv[A\,
 B]\,
 A\,
 B == A\,
 B\\
Pinv[A\,
 B]\,
 A\,
 B\,
 Pinv[A\,
 B] == Pinv[A\,
 B]\\
B{}^{ T }\,
 A{}^{ T }\,
 \left(Pinv[A\,
 B]\right){}^{ T } == Pinv[A\,
 B]\,
 A\,
 B\\
\left(Pinv[A\,
 B]\right){}^{ T }\,
 B{}^{ T }\,
 A{}^{ T } == A\,
 B\,
 Pinv[A\,
 B]\\
\left(Pinv[A\,
 B]\right){}^{ T } == Pinv[B{}^{ T }\,
 A{}^{ T }]\\
B{}^{ T }\,
 A{}^{ T }\,
 A\,
 B\,
 Pinv[A\,
 B] == B{}^{ T }\,
 A{}^{ T }\\
A\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }] == Pinv[B{}^{ T }\,
 A{}^{ T }]\\
$
File Name = PinvAB-3iters\\
NCMakeGB Iterations = 3\\
NCMakeGB on Digested Iterations = 0\\
SmallBasis Iterations = 0\\
SmallBasis on Knowns Iterations = 0\\
Deselect$\rightarrow \{\}$\\
UserSelect$\rightarrow \{\}$\\
UserUnknowns$\rightarrow \{\}$\\
NCShortFormulas$\rightarrow$-1\\
RR$\rightarrow $False\\
RRByCat$\rightarrow $False\\
SB$\rightarrow $False\\
SBByCat$\rightarrow $False\\
DegreeCap$\rightarrow $-1\\
DegreeSumCap$\rightarrow $-1\\
DegreeCapSB$\rightarrow $-1\\
DegreeSumCapSB$\rightarrow $-1\\
NCCV$\rightarrow $False\\
THE ORDER IS NOW THE FOLLOWING:\hfil\break
$
A<B<A{}^{ T }<B{}^{ T }<Pinv[A]<Pinv[B]<Pinv[A{}^{ T }]<Pinv[B{}^{ T }]<\left(Pinv[A]\right){}^{ T }<\left(Pinv[B]\right){}^{ T }\ll
Pinv[A\,
 B]<Pinv[B{}^{ T }\,
 A{}^{ T }]<\left(Pinv[A\,
 B]\right){}^{ T }\\
$
\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
$\{\left(Pinv[A]\right){}^{ T },
$ $
\left(Pinv[B]\right){}^{ T },
$ $
\left(Pinv[A\,
 B]\right){}^{ T }\}$
\smallskip\\
The corresponding rules are the following:\smallskip\\
\begin{minipage}{6in}
$
\left(Pinv[A]\right){}^{ T }\rightarrow Pinv[A{}^{ T }]
$
\end{minipage}\medskip\\
\begin{minipage}{6in}
$
\left(Pinv[B]\right){}^{ T }\rightarrow Pinv[B{}^{ T }]
$
\end{minipage}\medskip\\
\begin{minipage}{6in}
$
\left(Pinv[A\,
 B]\right){}^{ T }\rightarrow Pinv[B{}^{ T }\,
 A{}^{ T }]
$
\end{minipage}\medskip\\
\rule[3pt]{6in}{.7pt}\\
The expressions with unknown variables $\{\}$\\
and knowns $\{A,
$ $
B,
$ $
Pinv[A],
$ $
Pinv[B],
$ $
Pinv[A{}^{ T }],
$ $
Pinv[B{}^{ T }],
$ $
A{}^{ T },
$ $
B{}^{ T }\}$\smallskip\\
\begin{minipage}{6in}
$
Pinv[A]\,
 A\rightarrow A{}^{ T }\,
 Pinv[A{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B]\,
 B\rightarrow B{}^{ T }\,
 Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[A{}^{ T }]\,
 A{}^{ T }\rightarrow A\,
 Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B{}^{ T }]\,
 B{}^{ T }\rightarrow B\,
 Pinv[B]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A\,
 Pinv[A]\,
 Pinv[A{}^{ T }]\rightarrow Pinv[A{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A\,
 A{}^{ T }\,
 Pinv[A{}^{ T }]\rightarrow A
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B\,
 Pinv[B]\,
 Pinv[B{}^{ T }]\rightarrow Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B\,
 B{}^{ T }\,
 Pinv[B{}^{ T }]\rightarrow B
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A{}^{ T }\,
 A\,
 Pinv[A]\rightarrow A{}^{ T }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A{}^{ T }\,
 Pinv[A{}^{ T }]\,
 Pinv[A]\rightarrow Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 B\,
 Pinv[B]\rightarrow B{}^{ T }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 Pinv[B{}^{ T }]\,
 Pinv[B]\rightarrow Pinv[B]
$
\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
$\{A,
$ $
B,
$ $
Pinv[A],
$ $
Pinv[B],
$ $
Pinv[A\,
 B],
$ $
Pinv[B{}^{ T }\,
 A{}^{ T }],
$ $
Pinv[A{}^{ T }],
$ $
Pinv[B{}^{ T }],
$ $
A{}^{ T },
$ $
B{}^{ T }\}$
\smallskip\\
\rule[3pt]{6in}{.7pt}\\
$0.7$  The expressions with unknown variables $\{Pinv[A\,
 B]\}$\\
and knowns $\{A,
$ $
B,
$ $
Pinv[A],
$ $
Pinv[B],
$ $
Pinv[A{}^{ T }],
$ $
Pinv[B{}^{ T }],
$ $
A{}^{ T },
$ $
B{}^{ T }\}$\smallskip\\
\begin{minipage}{6in}
$
Pinv[A\,
 B]\,
 A\,
 Pinv[A]\rightarrow Pinv[A\,
 B]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 Pinv[B{}^{ T }]\,
 Pinv[A\,
 B]\rightarrow Pinv[A\,
 B]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A\,
 B\,
 Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]\rightarrow A\,
 Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B]\,
 A{}^{ T }\,
 A\,
 B\,
 Pinv[A\,
 B]\rightarrow Pinv[B]\,
 A{}^{ T }
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[A{}^{ T }]\,
 B\,
 Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]\rightarrow Pinv[A{}^{ T }]\,
 Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 A{}^{ T }\,
 A\,
 B\,
 Pinv[A\,
 B]\rightarrow B{}^{ T }\,
 A{}^{ T }
$
\end{minipage}\\
\rule[3pt]{6in}{.7pt}\\
$0.9$  The expressions with unknown variables $\{Pinv[B{}^{ T }\,
 A{}^{ T }]\}$\\
and knowns $\{A,
$ $
B,
$ $
Pinv[A],
$ $
Pinv[B],
$ $
Pinv[A{}^{ T }],
$ $
Pinv[B{}^{ T }],
$ $
A{}^{ T },
$ $
B{}^{ T }\}$\smallskip\\
\begin{minipage}{6in}
$
A\,
 Pinv[A]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\rightarrow Pinv[B{}^{ T }\,
 A{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[B{}^{ T }]\rightarrow Pinv[B{}^{ T }\,
 A{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A\,
 B\,
 B{}^{ T }\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\rightarrow A\,
 B
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B]\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]\rightarrow Pinv[B]\,
 Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[A{}^{ T }]\,
 B\,
 B{}^{ T }\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\rightarrow Pinv[A{}^{ T }]\,
 B
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]\rightarrow B{}^{ T }\,
 Pinv[A]
$
\end{minipage}\\
\rule[3pt]{6in}{.7pt}\\
$1.6$  The expressions with unknown variables $\{Pinv[B{}^{ T }\,
 A{}^{ T }],
$ $
Pinv[A\,
 B]\}$\\
and knowns $\{A,
$ $
B,
$ $
Pinv[A],
$ $
Pinv[B],
$ $
Pinv[A{}^{ T }],
$ $
Pinv[B{}^{ T }],
$ $
A{}^{ T },
$ $
B{}^{ T }\}$\smallskip\\
\begin{minipage}{6in}
$
Pinv[A\,
 B]\,
 A\,
 B\rightarrow B{}^{ T }\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 A{}^{ T }\rightarrow A\,
 B\,
 Pinv[A\,
 B]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\rightarrow Pinv[B{}^{ T }\,
 A{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B]\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[A\,
 B]\rightarrow Pinv[B]\,
 Pinv[B{}^{ T }]\,
 Pinv[A\,
 B]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[A\,
 B]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]\rightarrow Pinv[A\,
 B]\,
 Pinv[A{}^{ T }]\,
 Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]\rightarrow Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[B]\,
 Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[A{}^{ T }]\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\rightarrow Pinv[A{}^{ T }]\,
 Pinv[A]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[A\,
 B]\rightarrow Pinv[A\,
 B]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[A{}^{ T }]\,
 Pinv[A]\rightarrow Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[B]\,
 Pinv[B{}^{ T }]\,
 Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]\rightarrow Pinv[B]\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[B]\,
 Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
Pinv[A{}^{ T }]\,
 Pinv[A]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]\rightarrow Pinv[A{}^{ T }]\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[A{}^{ T }]\,
 Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[B]\,
 Pinv[B{}^{ T }]\rightarrow Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B\,
 Pinv[B]\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[B]\,
 Pinv[B{}^{ T }]\rightarrow Pinv[B{}^{ T }]\,
 Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A{}^{ T }\,
 Pinv[A{}^{ T }]\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[A{}^{ T }]\,
 Pinv[A]\rightarrow Pinv[A]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
A\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[A{}^{ T }]\,
 B\,
 Pinv[A\,
 B]\,
 Pinv[A{}^{ T }]\,
 Pinv[A]\rightarrow Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 B{}^{ T }\,
 Pinv[A]
$
\end{minipage}\medskip \\
\begin{minipage}{6in}
$
B{}^{ T }\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[B]\,
 A{}^{ T }\,
 Pinv[B{}^{ T }\,
 A{}^{ T }]\,
 Pinv[B]\,
 Pinv[B{}^{ T }]\rightarrow Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]\,
 Pinv[A\,
 B]\,
 A\,
 Pinv[B{}^{ T }]
$
\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 0:00:00\\
The time for CreateCategories was 0:00:01\\
The time for NCCV was 0:00:00\\
The time for RegularOutput was 0:00:00\\
The time for everything so far was 0:00:02\\
\end{document}
\end