Av(12354)
Counting Sequence
1, 1, 2, 6, 24, 119, 694, 4582, 33324, 261808, 2190688, 19318688, 178108704, 1705985883, 16891621166, ...
This specification was found using the strategy pack "All The Strategies 1 Tracked Fusion Req Corrob Expand Verified" and has 30 rules.
Found on January 22, 2022.Finding the specification took 131 seconds.
Copy 30 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{4}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= \frac{y_{0} F_{6}\! \left(x , y_{0}\right)-F_{6}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}, 1\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{1}, y_{0}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{13}\! \left(x , y_{0}, y_{1}\right)-F_{13}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{17}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{12}\! \left(x , y_{0}, 1\right)-y_{1} F_{12}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{1}, y_{0}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{29}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{21}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{26}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{1}, y_{0}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{20}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{20}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{21}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
\end{align*}\)
This specification was found using the strategy pack "Row Placements Tracked Fusion Expand Verified" and has 31 rules.
Found on January 22, 2022.Finding the specification took 17 seconds.
Copy 31 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\
F_{4}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)\\
F_{6}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , 1, y_{0}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{11}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{17}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{16}\! \left(x , y_{0}, 1\right)-y_{1} F_{16}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{17}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{1}\right) F_{19}\! \left(x , y_{0}, y_{1}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{0} F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{26}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{29}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{29}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x , y_{2}\right) F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
\end{align*}\)
This specification was found using the strategy pack "Row Placements Tracked Fusion Req Corrob Expand Verified" and has 35 rules.
Found on November 19, 2021.Finding the specification took 46 seconds.
Copy 35 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{7}\! \left(x , y_{0}\right)+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{7}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{6}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= x\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}, 1\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x \right)\\
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} y_{1} F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{17}\! \left(x , \frac{1}{y_{1}}, y_{1}, y_{2}\right)}{y_{0} y_{1}-1}\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}, y_{1}\right) F_{20}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{12}\! \left(x , y_{0}, 1\right)-y_{1} F_{12}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{20}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{1}\right) F_{22}\! \left(x , y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x \right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{20}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{29}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{29}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{20}\! \left(x , y_{1}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{23}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{23}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{20}\! \left(x , y_{2}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{11}\! \left(x , 1\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row And Col Placements Tracked Fusion Req Corrob Expand Verified" and has 32 rules.
Found on January 22, 2022.Finding the specification took 102 seconds.
Copy 32 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{4}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{6}\! \left(x , y_{0}\right)+F_{6}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , 1, y_{0}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{1}, y_{0}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{13}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{17}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{18}\! \left(x , y_{0}, 1\right)-y_{1} F_{18}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{1}, y_{0}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{31}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{0} F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{27}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{27}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{1}, y_{0}, y_{2}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{30}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{30}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
\end{align*}\)
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion Expand Verified" and has 31 rules.
Found on January 22, 2022.Finding the specification took 82 seconds.
Copy 31 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{8}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , 1, y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{1}, y_{0}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{17}\! \left(x , y_{0}, 1\right)-y_{1} F_{17}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{30}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{0} F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{26}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{28}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{29}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{29}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
\end{align*}\)