Av(12345, 12354, 12453, 13245, 13254)
Counting Sequence
1, 1, 2, 6, 24, 115, 615, 3533, 21338, 133676, 860882, 5664168, 37907198, 257219387, 1765359837, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 117 rules.
Finding the specification took 2428 seconds.
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\(\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_{57}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{57}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{109}\! \left(x , y_{0}\right)+F_{111}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}, 1\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{0} 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_{8}\! \left(x , y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{1}\right) F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{57}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{107}\! \left(x , y_{0}, y_{1}\right)+F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{1}\right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{19}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}, 1\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{10}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{10}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}, y_{1}\right) F_{57}\! \left(x \right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{24}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{24}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{0}, y_{1}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{26}\! \left(x , y_{0}\right) y_{0}-F_{26}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)\\
F_{27}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)+F_{29}\! \left(x \right)+F_{30}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)\\
F_{28}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}, 1\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right) F_{57}\! \left(x \right)\\
F_{33}\! \left(x , y_{0}\right) &= -\frac{-F_{34}\! \left(x , y_{0}\right) y_{0}+F_{34}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{34}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{100}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}\right) F_{57}\! \left(x \right)\\
F_{37}\! \left(x , y_{0}\right) &= -\frac{-F_{38}\! \left(x , y_{0}\right) y_{0}+F_{38}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{38}\! \left(x , y_{0}\right) &= F_{39}\! \left(x , y_{0}, 1\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}\right)\\
F_{43}\! \left(x , y_{0}\right) &= F_{39}\! \left(x , 1, y_{0}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{45}\! \left(x , y_{0}, y_{1}\right) F_{57}\! \left(x \right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{0}, y_{1}\right)+F_{75}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{48}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= F_{50}\! \left(x , y_{0}, 1\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{51}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{51}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}\right) &= F_{53}\! \left(x , y_{0}, y_{1}\right) F_{57}\! \left(x \right)\\
F_{53}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{54}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{54}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{1}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{56}\! \left(x , y_{0}\right) y_{0}-F_{56}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{56}\! \left(x , y_{0}\right) &= F_{38}\! \left(x , y_{0}\right)\\
F_{57}\! \left(x \right) &= x\\
F_{58}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x \right) F_{59}\! \left(x , y_{0}, y_{1}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{60}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{61}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{63}\! \left(x , y_{1}, y_{2}\right)+F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}\right) F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{64}\! \left(x , y_{0}, y_{1}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{10}\! \left(x , y_{0}, 1\right) y_{0}-F_{10}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{68}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{68}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{68}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{69}\! \left(x , 1, y_{1}\right) y_{1}-F_{69}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x \right) F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x \right) F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{73}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{73}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{73}\! \left(x , y_{0}, y_{1}\right) &= F_{74}\! \left(x , y_{0}, y_{1}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{34}\! \left(x , y_{0}\right) y_{0}-F_{34}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x \right) F_{76}\! \left(x , y_{0}, y_{1}\right)\\
F_{76}\! \left(x , y_{0}, y_{1}\right) &= F_{77}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{78}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{78}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{78}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{79}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{80}\! \left(x , y_{1}, y_{2}\right)+F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{79}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{80}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{81}\! \left(x , y_{0}, y_{1}\right)\\
F_{81}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{51}\! \left(x , y_{0}, 1\right) y_{0}-F_{51}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{85}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{85}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{85}\! \left(x , y_{0}, y_{1}\right) &= F_{86}\! \left(x , y_{0}, y_{1}\right)\\
F_{86}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{39}\! \left(x , 1, y_{1}\right) y_{1}-F_{39}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x \right) F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{88}\! \left(x , y_{0}\right) &= F_{57}\! \left(x \right) F_{89}\! \left(x , y_{0}\right)\\
F_{89}\! \left(x , y_{0}\right) &= F_{90}\! \left(x , y_{0}, 1\right)\\
F_{90}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{91}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{91}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{91}\! \left(x , y_{0}, y_{1}\right) &= F_{92}\! \left(x , y_{0}, y_{1}\right)\\
F_{92}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{93}\! \left(x , y_{0}, y_{1}\right)+F_{94}\! \left(x , y_{0}, y_{1}\right)+F_{96}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{0}, y_{1}\right)\\
F_{93}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{92}\! \left(x , y_{0}, y_{1}\right)\\
F_{94}\! \left(x , y_{0}, y_{1}\right) &= F_{95}\! \left(x , y_{0}, y_{1}\right)\\
F_{95}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}\right) F_{68}\! \left(x , y_{0}, y_{1}\right)\\
F_{96}\! \left(x , y_{0}, y_{1}\right) &= F_{97}\! \left(x , y_{0}, y_{1}\right)\\
F_{97}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x \right) F_{90}\! \left(x , y_{0}, y_{1}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}\right) &= F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{99}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x \right) F_{74}\! \left(x , y_{0}, y_{1}\right)\\
F_{100}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right) F_{57}\! \left(x \right)\\
F_{101}\! \left(x , y_{0}\right) &= F_{102}\! \left(x , y_{0}, 1\right)\\
F_{102}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{103}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{103}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{103}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{104}\! \left(x , y_{0}, y_{1}\right)+F_{105}\! \left(x , y_{0}, y_{1}\right)+F_{106}\! \left(x , y_{0}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}\right)\\
F_{104}\! \left(x , y_{0}, y_{1}\right) &= F_{103}\! \left(x , y_{0}, y_{1}\right) F_{13}\! \left(x , y_{0}\right)\\
F_{105}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}\right) F_{86}\! \left(x , y_{0}, y_{1}\right)\\
F_{106}\! \left(x , y_{0}, y_{1}\right) &= F_{102}\! \left(x , y_{0}, y_{1}\right) F_{57}\! \left(x \right)\\
F_{107}\! \left(x , y_{0}, y_{1}\right) &= F_{108}\! \left(x , y_{0}, y_{1}\right) F_{57}\! \left(x \right)\\
F_{108}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{73}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{73}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{109}\! \left(x , y_{0}\right) &= F_{110}\! \left(x , y_{0}\right) F_{57}\! \left(x \right)\\
F_{110}\! \left(x , y_{0}\right) &= -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{111}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right) F_{57}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x , 1\right)\\
F_{114}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{109}\! \left(x , y_{0}\right)+F_{115}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}\right)\\
F_{115}\! \left(x , y_{0}\right) &= F_{116}\! \left(x , y_{0}\right) F_{57}\! \left(x \right)\\
F_{116}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{114}\! \left(x , y_{0}\right)+F_{114}\! \left(x , 1\right)}{-1+y_{0}}\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 206 rules.
Finding the specification took 294927 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 206 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_{58}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{58}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{203}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right)+F_{14}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{14}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right) F_{58}\! \left(x \right)\\
F_{16}\! \left(x , y_{0}\right) &= -\frac{-F_{17}\! \left(x , y_{0}\right) y_{0}+F_{17}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{19}\! \left(x \right)+F_{200}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x , 1\right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right)\\
F_{21}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{194}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{193}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{104}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}\right) &= F_{184}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)+F_{90}\! \left(x , y_{0}\right)\\
F_{27}\! \left(x , y_{0}\right) &= F_{28}\! \left(x , y_{0}, 1\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{30}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}, 1\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}\right) &= F_{36}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{38}\! \left(x , y_{0}, y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0}, y_{1}\right) F_{59}\! \left(x , y_{0}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{41}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{28}\! \left(x , y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{59}\! \left(x , y_{0}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{2} F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{46}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{58}\! \left(x \right)\\
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x , y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{1} F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{58}\! \left(x \right) &= x\\
F_{59}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{59}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{47}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0}\right) F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{69}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{52}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{65}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{1}\right)+F_{73}\! \left(x , y_{0}, y_{1}\right)\\
F_{73}\! \left(x , y_{0}, y_{1}\right) &= F_{74}\! \left(x , y_{0}, y_{1}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{0}, y_{1}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{1} \left(F_{76}\! \left(x , y_{0}, 1\right)-F_{76}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}\\
F_{76}\! \left(x , y_{0}, y_{1}\right) &= F_{77}\! \left(x , y_{0}, y_{1}\right)\\
F_{77}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}\right) F_{78}\! \left(x , y_{0}, y_{1}\right)\\
F_{78}\! \left(x , y_{0}, y_{1}\right) &= F_{79}\! \left(x , y_{0}, y_{1}\right)+F_{81}\! \left(x , y_{0}, y_{1}\right)\\
F_{80}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}\right) F_{79}\! \left(x , y_{0}, y_{1}\right)\\
F_{80}\! \left(x , y_{0}, y_{1}\right) &= F_{72}\! \left(x , y_{0}, y_{1}\right)\\
F_{81}\! \left(x , y_{0}, y_{1}\right) &= F_{82}\! \left(x , y_{0}\right)+F_{87}\! \left(x , y_{0}, y_{1}\right)\\
F_{82}\! \left(x , y_{0}\right) &= F_{83}\! \left(x , y_{0}, 1\right)\\
F_{83}\! \left(x , y_{0}, y_{1}\right) &= F_{84}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{84}\! \left(x , y_{0}, y_{1}\right) &= F_{85}\! \left(x , y_{0}, y_{1}\right)\\
F_{85}\! \left(x , y_{0}, y_{1}\right) &= F_{86}\! \left(x , y_{0}, y_{1}\right)\\
F_{86}\! \left(x , y_{0}, y_{1}\right) &= F_{59}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}, y_{1}\right)\\
F_{87}\! \left(x , y_{0}, y_{1}\right) &= F_{88}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0} y_{1}-F_{89}\! \left(x , y_{0}, \frac{1}{y_{0}}, y_{2}\right)}{y_{0} y_{1}-1}\\
F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{63}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{90}\! \left(x , y_{0}\right) &= F_{91}\! \left(x , y_{0}, 1\right)\\
F_{91}\! \left(x , y_{0}, y_{1}\right) &= F_{181}\! \left(x , y_{0}, y_{1}\right)+F_{92}\! \left(x , y_{1}\right)\\
F_{92}\! \left(x , y_{0}\right) &= F_{93}\! \left(x , y_{0}\right)\\
F_{93}\! \left(x , y_{0}\right) &= F_{58}\! \left(x \right) F_{94}\! \left(x , y_{0}\right)\\
F_{95}\! \left(x , y_{0}\right) &= F_{161}\! \left(x , y_{0}\right)+F_{94}\! \left(x , y_{0}\right)\\
F_{95}\! \left(x , y_{0}\right) &= F_{96}\! \left(x , 1, y_{0}\right)\\
F_{96}\! \left(x , y_{0}, y_{1}\right) &= F_{160}\! \left(x , y_{0}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}\right) &= F_{159}\! \left(x , y_{0}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}\right) &= F_{105}\! \left(x , y_{0}, y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{99}\! \left(x , y_{0}, y_{1}\right) &= F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{157}\! \left(x , y_{0}, y_{1}\right)\\
F_{101}\! \left(x , y_{0}, y_{1}\right) &= F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{135}\! \left(x , y_{0}, y_{1}\right)\\
F_{102}\! \left(x , y_{0}, y_{1}\right) &= F_{101}\! \left(x , y_{0}, y_{1}\right)+F_{104}\! \left(x , y_{0}\right)\\
F_{102}\! \left(x , y_{0}, y_{1}\right) &= F_{103}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}, y_{1}\right) &= F_{65}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{104}\! \left(x , y_{0}\right) &= F_{105}\! \left(x , y_{0}, 1\right)\\
F_{105}\! \left(x , y_{0}, y_{1}\right) &= F_{106}\! \left(x , y_{0}, y_{1}\right)\\
F_{106}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}, y_{1}\right) F_{13}\! \left(x , y_{1}\right)\\
F_{107}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{108}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{108}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{108}\! \left(x , y_{0}, y_{1}\right) &= F_{109}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{0}, y_{1}\right)\\
F_{109}\! \left(x , y_{0}, y_{1}\right) &= F_{110}\! \left(x , y_{0}, y_{1}\right)\\
F_{110}\! \left(x , y_{0}, y_{1}\right) &= F_{111}\! \left(x , y_{0}, y_{1}\right) F_{13}\! \left(x , y_{1}\right)\\
F_{111}\! \left(x , y_{0}, y_{1}\right) &= F_{112}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{113}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{58}\! \left(x \right)\\
F_{113}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{122}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{116}\! \left(x , y_{1}, y_{2}\right)+F_{118}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{116}\! \left(x , y_{0}, y_{1}\right) &= F_{117}\! \left(x , y_{0}, y_{1}\right)\\
F_{117}\! \left(x , y_{0}, y_{1}\right) &= F_{58}\! \left(x \right) F_{97}\! \left(x , y_{0}, y_{1}\right)\\
F_{118}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{119}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{119}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{120}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{59}\! \left(x , y_{0}\right)\\
F_{120}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{121}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{121}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{121}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{122}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{123}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{123}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{124}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{58}\! \left(x \right)\\
F_{124}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{125}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{131}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{125}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{1} F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{126}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{128}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{13}\! \left(x , y_{2}\right)\\
F_{128}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{129}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{129}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{130}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{130}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{125}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{131}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{132}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{132}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{134}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{135}\! \left(x , y_{0}, y_{1}\right) &= F_{136}\! \left(x , y_{0}\right)+F_{138}\! \left(x , y_{0}, y_{1}\right)\\
F_{136}\! \left(x , y_{0}\right) &= F_{137}\! \left(x , y_{0}, 1\right)\\
F_{137}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{72}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{72}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{103}\! \left(x , y_{0}, y_{1}\right) &= F_{138}\! \left(x , y_{0}, y_{1}\right)+F_{139}\! \left(x , y_{0}, y_{1}\right)\\
F_{139}\! \left(x , y_{0}, y_{1}\right) &= F_{140}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{142}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{142}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{143}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{143}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{144}\! \left(x , y_{0}, y_{1}\right)+F_{155}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{144}\! \left(x , y_{0}, y_{1}\right) &= F_{145}\! \left(x , y_{1}\right)+F_{85}\! \left(x , y_{0}, y_{1}\right)\\
F_{145}\! \left(x , y_{0}\right) &= F_{146}\! \left(x , y_{0}\right)+F_{4}\! \left(x \right)\\
F_{146}\! \left(x , y_{0}\right) &= F_{147}\! \left(x , y_{0}\right)\\
F_{147}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{148}\! \left(x , y_{0}\right)\\
F_{148}\! \left(x , y_{0}\right) &= F_{149}\! \left(x , y_{0}\right)+F_{150}\! \left(x , y_{0}\right)\\
F_{149}\! \left(x , y_{0}\right) &= F_{79}\! \left(x , y_{0}, 1\right)\\
F_{150}\! \left(x , y_{0}\right) &= F_{151}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)\\
F_{151}\! \left(x , y_{0}\right) &= F_{152}\! \left(x , y_{0}, 1\right)\\
F_{152}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{153}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{153}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{153}\! \left(x , y_{0}, y_{1}\right) &= F_{154}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{154}\! \left(x , y_{0}, y_{1}\right) &= F_{63}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{155}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{156}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{156}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{156}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{157}\! \left(x , y_{0}, y_{1}\right) &= F_{137}\! \left(x , y_{0}, y_{1}\right)+F_{158}\! \left(x , y_{0}, y_{1}\right)\\
F_{159}\! \left(x , y_{0}, y_{1}\right) &= F_{139}\! \left(x , y_{0}, y_{1}\right)+F_{158}\! \left(x , y_{0}, y_{1}\right)\\
F_{159}\! \left(x , y_{0}, y_{1}\right) &= F_{126}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{160}\! \left(x , y_{0}, y_{1}\right) &= F_{48}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{161}\! \left(x , y_{0}\right) &= F_{162}\! \left(x , y_{0}\right)\\
F_{162}\! \left(x , y_{0}\right) &= F_{163}\! \left(x , y_{0}\right) F_{58}\! \left(x \right)\\
F_{163}\! \left(x , y_{0}\right) &= -\frac{-F_{164}\! \left(x , y_{0}\right) y_{0}+F_{164}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{164}\! \left(x , y_{0}\right) &= F_{165}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)\\
F_{165}\! \left(x , y_{0}\right) &= F_{166}\! \left(x , y_{0}\right)\\
F_{166}\! \left(x , y_{0}\right) &= F_{167}\! \left(x , y_{0}\right) F_{58}\! \left(x \right)\\
F_{168}\! \left(x , y_{0}\right) &= F_{167}\! \left(x , y_{0}\right) F_{58}\! \left(x \right)\\
F_{168}\! \left(x , y_{0}\right) &= F_{169}\! \left(x , y_{0}\right)\\
F_{169}\! \left(x , y_{0}\right) &= F_{170}\! \left(x , 1, y_{0}\right)\\
F_{170}\! \left(x , y_{0}, y_{1}\right) &= F_{171}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{171}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{172}\! \left(x , y_{0}, y_{1}\right)+F_{173}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{172}\! \left(x , y_{0}, y_{1}\right) &= F_{115}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{173}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{174}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{174}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{175}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{175}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{176}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{180}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{176}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{177}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{177}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{178}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{58}\! \left(x \right)\\
F_{178}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{179}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{179}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{68}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{180}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{1} F_{171}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{171}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{181}\! \left(x , y_{0}, y_{1}\right) &= F_{182}\! \left(x , y_{0}, y_{1}\right)\\
F_{182}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{183}\! \left(x , y_{0}, y_{1}\right)\\
F_{183}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{91}\! \left(x , y_{0}, y_{1}\right)+F_{91}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{184}\! \left(x , y_{0}\right) &= F_{185}\! \left(x , y_{0}\right)+F_{190}\! \left(x , y_{0}\right)\\
F_{185}\! \left(x , y_{0}\right) &= F_{186}\! \left(x , y_{0}\right)+F_{188}\! \left(x , y_{0}\right)\\
F_{186}\! \left(x , y_{0}\right) &= F_{187}\! \left(x , y_{0}\right)+F_{5}\! \left(x \right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{187}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)\\
F_{188}\! \left(x , y_{0}\right) &= -\frac{-F_{189}\! \left(x , y_{0}\right)+F_{189}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{189}\! \left(x , y_{0}\right) &= F_{73}\! \left(x , y_{0}, 1\right)\\
F_{190}\! \left(x , y_{0}\right) &= F_{191}\! \left(x , y_{0}, 1\right)\\
F_{192}\! \left(x , y_{0}, y_{1}\right) &= F_{191}\! \left(x , y_{0}, y_{1}\right)+F_{90}\! \left(x , y_{0}\right)\\
F_{192}\! \left(x , y_{0}, y_{1}\right) &= F_{65}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{193}\! \left(x , y_{0}\right) &= F_{159}\! \left(x , y_{0}, 1\right)\\
F_{194}\! \left(x , y_{0}\right) &= F_{195}\! \left(x , y_{0}\right)\\
F_{195}\! \left(x , y_{0}\right) &= F_{196}\! \left(x , y_{0}, 1\right)\\
F_{196}\! \left(x , y_{0}, y_{1}\right) &= F_{197}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{197}\! \left(x , y_{0}, y_{1}\right) &= F_{198}\! \left(x , y_{0}, y_{1}\right)\\
F_{198}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{199}\! \left(x , y_{0}, y_{1}\right)\\
F_{199}\! \left(x , y_{0}, y_{1}\right) &= F_{112}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{200}\! \left(x , y_{0}\right) &= F_{201}\! \left(x , 1, y_{0}\right)\\
F_{201}\! \left(x , y_{0}, y_{1}\right) &= F_{202}\! \left(x , y_{0}, y_{1}\right)\\
F_{202}\! \left(x , y_{0}, y_{1}\right) &= F_{103}\! \left(x , y_{0}, y_{1}\right) F_{13}\! \left(x , y_{0}\right)\\
F_{203}\! \left(x , y_{0}\right) &= F_{204}\! \left(x , y_{0}\right)\\
F_{204}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{205}\! \left(x , y_{0}\right)\\
F_{205}\! \left(x , y_{0}\right) &= F_{108}\! \left(x , 1, y_{0}\right)\\
\end{align*}\)