Av(12354, 12453, 12543, 13254, 13452, 13542, 14253, 14352, 23154, 24153)
Counting Sequence
1, 1, 2, 6, 24, 110, 542, 2800, 14968, 82116, 459738, 2616234, 15088708, 87998672, 518093030, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 295 rules.
Finding the specification took 41421 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_{7}\! \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_{7}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right)+F_{291}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right)+F_{4}\! \left(x \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_{22}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
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_{7}\! \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_{13}\! \left(x , y_{0}\right)+F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , 1, y_{0}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{168}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{1}, y_{2}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{290}\! \left(x , y_{0}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{1}, y_{0}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{158}\! \left(x , y_{1}, y_{0}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}, y_{0}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{287}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{1}\right)+F_{74}\! \left(x , y_{0}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right)+F_{43}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{36}\! \left(x , y_{0}\right)+F_{39}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{0}\right)\\
F_{37}\! \left(x , y_{0}\right) &= F_{38}\! \left(x , y_{0}\right)\\
F_{38}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)\\
F_{39}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}\right)+F_{40}\! \left(x , y_{0}\right)\\
F_{40}\! \left(x , y_{0}\right) &= F_{41}\! \left(x , y_{0}\right)\\
F_{41}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}\right)\\
F_{42}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}\right)+F_{40}\! \left(x , y_{0}\right)\\
F_{43}\! \left(x , y_{0}\right) &= F_{44}\! \left(x , y_{0}\right)\\
F_{44}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{45}\! \left(x , y_{0}\right)\\
F_{45}\! \left(x , y_{0}\right) &= F_{46}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)\\
F_{46}\! \left(x , y_{0}\right) &= F_{47}\! \left(x , 1, y_{0}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{48}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{48}\! \left(x , y_{1}\right)}{-1+y_{0}}\\
F_{48}\! \left(x , y_{0}\right) &= F_{2}\! \left(x \right)+F_{49}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= F_{50}\! \left(x , y_{0}\right)\\
F_{50}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)\\
F_{51}\! \left(x , y_{0}\right) &= F_{48}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)\\
F_{52}\! \left(x , y_{0}\right) &= F_{53}\! \left(x , y_{0}\right)\\
F_{53}\! \left(x , y_{0}\right) &= F_{54}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)\\
F_{54}\! \left(x , y_{0}\right) &= F_{55}\! \left(x , y_{0}\right)\\
F_{55}\! \left(x , y_{0}\right) &= F_{284}\! \left(x , y_{0}\right)+F_{56}\! \left(x , y_{0}\right)\\
F_{56}\! \left(x , y_{0}\right) &= F_{57}\! \left(x , y_{0}\right)\\
F_{57}\! \left(x , y_{0}\right) &= F_{58}\! \left(x , y_{0}\right)+F_{61}\! \left(x , y_{0}\right)\\
F_{58}\! \left(x , y_{0}\right) &= F_{52}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)\\
F_{59}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{60}\! \left(x , y_{0}\right)\\
F_{60}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)\\
F_{61}\! \left(x , y_{0}\right) &= F_{62}\! \left(x , y_{0}\right)\\
F_{62}\! \left(x , y_{0}\right) &= F_{63}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)\\
F_{63}\! \left(x , y_{0}\right) &= F_{64}\! \left(x , y_{0}\right)\\
F_{64}\! \left(x , y_{0}\right) &= F_{281}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)\\
F_{65}\! \left(x , y_{0}\right) &= F_{66}\! \left(x , y_{0}\right)\\
F_{66}\! \left(x , y_{0}\right) &= F_{67}\! \left(x , 1, y_{0}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}\right) &= F_{278}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{1}, y_{0}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{1}\right) F_{68}\! \left(x , y_{0}, y_{1}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{70}\! \left(x , y_{1}, y_{0}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= F_{275}\! \left(x , y_{0}, y_{1}\right)+F_{71}\! \left(x , y_{0}, y_{1}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{72}\! \left(x , y_{0}\right)+F_{74}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}\right) &= F_{73}\! \left(x , y_{0}\right)\\
F_{73}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= F_{75}\! \left(x , y_{0}, y_{1}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{1}\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}\right)+F_{85}\! \left(x , y_{0}, y_{1}\right)\\
F_{77}\! \left(x , y_{0}, y_{1}\right) &= F_{78}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{78}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{79}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{79}\! \left(x , y_{0}, y_{2}\right)}{-1+y_{1}}\\
F_{79}\! \left(x , y_{0}, y_{1}\right) &= F_{80}\! \left(x , y_{1}, y_{0}\right)\\
F_{80}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{1}\right) F_{81}\! \left(x , y_{0}, y_{1}\right)\\
F_{81}\! \left(x , y_{0}, y_{1}\right) &= F_{273}\! \left(x , y_{0}, y_{1}\right)+F_{82}\! \left(x , y_{0}, y_{1}\right)\\
F_{82}\! \left(x , y_{0}, y_{1}\right) &= F_{83}\! \left(x , y_{0}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{83}\! \left(x , y_{0}\right) &= F_{58}\! \left(x , y_{0}\right)\\
F_{84}\! \left(x , y_{0}, y_{1}\right) &= F_{85}\! \left(x , y_{1}, y_{0}\right)\\
F_{86}\! \left(x , y_{0}, y_{1}\right) &= F_{269}\! \left(x , y_{0}, y_{1}\right)+F_{85}\! \left(x , y_{0}, y_{1}\right)\\
F_{87}\! \left(x , y_{0}, y_{1}\right) &= F_{125}\! \left(x , y_{0}, y_{1}\right)+F_{86}\! \left(x , y_{0}, y_{1}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{1}\right) F_{87}\! \left(x , y_{0}, y_{1}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}\right) &= F_{89}\! \left(x , y_{0}, y_{1}\right)\\
F_{89}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{90}\! \left(x , y_{0}, y_{1}\right)\\
F_{90}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{1} \left(F_{91}\! \left(x , y_{0}\right)-F_{91}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{91}\! \left(x , y_{0}\right) &= F_{267}\! \left(x , y_{0}\right)+F_{92}\! \left(x , y_{0}\right)\\
F_{92}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right)+F_{93}\! \left(x , y_{0}\right)\\
F_{93}\! \left(x , y_{0}\right) &= F_{94}\! \left(x , y_{0}\right)\\
F_{94}\! \left(x , y_{0}\right) &= F_{7}\! \left(x \right) F_{95}\! \left(x , y_{0}\right)\\
F_{95}\! \left(x , y_{0}\right) &= F_{96}\! \left(x , 1, y_{0}\right)\\
F_{97}\! \left(x , y_{0}, y_{1}\right) &= F_{236}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}, y_{1}\right)\\
F_{97}\! \left(x , y_{0}, y_{1}\right) &= F_{233}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{1}\right)\\
F_{99}\! \left(x , y_{0}\right) &= F_{232}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{100}\! \left(x , y_{0}\right) &= F_{7}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)\\
F_{100}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)\\
F_{102}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{229}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}\right) &= F_{102}\! \left(x , y_{0}\right)+F_{225}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}\right) &= F_{104}\! \left(x , y_{0}\right)+F_{108}\! \left(x , y_{0}\right)\\
F_{104}\! \left(x , y_{0}\right) &= F_{105}\! \left(x , 1, y_{0}\right)\\
F_{105}\! \left(x , y_{0}, y_{1}\right) &= F_{106}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{106}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{107}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{72}\! \left(x , y_{0}\right)\\
F_{108}\! \left(x , y_{0}\right) &= F_{109}\! \left(x , y_{0}\right)\\
F_{109}\! \left(x , y_{0}\right) &= F_{110}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)\\
F_{110}\! \left(x , y_{0}\right) &= F_{111}\! \left(x , y_{0}\right)+F_{124}\! \left(x , y_{0}\right)\\
F_{111}\! \left(x , y_{0}\right) &= F_{112}\! \left(x , 1, y_{0}\right)\\
F_{112}\! \left(x , y_{0}, y_{1}\right) &= F_{113}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{113}\! \left(x , y_{0}, y_{1}\right) &= F_{114}\! \left(x , y_{0}, y_{1}\right)+F_{115}\! \left(x , y_{0}, y_{1}\right)\\
F_{114}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{115}\! \left(x , y_{0}, y_{1}\right) &= F_{116}\! \left(x , y_{1}\right)+F_{117}\! \left(x , y_{0}, y_{1}\right)\\
F_{116}\! \left(x , y_{0}\right) &= F_{85}\! \left(x , 1, y_{0}\right)\\
F_{117}\! \left(x , y_{0}, y_{1}\right) &= F_{118}\! \left(x , y_{0}, y_{1}\right)\\
F_{118}\! \left(x , y_{0}, y_{1}\right) &= F_{119}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)\\
F_{119}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} \left(F_{120}\! \left(x , y_{0}\right)-F_{120}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{120}\! \left(x , y_{0}\right) &= F_{121}\! \left(x , 1, y_{0}\right)\\
F_{121}\! \left(x , y_{0}, y_{1}\right) &= F_{122}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{1}\right)\\
F_{122}\! \left(x , y_{0}, y_{1}\right) &= F_{123}\! \left(x , y_{0}, y_{1}\right)\\
F_{123}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{124}\! \left(x , y_{0}\right) &= F_{125}\! \left(x , 1, y_{0}\right)\\
F_{125}\! \left(x , y_{0}, y_{1}\right) &= F_{126}\! \left(x , y_{0}, y_{1}\right)\\
F_{126}\! \left(x , y_{0}, y_{1}\right) &= F_{127}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{127}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{222}\! \left(x , y_{0}, y_{1}\right)\\
F_{128}\! \left(x , y_{0}, y_{1}\right) &= F_{129}\! \left(x , y_{1}, y_{0}\right)+F_{133}\! \left(x , y_{0}, y_{1}\right)\\
F_{130}\! \left(x , y_{0}, y_{1}\right) &= F_{129}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{130}\! \left(x , y_{0}, y_{1}\right) &= F_{131}\! \left(x , y_{1}, y_{0}\right)\\
F_{131}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{132}\! \left(x , 1, y_{1}\right)-F_{132}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{132}\! \left(x , y_{0}, y_{1}\right) &= F_{70}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{133}\! \left(x , y_{0}, y_{1}\right) &= F_{134}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{135}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{135}\! \left(x , y_{0}, y_{2}\right)}{-1+y_{1}}\\
F_{135}\! \left(x , y_{0}, y_{1}\right) &= F_{136}\! \left(x , y_{1}, y_{0}\right)\\
F_{137}\! \left(x , y_{0}, y_{1}\right) &= F_{136}\! \left(x , y_{0}, y_{1}\right)+F_{216}\! \left(x , y_{0}, y_{1}\right)\\
F_{138}\! \left(x , y_{0}, y_{1}\right) &= F_{137}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , 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}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{140}\! \left(x , y_{0}, y_{1}\right) &= F_{141}\! \left(x , y_{0}, y_{1}\right)+F_{184}\! \left(x , y_{0}, y_{1}\right)\\
F_{141}\! \left(x , y_{0}, y_{1}\right) &= F_{142}\! \left(x , y_{0}, y_{1}\right)+F_{178}\! \left(x , y_{0}, y_{1}\right)\\
F_{142}\! \left(x , y_{0}, y_{1}\right) &= F_{143}\! \left(x , y_{1}, y_{0}\right)\\
F_{144}\! \left(x , y_{0}, y_{1}\right) &= F_{143}\! \left(x , y_{1}, y_{0}\right)+F_{146}\! \left(x , y_{0}, y_{1}\right)\\
F_{145}\! \left(x , y_{0}, y_{1}\right) &= F_{144}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{145}\! \left(x , y_{0}, y_{1}\right) &= F_{70}\! \left(x , y_{1}, y_{0}\right)\\
F_{146}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{147}\! \left(x , y_{0}, y_{0}\right)\\
F_{147}\! \left(x , y_{0}, y_{1}\right) &= F_{148}\! \left(x , y_{0}, y_{1}\right)\\
F_{148}\! \left(x , y_{0}, y_{1}\right) &= F_{149}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)\\
F_{149}\! \left(x , y_{0}, y_{1}\right) &= F_{150}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{151}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{151}\! \left(x , y_{0}, y_{2}\right)}{-1+y_{1}}\\
F_{152}\! \left(x , y_{0}, y_{1}\right) &= F_{151}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{152}\! \left(x , y_{0}, y_{1}\right) &= F_{153}\! \left(x , y_{0}, y_{1}\right)\\
F_{154}\! \left(x , y_{0}, y_{1}\right) &= F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{156}\! \left(x , y_{0}, y_{1}\right)\\
F_{155}\! \left(x , y_{0}, y_{1}\right) &= F_{154}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{155}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{156}\! \left(x , y_{0}, y_{1}\right) &= F_{120}\! \left(x , y_{1}\right)+F_{157}\! \left(x , y_{0}, y_{1}\right)\\
F_{158}\! \left(x , y_{0}, y_{1}\right) &= F_{157}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}\right)\\
F_{154}\! \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_{159}\! \left(x , y_{0}, y_{1}\right) &= F_{160}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{160}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{161}\! \left(x , y_{1}, y_{2}\right)+F_{165}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{161}\! \left(x , y_{0}, y_{1}\right) &= F_{162}\! \left(x , y_{1}, y_{0}\right)\\
F_{162}\! \left(x , y_{0}, y_{1}\right) &= F_{163}\! \left(x , y_{0}\right) F_{82}\! \left(x , y_{0}, y_{1}\right)\\
F_{163}\! \left(x , y_{0}\right) &= F_{164}\! \left(x , y_{0}\right)\\
F_{164}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{165}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{166}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{166}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{163}\! \left(x , y_{0}\right) F_{167}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{167}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{168}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
F_{168}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{169}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{169}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{170}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{170}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{24}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{171}\! \left(x , y_{0}\right) &= F_{172}\! \left(x , y_{0}\right)\\
F_{172}\! \left(x , y_{0}\right) &= F_{173}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{173}\! \left(x , y_{0}\right) &= F_{174}\! \left(x , 1, y_{0}\right)\\
F_{174}\! \left(x , y_{0}, y_{1}\right) &= F_{175}\! \left(x , y_{0}, y_{1}\right)+F_{9}\! \left(x , y_{1}\right)\\
F_{175}\! \left(x , y_{0}, y_{1}\right) &= F_{176}\! \left(x , y_{0}, y_{1}\right)\\
F_{176}\! \left(x , y_{0}, y_{1}\right) &= F_{177}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{177}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{178}\! \left(x , y_{0}, y_{1}\right) &= y_{1} F_{179}\! \left(x , y_{0}, y_{1}\right)\\
F_{179}\! \left(x , y_{0}, y_{1}\right) &= F_{180}\! \left(x , y_{0}, y_{1}\right)\\
F_{180}\! \left(x , y_{0}, y_{1}\right) &= F_{181}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)\\
F_{181}\! \left(x , y_{0}, y_{1}\right) &= F_{182}\! \left(x , y_{1}, y_{0}\right)\\
F_{182}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{183}\! \left(x , y_{0}, 1\right) y_{0}-F_{183}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{183}\! \left(x , y_{0}, y_{1}\right) &= F_{151}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{184}\! \left(x , y_{0}, y_{1}\right) &= F_{185}\! \left(x , y_{1}, y_{0}\right)\\
F_{185}\! \left(x , y_{0}, y_{1}\right) &= F_{186}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{186}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{187}\! \left(x , y_{0}\right) y_{0}-F_{187}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{187}\! \left(x , y_{0}\right) &= F_{188}\! \left(x , y_{0}\right)+F_{58}\! \left(x , y_{0}\right)\\
F_{188}\! \left(x , y_{0}\right) &= F_{189}\! \left(x , y_{0}\right)\\
F_{190}\! \left(x , y_{0}\right) &= F_{189}\! \left(x , y_{0}\right)+F_{196}\! \left(x , y_{0}\right)\\
F_{191}\! \left(x , y_{0}\right) &= F_{190}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{191}\! \left(x , y_{0}\right) &= F_{192}\! \left(x , y_{0}\right)\\
F_{192}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right)+F_{193}\! \left(x , y_{0}\right)\\
F_{193}\! \left(x , y_{0}\right) &= F_{194}\! \left(x , y_{0}\right)\\
F_{194}\! \left(x , y_{0}\right) &= F_{195}\! \left(x , y_{0}\right)\\
F_{195}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{197}\! \left(x , y_{0}\right) &= F_{196}\! \left(x , y_{0}\right)+F_{215}\! \left(x , y_{0}\right)\\
F_{198}\! \left(x , y_{0}\right) &= F_{197}\! \left(x , y_{0}\right)+F_{210}\! \left(x , y_{0}\right)\\
F_{199}\! \left(x , y_{0}\right) &= F_{198}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{199}\! \left(x , y_{0}\right) &= F_{200}\! \left(x , y_{0}\right)\\
F_{200}\! \left(x , y_{0}\right) &= F_{201}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{201}\! \left(x , y_{0}\right) &= F_{202}\! \left(x , y_{0}\right)+F_{209}\! \left(x , y_{0}\right)\\
F_{202}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{203}\! \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) &= y_{0} F_{205}\! \left(x , y_{0}\right)\\
F_{205}\! \left(x , y_{0}\right) &= F_{206}\! \left(x , y_{0}\right)\\
F_{206}\! \left(x , y_{0}\right) &= F_{207}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)\\
F_{207}\! \left(x , y_{0}\right) &= F_{208}\! \left(x , 1, y_{0}\right)\\
F_{208}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{209}\! \left(x , y_{0}\right) &= F_{173}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{210}\! \left(x , y_{0}\right) &= y_{0} F_{211}\! \left(x , y_{0}\right)\\
F_{211}\! \left(x , y_{0}\right) &= F_{212}\! \left(x , y_{0}\right)\\
F_{212}\! \left(x , y_{0}\right) &= F_{213}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)\\
F_{213}\! \left(x , y_{0}\right) &= F_{214}\! \left(x , 1, y_{0}\right)\\
F_{214}\! \left(x , y_{0}, y_{1}\right) &= F_{151}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{215}\! \left(x , y_{0}\right) &= F_{187}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{216}\! \left(x , y_{0}, y_{1}\right) &= F_{217}\! \left(x , y_{0}, y_{1}\right)+F_{218}\! \left(x , y_{0}, y_{1}\right)\\
F_{217}\! \left(x , y_{0}, y_{1}\right) &= F_{67}\! \left(x , y_{1}, y_{0}\right)\\
F_{218}\! \left(x , y_{0}, y_{1}\right) &= F_{219}\! \left(x , y_{1}, y_{0}\right)\\
F_{219}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{220}\! \left(x , y_{0}, y_{1}\right)\\
F_{221}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{220}\! \left(x , y_{0}, y_{1}\right)\\
F_{221}\! \left(x , y_{0}, y_{1}\right) &= F_{153}\! \left(x , y_{0}, y_{1}\right)\\
F_{222}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{223}\! \left(x , y_{0}, y_{1}\right)\\
F_{223}\! \left(x , y_{0}, y_{1}\right) &= F_{224}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{224}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{220}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{220}\! \left(x , y_{0}, y_{2}\right)}{-1+y_{1}}\\
F_{225}\! \left(x , y_{0}\right) &= F_{226}\! \left(x , y_{0}\right)\\
F_{226}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{227}\! \left(x , y_{0}\right)\\
F_{227}\! \left(x , y_{0}\right) &= F_{228}\! \left(x , y_{0}, 1\right)\\
F_{228}\! \left(x , y_{0}, y_{1}\right) &= F_{144}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{229}\! \left(x , y_{0}\right) &= F_{230}\! \left(x , y_{0}\right)+F_{231}\! \left(x , y_{0}\right)\\
F_{230}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)\\
F_{231}\! \left(x , y_{0}\right) &= F_{2}\! \left(x \right)+F_{43}\! \left(x , y_{0}\right)\\
F_{232}\! \left(x , y_{0}\right) &= F_{233}\! \left(x , 1, y_{0}\right)\\
F_{233}\! \left(x , y_{0}, y_{1}\right) &= F_{234}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{234}\! \left(x , y_{0}, y_{1}\right) &= F_{235}\! \left(x , y_{0}, y_{1}\right)\\
F_{235}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} \left(F_{194}\! \left(x , y_{0}\right)-F_{194}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{236}\! \left(x , y_{0}\right) &= F_{192}\! \left(x , y_{0}\right)+F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{250}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{0}\! \left(x \right) F_{241}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x , 1\right)\\
F_{242}\! \left(x , y_{0}\right) &= F_{243}\! \left(x , y_{0}\right)+F_{4}\! \left(x \right)\\
F_{243}\! \left(x , y_{0}\right) &= F_{244}\! \left(x , y_{0}\right)\\
F_{244}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{245}\! \left(x , y_{0}\right)\\
F_{245}\! \left(x , y_{0}\right) &= F_{246}\! \left(x , y_{0}\right)+F_{8}\! \left(x \right)\\
F_{246}\! \left(x , y_{0}\right) &= F_{247}\! \left(x , y_{0}\right)\\
F_{247}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{248}\! \left(x , y_{0}\right)\\
F_{248}\! \left(x , y_{0}\right) &= F_{249}\! \left(x , y_{0}, 1\right)\\
F_{249}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)+F_{258}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{0}\! \left(x \right) F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{202}\! \left(x , 1\right)\\
F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right) F_{265}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{260}\! \left(x \right) &= \frac{F_{261}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= \frac{F_{264}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{264}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{255}\! \left(x \right)\\
F_{267}\! \left(x , y_{0}\right) &= F_{268}\! \left(x , y_{0}\right)\\
F_{268}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{227}\! \left(x , y_{0}\right)\\
F_{269}\! \left(x , y_{0}, y_{1}\right) &= F_{270}\! \left(x , y_{0}, y_{1}\right)\\
F_{270}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right) F_{271}\! \left(x , y_{1}\right)\\
F_{271}\! \left(x , y_{0}\right) &= F_{272}\! \left(x , 1, y_{0}\right)\\
F_{272}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{120}\! \left(x , y_{1}\right)-F_{120}\! \left(x , y_{0} y_{1}\right)\right)}{-1+y_{0}}\\
F_{273}\! \left(x , y_{0}, y_{1}\right) &= F_{274}\! \left(x , y_{0}, y_{1}\right)\\
F_{274}\! \left(x , y_{0}, y_{1}\right) &= F_{137}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{275}\! \left(x , y_{0}, y_{1}\right) &= F_{276}\! \left(x , y_{0}, y_{1}\right)\\
F_{276}\! \left(x , y_{0}, y_{1}\right) &= F_{277}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)\\
F_{277}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{233}\! \left(x , 1, y_{1}\right)-F_{233}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}\\
F_{278}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{279}\! \left(x , y_{0}, y_{0}\right)\\
F_{279}\! \left(x , y_{0}, y_{1}\right) &= F_{280}\! \left(x , y_{0}, y_{1}\right)\\
F_{280}\! \left(x , y_{0}, y_{1}\right) &= F_{223}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)\\
F_{281}\! \left(x , y_{0}\right) &= F_{163}\! \left(x , y_{0}\right) F_{282}\! \left(x , y_{0}\right)\\
F_{282}\! \left(x , y_{0}\right) &= F_{283}\! \left(x , y_{0}\right)\\
F_{283}\! \left(x , y_{0}\right) &= F_{220}\! \left(x , 1, y_{0}\right)\\
F_{284}\! \left(x , y_{0}\right) &= F_{285}\! \left(x , y_{0}\right)\\
F_{99}\! \left(x , y_{0}\right) &= F_{285}\! \left(x , y_{0}\right)+F_{286}\! \left(x , y_{0}\right)\\
F_{286}\! \left(x , y_{0}\right) &= F_{114}\! \left(x , 1, y_{0}\right)\\
F_{287}\! \left(x , y_{0}, y_{1}\right) &= F_{288}\! \left(x , y_{0}, y_{1}\right)\\
F_{288}\! \left(x , y_{0}, y_{1}\right) &= F_{289}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)\\
F_{289}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{96}\! \left(x , y_{0}, y_{1}\right)+F_{96}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{290}\! \left(x , y_{0}, y_{1}\right) &= F_{168}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{291}\! \left(x , y_{0}\right) &= F_{292}\! \left(x , y_{0}\right)\\
F_{292}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{293}\! \left(x , y_{0}\right)\\
F_{293}\! \left(x , y_{0}\right) &= F_{294}\! \left(x , y_{0}, 1\right)\\
F_{294}\! \left(x , y_{0}, y_{1}\right) &= F_{154}\! \left(x , y_{0} y_{1}, y_{0}\right)\\
\end{align*}\)