Av(13524, 14523, 14532, 24531)
Counting Sequence
1, 1, 2, 6, 24, 116, 634, 3762, 23639, 154842, 1046412, 7244248, 51118497, 366321049, 2658572316, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 230 rules.
Finding the specification took 22154 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_{82}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x^{3} F_{5} \left(x \right)^{2}+3 x^{2} F_{5} \left(x \right)^{2}+8 x^{2} F_{5}\! \left(x \right)+3 x F_{5} \left(x \right)^{2}-20 x F_{5}\! \left(x \right)+F_{5} \left(x \right)^{2}+16 x\\
F_{6}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{82}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)+F_{6}\! \left(x \right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{80}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right)+F_{4}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , 1, y_{0}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{205}\! \left(x , y_{0}, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x , y_{0}\right)\\
F_{23}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right)^{2} F_{25}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{1}\right) F_{82}\! \left(x \right)\\
F_{28}\! \left(x , y_{0}\right) &= F_{29}\! \left(x , 1, y_{0}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{30}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{30}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{31}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}, y_{1}\right)\\
F_{31}\! \left(x , y_{0}\right) &= x^{3} F_{31}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{31}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{31}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{31}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{31}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{31}\! \left(x , y_{0}\right)^{2}\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{34}\! \left(y_{0} x , y_{1}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)+F_{34}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{186}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)\\
F_{37}\! \left(x , y_{0}\right) &= F_{36}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{37}\! \left(x , y_{0}\right) &= F_{38}\! \left(x , y_{0}\right)\\
F_{38}\! \left(x , y_{0}\right) &= F_{2}\! \left(x \right)+F_{39}\! \left(x , y_{0}\right)\\
F_{39}\! \left(x , y_{0}\right) &= F_{40}\! \left(x , y_{0}\right)\\
F_{40}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}\right)\\
F_{41}\! \left(x , y_{0}\right) &= F_{42}\! \left(x , y_{0}\right)+F_{43}\! \left(x , y_{0}\right)\\
F_{42}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{38}\! \left(x , y_{0}\right)\\
F_{44}\! \left(x , y_{0}\right) &= F_{184}\! \left(x , y_{0}\right)+F_{43}\! \left(x , y_{0}\right)\\
F_{45}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}\right)\\
F_{45}\! \left(x , y_{0}\right) &= F_{46}\! \left(x , y_{0}\right)\\
F_{46}\! \left(x , y_{0}\right) &= F_{47}\! \left(x , y_{0}\right)\\
F_{47}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{48}\! \left(x , y_{0}\right)\\
F_{48}\! \left(x , y_{0}\right) &= F_{49}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= F_{50}\! \left(x , 1, y_{0}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{51}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{51}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{0}\! \left(x \right)+F_{52}\! \left(x , y_{0}, y_{1}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}\right) &= F_{53}\! \left(x , y_{0}, y_{1}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}\right) &= y_{0} y_{1} F_{54}\! \left(x , y_{0}, y_{1}\right)\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{56}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{35}\! \left(x , y_{2}\right) F_{61}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)\\
F_{61}\! \left(x , y_{0}, y_{1}\right) &= F_{5}\! \left(x \right)+F_{62}\! \left(x , y_{0}, y_{1}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}\right) &= F_{63}\! \left(x , y_{0}, y_{1}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}\right) &= y_{0} y_{1} F_{64}\! \left(x , y_{0}, y_{1}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{65}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)\\
F_{65}\! \left(x , y_{0}, y_{1}\right) &= F_{66}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{67}\! \left(x , y_{0}, y_{1} y_{2}, 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_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{2}\right) F_{61}\! \left(x , y_{0}, y_{1}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{61}\! \left(x , y_{0}, y_{1}\right) F_{71}\! \left(x , y_{2}\right) F_{82}\! \left(x \right)\\
F_{72}\! \left(x , y_{0}\right) &= F_{71}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{72}\! \left(x , y_{0}\right) &= F_{73}\! \left(x , y_{0}\right)\\
F_{74}\! \left(x , y_{0}\right) &= F_{73}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)\\
F_{75}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{74}\! \left(x , y_{0}\right)\\
F_{75}\! \left(x , y_{0}\right) &= F_{76}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)\\
F_{77}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}\right)\\
F_{78}\! \left(x , y_{0}\right) &= F_{76}\! \left(x , y_{0}\right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= x^{3} F_{79} \left(x \right)^{2}+2 x^{3} F_{79}\! \left(x \right)+3 x^{2} F_{79} \left(x \right)^{2}+x^{3}+14 x^{2} F_{79}\! \left(x \right)+3 x F_{79} \left(x \right)^{2}+11 x^{2}-14 x F_{79}\! \left(x \right)+F_{79} \left(x \right)^{2}-x +2 F_{79}\! \left(x \right)\\
F_{81}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{81}\! \left(x , y_{0}\right) &= F_{43}\! \left(x , y_{0}\right)\\
F_{82}\! \left(x \right) &= x\\
F_{83}\! \left(x , y_{0}\right) &= F_{84}\! \left(x , y_{0}\right)\\
F_{84}\! \left(x , y_{0}\right) &= F_{82}\! \left(x \right) F_{85}\! \left(x , y_{0}\right)\\
F_{86}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{85}\! \left(x , y_{0}\right)\\
F_{86}\! \left(x , y_{0}\right) &= F_{87}\! \left(x , y_{0}\right)\\
F_{87}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{88}\! \left(x , y_{0}\right)\\
F_{88}\! \left(x , y_{0}\right) &= F_{89}\! \left(x , 1, y_{0}\right)\\
F_{89}\! \left(x , y_{0}, y_{1}\right) &= F_{182}\! \left(x , y_{0}, y_{1}\right)+F_{90}\! \left(x , y_{0}, y_{1}\right)\\
F_{90}\! \left(x , y_{0}, y_{1}\right) &= F_{126}\! \left(x , y_{0}, y_{1}\right)+F_{91}\! \left(x , y_{0}, y_{1}\right)\\
F_{91}\! \left(x , y_{0}, y_{1}\right) &= F_{111}\! \left(x , y_{0}, y_{1}\right) F_{92}\! \left(x , y_{0}\right)\\
F_{92}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{93}\! \left(x , y_{0}\right)\\
F_{93}\! \left(x , y_{0}\right) &= F_{94}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)\\
F_{94}\! \left(x , y_{0}\right) &= x^{2} F_{94}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+x F_{94}\! \left(x , y_{0}\right)^{4} y_{0}+2 x^{2} F_{94}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{94}\! \left(x , y_{0}\right)^{3} y_{0}+x^{2} y_{0}^{2}+x F_{94}\! \left(x , y_{0}\right)^{2} y_{0}-x F_{94}\! \left(x , y_{0}\right) y_{0}-F_{94}\! \left(x , y_{0}\right)^{3}+F_{94}\! \left(x , y_{0}\right)\\
F_{95}\! \left(x , y_{0}\right) &= F_{96}\! \left(x , y_{0}\right)\\
F_{96}\! \left(x , y_{0}\right) &= F_{82}\! \left(x \right) F_{97}\! \left(x , y_{0}\right)\\
F_{97}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{98}\! \left(x , y_{0}\right) &= F_{99}\! \left(x , y_{0}\right)\\
F_{99}\! \left(x , y_{0}\right) &= F_{100}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)\\
F_{101}\! \left(x , y_{0}\right) &= F_{100}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{101}\! \left(x , y_{0}\right) &= F_{102}\! \left(x , y_{0}\right)\\
F_{102}\! \left(x , y_{0}\right) &= F_{103}\! \left(x , y_{0}\right)+F_{104}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}\right) &= F_{2}\! \left(x \right)+F_{95}\! \left(x , y_{0}\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_{25}\! \left(x , y_{1}\right)\\
F_{107}\! \left(x , y_{0}, y_{1}\right) &= F_{108}\! \left(x , y_{0}, y_{1}\right)+F_{124}\! \left(x , y_{0}, y_{1}\right)\\
F_{108}\! \left(x , y_{0}, y_{1}\right) &= F_{109}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)\\
F_{109}\! \left(x , y_{0}, y_{1}\right) &= F_{103}\! \left(x , y_{0}\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_{0} y_{1}\right)\\
F_{111}\! \left(x , y_{0}, y_{1}\right) &= F_{112}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{113}\! \left(x , y_{1}\right)+F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{113}\! \left(x , y_{0}\right) &= x^{2} F_{113}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+y_{0} x F_{113}\! \left(x , y_{0}\right)^{4}-x F_{113}\! \left(x , y_{0}\right)^{3} y_{0}-2 x F_{113}\! \left(x , y_{0}\right)^{2} y_{0}+2 x F_{113}\! \left(x , y_{0}\right) y_{0}-F_{113}\! \left(x , y_{0}\right)^{3}+3 F_{113}\! \left(x , y_{0}\right)^{2}-2 F_{113}\! \left(x , y_{0}\right)+1\\
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{113}\! \left(x , y_{1}\right) F_{116}\! \left(x , y_{0}, y_{2}, y_{1}\right) F_{118}\! \left(x , y_{0}, y_{2}\right)\\
F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= y_{0} y_{1} F_{117}\! \left(x , y_{2}, y_{1}\right)\\
F_{117}\! \left(x , y_{0}, y_{1}\right) &= F_{111}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)\\
F_{118}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{119}\! \left(x , y_{0}, y_{1}\right)\\
F_{119}\! \left(x , y_{0}, y_{1}\right) &= F_{120}\! \left(x , y_{0}, y_{1}\right)\\
F_{120}\! \left(x , y_{0}, y_{1}\right) &= F_{118}\! \left(x , y_{0}, y_{1}\right) F_{121}\! \left(x , y_{0}, y_{1}\right)\\
F_{121}\! \left(x , y_{0}, y_{1}\right) &= y_{0} y_{1} F_{122}\! \left(x , y_{1}\right)\\
F_{122}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{123}\! \left(x , y_{0}, y_{1}\right) &= F_{105}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{124}\! \left(x , y_{0}, y_{1}\right) &= F_{125}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{125}\! \left(x , y_{0}, y_{1}\right) &= F_{126}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \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_{127}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{129}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right) F_{178}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{129}\! \left(x , y_{0}, y_{1}\right) &= F_{130}\! \left(x , y_{0}, y_{1}\right)\\
F_{130}\! \left(x , y_{0}, y_{1}\right) &= F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{172}\! \left(x , y_{0}, y_{1}\right)\\
F_{132}\! \left(x , y_{0}, y_{1}\right) &= F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)\\
F_{132}\! \left(x , y_{0}, y_{1}\right) &= F_{133}\! \left(x , y_{0}, y_{1}\right)+F_{136}\! \left(x , y_{0}, y_{1}\right)\\
F_{133}\! \left(x , y_{0}, y_{1}\right) &= F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{92}\! \left(x , y_{0}\right)\\
F_{134}\! \left(x , y_{0}, y_{1}\right) &= F_{135}\! \left(x , y_{0}, y_{1}\right)\\
F_{135}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{1}\right) F_{89}\! \left(x , y_{0}, y_{1}\right)\\
F_{136}\! \left(x , y_{0}, y_{1}\right) &= F_{137}\! \left(x , y_{0}, y_{1}\right)\\
F_{137}\! \left(x , y_{0}, y_{1}\right) &= F_{138}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)\\
F_{138}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{139}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{139}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{139}\! \left(x , y_{0}, y_{1}\right) &= F_{130}\! \left(x , y_{0}, y_{1}\right)+F_{140}\! \left(x , y_{0}, y_{1}\right)\\
F_{140}\! \left(x , y_{0}, y_{1}\right) &= F_{111}\! \left(x , y_{0}, y_{1}\right) F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x , 1\right)\\
F_{149}\! \left(x , y_{0}\right) &= F_{90}\! \left(x , 1, y_{0}\right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{17}\! \left(x , 1\right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x , 1\right)\\
F_{155}\! \left(x , y_{0}\right) &= F_{156}\! \left(x , y_{0}\right)+F_{160}\! \left(x , y_{0}\right)\\
F_{156}\! \left(x , y_{0}\right) &= F_{157}\! \left(x \right) F_{22}\! \left(x , y_{0}\right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{85}\! \left(x , 1\right)\\
F_{160}\! \left(x , y_{0}\right) &= F_{161}\! \left(x , y_{0}\right)\\
F_{161}\! \left(x , y_{0}\right) &= F_{162}\! \left(x \right) F_{35}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x , 1\right)\\
F_{164}\! \left(x , y_{0}\right) &= F_{163}\! \left(x , y_{0}\right)+F_{167}\! \left(x , y_{0}\right)\\
F_{165}\! \left(x , y_{0}\right) &= F_{164}\! \left(x , y_{0}\right) F_{25}\! \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_{33}\! \left(x , y_{0}, 1\right)\\
F_{167}\! \left(x , y_{0}\right) &= F_{168}\! \left(y_{0} x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x , 1\right)\\
F_{169}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{170}\! \left(x , y_{0}\right)+F_{170}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{170}\! \left(x , y_{0}\right) &= F_{61}\! \left(x , y_{0}, 1\right)\\
F_{171}\! \left(x , y_{0}, y_{1}\right) &= F_{0}\! \left(x \right) F_{111}\! \left(x , y_{0}, y_{1}\right)\\
F_{172}\! \left(x , y_{0}, y_{1}\right) &= F_{173}\! \left(x , y_{0}, y_{1}\right)\\
F_{173}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right) F_{174}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x , 1\right)\\
F_{177}\! \left(x , y_{0}\right) &= F_{65}\! \left(x , 1, y_{0}\right)\\
F_{178}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{5}\! \left(x \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_{35}\! \left(x , y_{1}\right) F_{82}\! \left(x \right)\\
F_{181}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{1} \left(F_{34}\! \left(x , y_{0}\right)-F_{34}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{182}\! \left(x , y_{0}, y_{1}\right) &= F_{179}\! \left(x , y_{0}, y_{1}\right)+F_{183}\! \left(x , y_{0}, y_{1}\right)\\
F_{183}\! \left(x , y_{0}, y_{1}\right) &= F_{134}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)\\
F_{184}\! \left(x , y_{0}\right) &= F_{185}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{185}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{46}\! \left(x , y_{0}\right)\\
F_{187}\! \left(x , y_{0}\right) &= F_{186}\! \left(x , y_{0}\right)+F_{204}\! \left(x , y_{0}\right)\\
F_{188}\! \left(x , y_{0}\right) &= F_{187}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{188}\! \left(x , y_{0}\right) &= F_{189}\! \left(x , y_{0}\right)\\
F_{189}\! \left(x , y_{0}\right) &= F_{190}\! \left(x , y_{0}\right)\\
F_{190}\! \left(x , y_{0}\right) &= F_{191}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{191}\! \left(x , y_{0}\right) &= F_{192}\! \left(x , y_{0}\right)+F_{195}\! \left(x , y_{0}\right)\\
F_{192}\! \left(x , y_{0}\right) &= F_{193}\! \left(x , y_{0}\right)\\
F_{193}\! \left(x , y_{0}\right) &= F_{194}\! \left(x \right) F_{35}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{80}\! \left(x , 1\right)\\
F_{88}\! \left(x , y_{0}\right) &= F_{195}\! \left(x , y_{0}\right)+F_{196}\! \left(x , y_{0}\right)\\
F_{196}\! \left(x , y_{0}\right) &= F_{197}\! \left(x , 1, y_{0}\right)\\
F_{197}\! \left(x , y_{0}, y_{1}\right) &= F_{198}\! \left(x , y_{0}, y_{1}\right)+F_{203}\! \left(x , y_{0}, y_{1}\right)\\
F_{198}\! \left(x , y_{0}, y_{1}\right) &= F_{199}\! \left(x , y_{0}, y_{1}\right)+F_{200}\! \left(x , y_{0}, y_{1}\right)\\
F_{199}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{1}\right) F_{92}\! \left(x , y_{0}\right)\\
F_{200}\! \left(x , y_{0}, y_{1}\right) &= F_{201}\! \left(x , y_{0}, y_{0} y_{1}\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_{35}\! \left(x , y_{1}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{203}\! \left(x , y_{0}, y_{1}\right) &= F_{182}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{204}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}\right) F_{79}\! \left(x \right)\\
F_{205}\! \left(x , y_{0}, y_{1}\right) &= F_{206}\! \left(x , y_{1}\right)+F_{228}\! \left(x , y_{0}, y_{1}\right)\\
F_{207}\! \left(x , y_{0}\right) &= F_{206}\! \left(x , y_{0}\right)+F_{224}\! \left(x , y_{0}\right)\\
F_{207}\! \left(x , y_{0}\right) &= F_{208}\! \left(x , y_{0}\right)+F_{212}\! \left(x , y_{0}\right)\\
F_{208}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)+F_{209}\! \left(x , y_{0}\right)\\
F_{209}\! \left(x , y_{0}\right) &= -\frac{-F_{210}\! \left(x , y_{0}\right) y_{0}+F_{210}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{210}\! \left(x , y_{0}\right) &= F_{189}\! \left(x , y_{0}\right)+F_{211}\! \left(x , y_{0}\right)\\
F_{211}\! \left(x , y_{0}\right) &= F_{2}\! \left(x \right) F_{22}\! \left(x , y_{0}\right)\\
F_{212}\! \left(x , y_{0}\right) &= F_{213}\! \left(x , y_{0}\right)\\
F_{213}\! \left(x , y_{0}\right) &= F_{214}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{214}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{215}\! \left(x , y_{0}\right)+F_{215}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{215}\! \left(x , y_{0}\right) &= F_{216}\! \left(x , y_{0}\right)+F_{218}\! \left(x , y_{0}\right)\\
F_{216}\! \left(x , y_{0}\right) &= F_{155}\! \left(x , y_{0}\right)+F_{217}\! \left(x , y_{0}\right)\\
F_{217}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , 1, y_{0}\right)\\
F_{218}\! \left(x , y_{0}\right) &= F_{219}\! \left(x , y_{0}\right)\\
F_{219}\! \left(x , y_{0}\right) &= F_{194}\! \left(x \right) F_{220}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{221}\! \left(x , y_{0}\right) &= F_{220}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{221}\! \left(x , y_{0}\right) &= F_{222}\! \left(x , y_{0}\right)\\
F_{222}\! \left(x , y_{0}\right) &= F_{223}\! \left(x , 1, y_{0}\right)\\
F_{223}\! \left(x , y_{0}, y_{1}\right) &= F_{205}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{224}\! \left(x , y_{0}\right) &= F_{225}\! \left(x , y_{0}\right)+F_{226}\! \left(x , y_{0}\right)\\
F_{225}\! \left(x , y_{0}\right) &= F_{185}\! \left(x , y_{0}\right)+F_{210}\! \left(x , y_{0}\right)\\
F_{226}\! \left(x , y_{0}\right) &= F_{227}\! \left(x , y_{0}\right)\\
F_{227}\! \left(x , y_{0}\right) &= F_{216}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
F_{228}\! \left(x , y_{0}, y_{1}\right) &= F_{229}\! \left(x , y_{0}, y_{1}\right)\\
F_{229}\! \left(x , y_{0}, y_{1}\right) &= F_{220}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)\\
\end{align*}\)