Av(12435, 12453, 12543, 21435, 21453, 21543, 24135, 24153, 24315)
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Counting Sequence
1, 1, 2, 6, 24, 111, 546, 2750, 13964, 71053, 361463, 1837101, 9326799, 47304609, 239726485, ...
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 289 rules.

Finding the specification took 39451 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_{27}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= 4 F_{5} \left(x \right)^{2} x +x^{2}-8 F_{5}\! \left(x \right) x -F_{5} \left(x \right)^{2}+4 x +3 F_{5}\! \left(x \right)-1\\ 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_{27}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{12}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{11}\! \left(x \right) &= 4 x F_{11} \left(x \right)^{2}+x^{2}-F_{11} \left(x \right)^{2}+F_{11}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{276}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{192}\! \left(x \right) F_{75}\! \left(x \right)}\\ F_{15}\! \left(x \right) &= -F_{262}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= \frac{F_{17}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= -F_{261}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{252}\! \left(x \right)\\ F_{20}\! \left(x \right) &= -F_{192}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{22}\! \left(x \right) &= -F_{206}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{25}\! \left(x \right) &= x^{2} F_{25} \left(x \right)^{2}+4 x^{2} F_{25}\! \left(x \right)+4 x F_{25} \left(x \right)^{2}+4 x^{2}-5 x F_{25}\! \left(x \right)-F_{25} \left(x \right)^{2}-x +2 F_{25}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{11}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= x\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{27}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{75}\! \left(x \right)}\\ F_{32}\! \left(x \right) &= -F_{119}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{27}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{27}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{27}\! \left(x \right) F_{44}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{27}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{45}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{45} \left(x \right)^{2} F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{27}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{27}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{27}\! \left(x \right) F_{75}\! \left(x \right)}\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{75} \left(x \right)^{2} F_{27}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{27}\! \left(x \right) F_{75}\! \left(x \right)}\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{67}\! \left(x \right) &= -F_{71}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{27}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= \frac{F_{74}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{74}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{27}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{75} \left(x \right)^{2} F_{27}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{75}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{27}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{27}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{27}\! \left(x \right) F_{45}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{57}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{45}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{27}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{27}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{104}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{83}\! \left(x \right)\\ F_{106}\! \left(x \right) &= \frac{F_{107}\! \left(x \right)}{F_{109}\! \left(x \right) F_{27}\! \left(x \right)}\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{45} \left(x \right)^{2} F_{109}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{109}\! \left(x \right) &= \frac{F_{110}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{110}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{113}\! \left(x \right) &= \frac{F_{114}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{27}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{25}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{122}\! \left(x \right)\\ F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{121}\! \left(x \right) &= F_{37}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{27}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{251}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{129}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{27}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{136}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{75} \left(x \right)^{2} F_{27}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{136}\! \left(x \right) &= \frac{F_{137}\! \left(x \right)}{F_{141}\! \left(x \right)}\\ F_{137}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{133}\! \left(x \right) F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{140}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{242}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{143}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{48}\! \left(x \right)}\\ F_{144}\! \left(x \right) &= -F_{239}\! \left(x \right)+F_{145}\! \left(x \right)\\ F_{145}\! \left(x \right) &= \frac{F_{146}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{150}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{2}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{155}\! \left(x \right) &= -F_{165}\! \left(x \right)+F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= \frac{F_{157}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{158}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{12}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{139}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{141}\! \left(x \right) F_{27}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{168}\! \left(x \right) &= \frac{F_{169}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\ F_{170}\! \left(x \right) &= -F_{173}\! \left(x \right)+F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= \frac{F_{172}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{172}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{229}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{141}\! \left(x \right) F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= -F_{212}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= -F_{193}\! \left(x \right)+F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= \frac{F_{178}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right) F_{27}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{134}\! \left(x \right) F_{186}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{136}\! \left(x \right) F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= x^{2} F_{192} \left(x \right)^{2}+2 x^{2} F_{192}\! \left(x \right)+4 x F_{192} \left(x \right)^{2}+x^{2}-13 x F_{192}\! \left(x \right)-F_{192} \left(x \right)^{2}+8 x +4 F_{192}\! \left(x \right)-2\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{208}\! \left(x \right)\\ F_{194}\! \left(x \right) &= -F_{207}\! \left(x \right)+F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= -F_{198}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= \frac{F_{197}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{197}\! \left(x \right) &= F_{179}\! \left(x \right)\\ F_{198}\! \left(x \right) &= -F_{201}\! \left(x \right)+F_{199}\! \left(x \right)\\ F_{199}\! \left(x \right) &= \frac{F_{200}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{200}\! \left(x \right) &= F_{180}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{204}\! \left(x \right) &= \frac{F_{205}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{207}\! \left(x \right) &= -F_{154}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{208}\! \left(x \right) &= -F_{228}\! \left(x \right)+F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= -F_{213}\! \left(x \right)+F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= \frac{F_{211}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\ F_{212}\! \left(x \right) &= -F_{22}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{215}\! \left(x \right) &= \frac{F_{216}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\ F_{217}\! \left(x \right) &= -F_{220}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= \frac{F_{219}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{219}\! \left(x \right) &= F_{212}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{227}\! \left(x \right)\\ F_{222}\! \left(x \right) &= -F_{225}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= \frac{F_{224}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{224}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{101}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{27}\! \left(x \right) F_{42}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{228}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right) F_{231}\! \left(x \right)\\ F_{230}\! \left(x \right) &= -F_{141}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{231}\! \left(x \right) &= -F_{232}\! \left(x \right)+F_{133}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{234}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{5}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{106}\! \left(x \right) F_{27}\! \left(x \right) F_{45}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{238}\! \left(x \right) F_{44}\! \left(x \right) F_{45}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{140}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{45} \left(x \right)^{2} F_{241}\! \left(x \right)\\ F_{241}\! \left(x \right) &= -F_{55}\! \left(x \right)+F_{238}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{244}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{244}\! \left(x \right) &= -F_{245}\! \left(x \right)+F_{161}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{250}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{248}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{248}\! \left(x \right) &= \frac{F_{249}\! \left(x \right)}{F_{27}\! \left(x \right)}\\ F_{249}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{230}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{27}\! \left(x \right) F_{44}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{254}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{192}\! \left(x \right) F_{256}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{259}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{260}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{11}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{11}\! \left(x \right) F_{186}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{132}\! \left(x \right) F_{265}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{267}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{269}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{270}\! \left(x \right)+F_{274}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{272}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{2}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{269}\! \left(x \right) F_{27}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{274}\! \left(x \right) &= -F_{275}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{27}\! \left(x \right) F_{278}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)+F_{284}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{133}\! \left(x \right) F_{280}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{281}\! \left(x \right)+F_{282}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{0}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{103}\! \left(x \right) F_{139}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{286}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{133}\! \left(x \right) F_{274}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{136}\! \left(x \right) F_{287}\! \left(x \right)\\ F_{287}\! \left(x \right) &= -F_{288}\! \left(x \right)+F_{141}\! \left(x \right)\\ F_{288}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{266}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 171 rules.

Finding the specification took 6434 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_{21}\! \left(x \right) F_{4}\! \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_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= 4 x F_{6} \left(x \right)^{2}+x^{2}-F_{6} \left(x \right)^{2}+F_{6}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{21}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{11}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{138}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20} \left(x \right)^{2} F_{21}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{21}\! \left(x \right) &= x\\ F_{22}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= -F_{121}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= -F_{27}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= \frac{F_{26}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{26}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{21}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{21}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{20}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x , 1\right)\\ F_{38}\! \left(x , y\right) &= -\frac{-F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}\\ F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)^{2} F_{42}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)\\ F_{42}\! \left(x , y\right) &= y x\\ F_{43}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= -F_{47}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{46}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{21}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{34}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x , 1\right)\\ F_{52}\! \left(x , y\right) &= -\frac{-y F_{41}\! \left(x , y\right)+F_{41}\! \left(x , 1\right)}{-1+y}\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{21}\! \left(x \right) F_{55}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{55}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= \frac{F_{58}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= -F_{17}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= -F_{61}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{105}\! \left(x \right) F_{21}\! \left(x \right)}\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x , 1\right)\\ F_{67}\! \left(x , y\right) &= -\frac{-y F_{68}\! \left(x , y\right)+F_{68}\! \left(x , 1\right)}{-1+y}\\ F_{68}\! \left(x , y\right) &= F_{69}\! \left(x , y\right)\\ F_{69}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{61}\! \left(x \right) F_{70}\! \left(x , y\right)\\ F_{70}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{71}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= \frac{F_{74}\! \left(x \right)}{F_{21}\! \left(x \right) F_{76}\! \left(x \right)}\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{20} \left(x \right)^{2} F_{21}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= \frac{F_{77}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{77}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= -F_{81}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= \frac{F_{80}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{80}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{21}\! \left(x \right) F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= -F_{86}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{88}\! \left(x \right) &= x^{2} F_{88} \left(x \right)^{2}+4 x^{2} F_{88}\! \left(x \right)+4 x F_{88} \left(x \right)^{2}+4 x^{2}-5 x F_{88}\! \left(x \right)-F_{88} \left(x \right)^{2}-x +2 F_{88}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{18}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{21}\! \left(x \right) F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{21}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{20}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{96}\! \left(x , 1\right)\\ F_{96}\! \left(x , y\right) &= F_{41}\! \left(x , y\right) F_{97}\! \left(x , y\right)\\ F_{97}\! \left(x , y\right) &= -\frac{y \left(-F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)\right)}{-1+y}\\ F_{98}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{21}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)\\ F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{41}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{72}\! \left(x \right)\\ F_{102}\! \left(x , y\right) &= -\frac{-y F_{41}\! \left(x , y\right)+F_{41}\! \left(x , 1\right)}{-1+y}\\ F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)\\ F_{104}\! \left(x , y\right) &= F_{41}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{70}\! \left(x , y\right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{105}\! \left(x \right) F_{20}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{114}\! \left(x \right) &= \frac{F_{115}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right) F_{15}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{70}\! \left(x , 1\right)\\ F_{119}\! \left(x \right) &= F_{35}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{120}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{136}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{133}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{130}\! \left(x \right) &= \frac{F_{131}\! \left(x \right)}{F_{133} \left(x \right)^{2} F_{21}\! \left(x \right)}\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{118}\! \left(x \right) F_{133}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{133}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{21}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{138}\! \left(x \right) &= \frac{F_{139}\! \left(x \right)}{F_{21}\! \left(x \right) F_{61}\! \left(x \right)}\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x , 1\right)\\ F_{142}\! \left(x , y\right) &= -\frac{y \left(F_{143}\! \left(x , 1\right)-F_{143}\! \left(x , y\right)\right)}{-1+y}\\ F_{143}\! \left(x , y\right) &= y^{2} x^{2}+4 x F_{143}\! \left(x , y\right)^{2} y -F_{143}\! \left(x , y\right)^{2}+F_{143}\! \left(x , y\right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{138}\! \left(x \right) F_{146}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{151}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{20}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{151}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= -F_{155}\! \left(x \right)+F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= \frac{F_{154}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{154}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{155}\! \left(x \right) &= \frac{F_{156}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= -F_{158}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{158}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{159}\! \left(x \right) &= \frac{F_{160}\! \left(x \right)}{F_{20}\! \left(x \right)}\\ F_{160}\! \left(x \right) &= -F_{163}\! \left(x \right)+F_{161}\! \left(x \right)\\ F_{161}\! \left(x \right) &= \frac{F_{162}\! \left(x \right)}{F_{21}\! \left(x \right)}\\ F_{162}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right) F_{21}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{165}\! \left(x \right) &= \frac{F_{166}\! \left(x \right)}{F_{20}\! \left(x \right) F_{21}\! \left(x \right)}\\ F_{166}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{133} \left(x \right)^{2} F_{130}\! \left(x \right) F_{21}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 441 rules.

Finding the specification took 22309 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_{25}\! \left(x \right) F_{4}\! \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_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= 4 x F_{6} \left(x \right)^{2}+x^{2}-F_{6} \left(x \right)^{2}+F_{6}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{25}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{11}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{434}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{183}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{15}\! \left(x \right) &= x^{2} F_{15} \left(x \right)^{2}+2 x^{2} F_{15}\! \left(x \right)+4 x F_{15} \left(x \right)^{2}+x^{2}-13 x F_{15}\! \left(x \right)-F_{15} \left(x \right)^{2}+8 x +4 F_{15}\! \left(x \right)-2\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{335}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{2}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{25}\! \left(x \right) &= x\\ F_{26}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{22}\! \left(x \right) F_{25}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{19}\! \left(x \right) F_{25}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{25}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{25}\! \left(x \right) F_{57}\! \left(x \right)}\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{57} \left(x \right)^{2} F_{25}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{25}\! \left(x \right) F_{57}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= -F_{22}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= \frac{F_{41}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{41}\! \left(x \right) &= -F_{44}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{43}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{433}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= -F_{48}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{47}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{2}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{25}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{19}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57} \left(x \right)^{2} F_{25}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{25}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{374}\! \left(x \right) F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= -F_{14}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{280}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{111}\! \left(x \right)}\\ F_{66}\! \left(x \right) &= -F_{430}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= -F_{429}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= \frac{F_{72}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{72}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= x^{2} F_{76} \left(x \right)^{2}+4 x^{2} F_{76}\! \left(x \right)+4 x F_{76} \left(x \right)^{2}+4 x^{2}-5 x F_{76}\! \left(x \right)-F_{76} \left(x \right)^{2}-x +2 F_{76}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{25}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{6}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= \frac{F_{82}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{82}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{63}\! \left(x \right) F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{15}\! \left(x \right) F_{57}\! \left(x \right)}\\ F_{85}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= -F_{194}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= -F_{15}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{92}\! \left(x \right) &= 4 F_{92} \left(x \right)^{2} x +x^{2}-8 F_{92}\! \left(x \right) x -F_{92} \left(x \right)^{2}+4 x +3 F_{92}\! \left(x \right)-1\\ F_{93}\! \left(x \right) &= -F_{186}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{25}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{25}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{177}\! \left(x \right)\\ F_{100}\! \left(x \right) &= \frac{F_{101}\! \left(x \right)}{F_{57}\! \left(x \right)}\\ F_{101}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= \frac{F_{103}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{132}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{121}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{23}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{22}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{22}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{22} \left(x \right)^{2} F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{25}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{129}\! \left(x \right)+F_{131}\! \left(x \right)\\ F_{128}\! \left(x \right) &= 0\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{25}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{146}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{22}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{145}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{31}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{140}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{139}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{134}\! \left(x \right) F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= \frac{F_{158}\! \left(x \right)}{F_{160}\! \left(x \right) F_{25}\! \left(x \right)}\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{22} \left(x \right)^{2} F_{160}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{160}\! \left(x \right) &= \frac{F_{161}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{161}\! \left(x \right) &= -F_{170}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{164}\! \left(x \right) &= \frac{F_{165}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{23}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{112}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{25}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right) F_{175}\! \left(x \right)\\ F_{173}\! \left(x \right) &= \frac{F_{174}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{174}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{25}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{185}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{167}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{183}\! \left(x \right) &= \frac{F_{184}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{184}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{119}\! \left(x \right) F_{25}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{15}\! \left(x \right) F_{191}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{124}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{181}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{121}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{121}\! \left(x \right) F_{196}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{196}\! \left(x \right) F_{25}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{201}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{350}\! \left(x \right)\\ F_{202}\! \left(x \right) &= -F_{265}\! \left(x \right)+F_{203}\! \left(x \right)\\ F_{203}\! \left(x \right) &= -F_{207}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= \frac{F_{205}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= -F_{74}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{209}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{209}\! \left(x \right) &= \frac{F_{210}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{257}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{213}\! \left(x \right) &= -F_{240}\! \left(x \right)+F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= -F_{221}\! \left(x \right)+F_{215}\! \left(x \right)\\ F_{215}\! \left(x \right) &= \frac{F_{216}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\ F_{217}\! \left(x \right) &= -F_{170}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{25}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{222}\! \left(x \right) &= -F_{234}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= -F_{226}\! \left(x \right)+F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= \frac{F_{225}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{225}\! \left(x \right) &= F_{217}\! \left(x \right)\\ F_{226}\! \left(x \right) &= -F_{229}\! \left(x \right)+F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= \frac{F_{228}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{228}\! \left(x \right) &= F_{218}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{232}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{232}\! \left(x \right) &= \frac{F_{233}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{233}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{234}\! \left(x \right) &= -F_{235}\! \left(x \right)+F_{232}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{236}\! \left(x \right) &= -F_{256}\! \left(x \right)+F_{237}\! \left(x \right)\\ F_{237}\! \left(x \right) &= -F_{241}\! \left(x \right)+F_{238}\! \left(x \right)\\ F_{238}\! \left(x \right) &= \frac{F_{239}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{243}\! \left(x \right) &= \frac{F_{244}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\ F_{245}\! \left(x \right) &= -F_{248}\! \left(x \right)+F_{246}\! \left(x \right)\\ F_{246}\! \left(x \right) &= \frac{F_{247}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{247}\! \left(x \right) &= F_{240}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)+F_{255}\! \left(x \right)\\ F_{250}\! \left(x \right) &= -F_{253}\! \left(x \right)+F_{251}\! \left(x \right)\\ F_{251}\! \left(x \right) &= \frac{F_{252}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{252}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{152}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{22}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{256}\! \left(x \right) &= -F_{92}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right) F_{259}\! \left(x \right)\\ F_{258}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{259}\! \left(x \right) &= -F_{261}\! \left(x \right)+F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{57}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{157}\! \left(x \right) F_{22}\! \left(x \right) F_{25}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= -F_{300}\! \left(x \right)+F_{267}\! \left(x \right)\\ F_{267}\! \left(x \right) &= \frac{F_{268}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= -F_{289}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= -F_{280}\! \left(x \right)+F_{271}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{25}\! \left(x \right) F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= \frac{F_{274}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{25}\! \left(x \right) F_{276}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)+F_{278}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{22}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{25}\! \left(x \right) F_{34}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{281}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{25}\! \left(x \right) F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= -F_{283}\! \left(x \right)+F_{276}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{284}\! \left(x \right)+F_{288}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{25}\! \left(x \right) F_{286}\! \left(x \right)\\ F_{286}\! \left(x \right) &= \frac{F_{287}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{287}\! \left(x \right) &= F_{278}\! \left(x \right)\\ F_{288}\! \left(x \right) &= F_{23}\! \left(x \right) F_{258}\! \left(x \right)\\ F_{289}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{290}\! \left(x \right)\\ F_{290}\! \left(x \right) &= -F_{291}\! \left(x \right)+F_{271}\! \left(x \right)\\ F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{25}\! \left(x \right) F_{293}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{25}\! \left(x \right) F_{295}\! \left(x \right)\\ F_{295}\! \left(x \right) &= F_{296}\! \left(x \right)+F_{297}\! \left(x \right)\\ F_{296}\! \left(x \right) &= F_{37}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{22}\! \left(x \right) F_{26}\! \left(x \right) F_{299}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{300}\! \left(x \right) &= F_{301}\! \left(x \right)\\ F_{301}\! \left(x \right) &= -F_{304}\! \left(x \right)+F_{302}\! \left(x \right)\\ F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{306}\! \left(x \right)\\ F_{303}\! \left(x \right) &= F_{22}\! \left(x \right) F_{304}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{305}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{25}\! \left(x \right) F_{278}\! \left(x \right)\\ F_{306}\! \left(x \right) &= F_{307}\! \left(x \right)\\ F_{307}\! \left(x \right) &= F_{25}\! \left(x \right) F_{308}\! \left(x \right)\\ F_{308}\! \left(x \right) &= \frac{F_{309}\! \left(x \right)}{F_{25}\! \left(x \right) F_{31}\! \left(x \right)}\\ F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)\\ F_{310}\! \left(x \right) &= -F_{344}\! \left(x \right)+F_{311}\! \left(x \right)\\ F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{314}\! \left(x \right)\\ F_{312}\! \left(x \right) &= F_{313}\! \left(x \right)\\ F_{313}\! \left(x \right) &= F_{25}\! \left(x \right) F_{278}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{314}\! \left(x \right) &= F_{315}\! \left(x \right)\\ F_{315}\! \left(x \right) &= -F_{320}\! \left(x \right)+F_{316}\! \left(x \right)\\ F_{316}\! \left(x \right) &= F_{317}\! \left(x \right)\\ F_{317}\! \left(x \right) &= F_{25}\! \left(x \right) F_{31}\! \left(x \right) F_{318}\! \left(x \right)\\ F_{318}\! \left(x \right) &= \frac{F_{319}\! \left(x \right)}{F_{22}\! \left(x \right) F_{25}\! \left(x \right)}\\ F_{319}\! \left(x \right) &= F_{283}\! \left(x \right)\\ F_{320}\! \left(x \right) &= \frac{F_{321}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{321}\! \left(x \right) &= F_{322}\! \left(x \right)\\ F_{322}\! \left(x \right) &= -F_{341}\! \left(x \right)+F_{323}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{324}\! \left(x \right)+F_{338}\! \left(x \right)\\ F_{324}\! \left(x \right) &= F_{325}\! \left(x \right)\\ F_{325}\! \left(x \right) &= F_{25}\! \left(x \right) F_{326}\! \left(x \right)\\ F_{326}\! \left(x \right) &= F_{327}\! \left(x \right)+F_{333}\! \left(x \right)\\ F_{327}\! \left(x \right) &= \frac{F_{328}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{328}\! \left(x \right) &= F_{329}\! \left(x \right)\\ F_{329}\! \left(x \right) &= F_{330}\! \left(x \right)+F_{331}\! \left(x \right)\\ F_{330}\! \left(x \right) &= F_{0}\! \left(x \right) F_{23}\! \left(x \right)\\ F_{331}\! \left(x \right) &= F_{332}\! \left(x \right)\\ F_{332}\! \left(x \right) &= F_{154}\! \left(x \right) F_{25}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{333}\! \left(x \right) &= F_{334}\! \left(x \right)+F_{337}\! \left(x \right)\\ F_{334}\! \left(x \right) &= F_{22}\! \left(x \right) F_{335}\! \left(x \right)\\ F_{335}\! \left(x \right) &= -F_{336}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{336}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{329}\! \left(x \right)\\ F_{337}\! \left(x \right) &= F_{312}\! \left(x \right)\\ F_{338}\! \left(x \right) &= F_{339}\! \left(x \right)\\ F_{339}\! \left(x \right) &= F_{22}\! \left(x \right) F_{340}\! \left(x \right)\\ F_{340}\! \left(x \right) &= F_{289}\! \left(x \right)\\ F_{341}\! \left(x \right) &= F_{22}\! \left(x \right) F_{342}\! \left(x \right)\\ F_{342}\! \left(x \right) &= F_{343}\! \left(x \right)\\ F_{343}\! \left(x \right) &= F_{289}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{344}\! \left(x \right) &= F_{22}\! \left(x \right) F_{345}\! \left(x \right)\\ F_{345}\! \left(x \right) &= F_{346}\! \left(x \right)\\ F_{346}\! \left(x \right) &= F_{25}\! \left(x \right) F_{31}\! \left(x \right) F_{347}\! \left(x \right)\\ F_{347}\! \left(x \right) &= \frac{F_{348}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{348}\! \left(x \right) &= F_{349}\! \left(x \right)\\ F_{349}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{350}\! \left(x \right) &= F_{351}\! \left(x \right)\\ F_{351}\! \left(x \right) &= -F_{428}\! \left(x \right)+F_{352}\! \left(x \right)\\ F_{352}\! \left(x \right) &= -F_{362}\! \left(x \right)+F_{353}\! \left(x \right)\\ F_{353}\! \left(x \right) &= \frac{F_{354}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{354}\! \left(x \right) &= F_{355}\! \left(x \right)\\ F_{355}\! \left(x \right) &= -F_{343}\! \left(x \right)+F_{356}\! \left(x \right)\\ F_{356}\! \left(x \right) &= -F_{359}\! \left(x \right)+F_{357}\! \left(x \right)\\ F_{357}\! \left(x \right) &= \frac{F_{358}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{358}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{359}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{360}\! \left(x \right)\\ F_{360}\! \left(x \right) &= F_{361}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{361}\! \left(x \right) &= F_{0}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{362}\! \left(x \right) &= F_{363}\! \left(x \right)\\ F_{363}\! \left(x \right) &= -F_{382}\! \left(x \right)+F_{364}\! \left(x \right)\\ F_{364}\! \left(x \right) &= \frac{F_{365}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{365}\! \left(x \right) &= F_{366}\! \left(x \right)\\ F_{366}\! \left(x \right) &= -F_{360}\! \left(x \right)+F_{367}\! \left(x \right)\\ F_{367}\! \left(x \right) &= F_{368}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{368}\! \left(x \right) &= F_{369}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{369}\! \left(x \right) &= F_{370}\! \left(x \right)\\ F_{370}\! \left(x \right) &= F_{25}\! \left(x \right) F_{371}\! \left(x \right)\\ F_{371}\! \left(x \right) &= F_{372}\! \left(x \right)+F_{373}\! \left(x \right)\\ F_{372}\! \left(x \right) &= F_{196}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{373}\! \left(x \right) &= F_{15}\! \left(x \right) F_{374}\! \left(x \right)\\ F_{374}\! \left(x \right) &= -F_{377}\! \left(x \right)+F_{375}\! \left(x \right)\\ F_{375}\! \left(x \right) &= \frac{F_{376}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{376}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{377}\! \left(x \right) &= F_{378}\! \left(x \right)+F_{379}\! \left(x \right)\\ F_{378}\! \left(x \right) &= F_{22}\! \left(x \right) F_{260}\! \left(x \right)\\ F_{379}\! \left(x \right) &= -F_{380}\! \left(x \right)+F_{375}\! \left(x \right)\\ F_{380}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{381}\! \left(x \right)\\ F_{381}\! \left(x \right) &= F_{23}\! \left(x \right) F_{260}\! \left(x \right)\\ F_{382}\! \left(x \right) &= F_{383}\! \left(x \right)\\ F_{383}\! \left(x \right) &= F_{25}\! \left(x \right) F_{384}\! \left(x \right)\\ F_{384}\! \left(x \right) &= F_{385}\! \left(x \right)+F_{426}\! \left(x \right)\\ F_{385}\! \left(x \right) &= F_{386}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{386}\! \left(x \right) &= -F_{393}\! \left(x \right)+F_{387}\! \left(x \right)\\ F_{387}\! \left(x \right) &= \frac{F_{388}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{388}\! \left(x \right) &= F_{389}\! \left(x \right)\\ F_{389}\! \left(x \right) &= -F_{392}\! \left(x \right)+F_{390}\! \left(x \right)\\ F_{390}\! \left(x \right) &= \frac{F_{391}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{391}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{392}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{343}\! \left(x \right)\\ F_{393}\! \left(x \right) &= F_{394}\! \left(x \right)+F_{409}\! \left(x \right)\\ F_{394}\! \left(x \right) &= F_{395}\! \left(x \right)\\ F_{395}\! \left(x \right) &= F_{22}\! \left(x \right) F_{26}\! \left(x \right) F_{396}\! \left(x \right)\\ F_{396}\! \left(x \right) &= \frac{F_{397}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{397}\! \left(x \right) &= -F_{407}\! \left(x \right)+F_{398}\! \left(x \right)\\ F_{398}\! \left(x \right) &= F_{399}\! \left(x \right)+F_{403}\! \left(x \right)\\ F_{399}\! \left(x \right) &= F_{400}\! \left(x \right)\\ F_{400}\! \left(x \right) &= F_{25}\! \left(x \right) F_{401}\! \left(x \right)\\ F_{401}\! \left(x \right) &= \frac{F_{402}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{402}\! \left(x \right) &= F_{329}\! \left(x \right)\\ F_{403}\! \left(x \right) &= F_{404}\! \left(x \right)\\ F_{404}\! \left(x \right) &= F_{26}\! \left(x \right) F_{405}\! \left(x \right)\\ F_{405}\! \left(x \right) &= F_{406}\! \left(x \right)\\ F_{406}\! \left(x \right) &= F_{25}\! \left(x \right) F_{299}\! \left(x \right)\\ F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)\\ F_{408}\! \left(x \right) &= F_{25}\! \left(x \right) F_{299}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{409}\! \left(x \right) &= F_{410}\! \left(x \right)\\ F_{410}\! \left(x \right) &= F_{25}\! \left(x \right) F_{299}\! \left(x \right) F_{411}\! \left(x \right)\\ F_{411}\! \left(x \right) &= \frac{F_{412}\! \left(x \right)}{F_{25}\! \left(x \right) F_{417}\! \left(x \right)}\\ F_{412}\! \left(x \right) &= F_{413}\! \left(x \right)\\ F_{413}\! \left(x \right) &= -F_{425}\! \left(x \right)+F_{414}\! \left(x \right)\\ F_{414}\! \left(x \right) &= \frac{F_{415}\! \left(x \right)}{F_{25}\! \left(x \right) F_{57} \left(x \right)^{2}}\\ F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)\\ F_{416}\! \left(x \right) &= F_{25}\! \left(x \right) F_{34}\! \left(x \right) F_{417}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{417}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{418}\! \left(x \right)\\ F_{418}\! \left(x \right) &= F_{419}\! \left(x \right)\\ F_{419}\! \left(x \right) &= F_{25}\! \left(x \right) F_{420}\! \left(x \right)\\ F_{420}\! \left(x \right) &= \frac{F_{421}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{421}\! \left(x \right) &= F_{422}\! \left(x \right)\\ F_{422}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{423}\! \left(x \right)\\ F_{423}\! \left(x \right) &= \frac{F_{424}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{424}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{425}\! \left(x \right) &= F_{26}\! \left(x \right) F_{417}\! \left(x \right)\\ F_{426}\! \left(x \right) &= F_{427}\! \left(x \right)\\ F_{427}\! \left(x \right) &= F_{57} \left(x \right)^{2} F_{25}\! \left(x \right) F_{37}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{428}\! \left(x \right) &= F_{23}\! \left(x \right) F_{336}\! \left(x \right)\\ F_{429}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{430}\! \left(x \right) &= F_{431}\! \left(x \right)\\ F_{431}\! \left(x \right) &= F_{22} \left(x \right)^{2} F_{432}\! \left(x \right)\\ F_{432}\! \left(x \right) &= -F_{119}\! \left(x \right)+F_{299}\! \left(x \right)\\ F_{433}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{434}\! \left(x \right) &= F_{435}\! \left(x \right)\\ F_{435}\! \left(x \right) &= F_{25}\! \left(x \right) F_{436}\! \left(x \right)\\ F_{436}\! \left(x \right) &= F_{437}\! \left(x \right)+F_{438}\! \left(x \right)\\ F_{437}\! \left(x \right) &= F_{260}\! \left(x \right) F_{329}\! \left(x \right)\\ F_{438}\! \left(x \right) &= F_{439}\! \left(x \right)+F_{440}\! \left(x \right)\\ F_{439}\! \left(x \right) &= F_{260}\! \left(x \right) F_{335}\! \left(x \right)\\ F_{440}\! \left(x \right) &= F_{374}\! \left(x \right) F_{62}\! \left(x \right)\\ \end{align*}\)