Av(13452, 14352, 14523, 14532, 31452, 34152, 41352, 41523, 41532, 43152)
Counting Sequence
1, 1, 2, 6, 24, 110, 542, 2786, 14758, 80008, 441856, 2477302, 14063768, 80683328, 467035458, ...
This specification was found using the strategy pack "Point Placements Req Corrob" and has 199 rules.
Finding the specification took 26094 seconds.
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Copy 199 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{11}\! \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_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= -F_{192}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{11}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{188}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{0}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= -F_{133}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{84}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{11}\! \left(x \right) F_{37}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{11}\! \left(x \right) F_{12}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{11}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{48}\! \left(x \right) &= -F_{79}\! \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_{37}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{79}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{64}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{63}\! \left(x \right) &= x^{2} F_{63} \left(x \right)^{3}+2 x^{2} F_{63} \left(x \right)^{2}+x^{2} F_{63}\! \left(x \right)+x F_{63} \left(x \right)^{2}+2 x F_{63}\! \left(x \right)+x\\
F_{64}\! \left(x \right) &= -F_{68}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{0}\! \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_{11}\! \left(x \right)}\\
F_{72}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{73}\! \left(x \right) &= -F_{76}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{75}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{2}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{77}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{37}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{12}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{11}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{40}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{0}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{0}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{95}\! \left(x \right) &= x^{2} F_{95} \left(x \right)^{3}-x^{2} F_{95} \left(x \right)^{2}+x F_{95} \left(x \right)^{2}+1\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{11}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{99}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{103}\! \left(x \right) F_{11}\! \left(x \right) F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= \frac{F_{112}\! \left(x \right)}{F_{11}\! \left(x \right) F_{94}\! \left(x \right)}\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= \frac{F_{115}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{115}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{116}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{11}\! \left(x \right) F_{111}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{11}\! \left(x \right) F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{125}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{11}\! \left(x \right) F_{111}\! \left(x \right) F_{124}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{101}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{122}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{134}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= \frac{F_{136}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{43}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= -F_{178}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{145}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= \frac{F_{147}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{147}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{11}\! \left(x \right) F_{150}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{150}\! \left(x \right) &= \frac{F_{151}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{151}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{11}\! \left(x \right) F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{0}\! \left(x \right) F_{156}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{11}\! \left(x \right) F_{159}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{11}\! \left(x \right) F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{11}\! \left(x \right) F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{146}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{172}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{2}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{5}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{11}\! \left(x \right) F_{142}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{180}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{186}\! \left(x \right) &= -F_{187}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{11}\! \left(x \right) F_{190}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{190}\! \left(x \right) &= \frac{F_{191}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{191}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{11}\! \left(x \right) F_{194}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{194}\! \left(x \right) &= \frac{F_{195}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{11}\! \left(x \right) F_{150}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Insertion Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 172 rules.
Finding the specification took 2915 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 172 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{15}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{15}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x^{2} F_{11} \left(x \right)^{3}+2 x^{2} F_{11} \left(x \right)^{2}+x^{2} F_{11}\! \left(x \right)+x F_{11} \left(x \right)^{2}+2 x F_{11}\! \left(x \right)+x\\
F_{12}\! \left(x \right) &= -F_{16}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{15}\! \left(x \right) &= x\\
F_{16}\! \left(x \right) &= x^{2} F_{16} \left(x \right)^{3}-x^{2} F_{16} \left(x \right)^{2}+x F_{16} \left(x \right)^{2}+1\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{2} \left(x \right)^{2}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{15}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{2} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{2} \left(x \right)^{2} F_{12}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{15}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{2}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{15}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{15}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{15}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{16}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{15}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{2}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= -F_{81}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{15}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{70}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{11}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= -F_{80}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= -F_{79}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= \frac{F_{78}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{78}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{11}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{11}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{52}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{16}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{15}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{15}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{2}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{15}\! \left(x \right) F_{50}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{2}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{15}\! \left(x \right) F_{90}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{115}\! \left(x \right) &= -F_{132}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= -F_{126}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= \frac{F_{118}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= -F_{91}\! \left(x \right)+F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= -F_{95}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= -F_{124}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= \frac{F_{123}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{123}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{11}\! \left(x \right) F_{131}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{121}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{108}\! \left(x \right) F_{125}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{2}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right) F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{23}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{153}\! \left(x \right) &= -F_{15}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{159}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{15}\! \left(x \right) F_{38}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{15}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{15}\! \left(x \right) F_{38}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{11}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{145}\! \left(x \right) F_{15}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{15}\! \left(x \right) F_{152}\! \left(x \right) F_{8}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 185 rules.
Finding the specification took 8945 seconds.
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Copy 185 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{11}\! \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_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= -F_{180}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{11}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{0}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= -F_{120}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{94}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{85}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{11}\! \left(x \right) F_{37}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{11}\! \left(x \right) F_{12}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{11}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{48}\! \left(x \right) &= -F_{80}\! \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_{37}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{80}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{64}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{63}\! \left(x \right) &= x^{2} F_{63} \left(x \right)^{3}-x^{2} F_{63} \left(x \right)^{2}+x F_{63} \left(x \right)^{2}+1\\
F_{64}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= -F_{74}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= x^{2} F_{73} \left(x \right)^{3}+2 x^{2} F_{73} \left(x \right)^{2}+x^{2} F_{73}\! \left(x \right)+x F_{73} \left(x \right)^{2}+2 x F_{73}\! \left(x \right)+x\\
F_{74}\! \left(x \right) &= -F_{77}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{2}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{78}\! \left(x \right) &= -F_{79}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{37}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{12}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{11}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{0}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{40}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{0}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{11}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{99}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{104}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{103}\! \left(x \right) F_{11}\! \left(x \right) F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= \frac{F_{111}\! \left(x \right)}{F_{11}\! \left(x \right) F_{95}\! \left(x \right)}\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= -F_{115}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= \frac{F_{114}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{114}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{115}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{11}\! \left(x \right) F_{110}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{11}\! \left(x \right) F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{11}\! \left(x \right) F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{11}\! \left(x \right) F_{110}\! \left(x \right) F_{123}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{121}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{101}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{133}\! \left(x \right) &= -F_{137}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{43}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{138}\! \left(x \right) &= -F_{174}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{144}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= \frac{F_{147}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{147}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{11}\! \left(x \right) F_{143}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{11}\! \left(x \right) F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{0}\! \left(x \right) F_{154}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{143}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{11}\! \left(x \right) F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{171}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{11}\! \left(x \right) F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{11}\! \left(x \right) F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{146}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{145}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{2}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{5}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{11}\! \left(x \right) F_{140}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{176}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{176}\! \left(x \right) &= \frac{F_{177}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{177}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{11}\! \left(x \right) F_{176}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{11}\! \left(x \right) F_{182}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{182}\! \left(x \right) &= \frac{F_{183}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
\end{align*}\)