Av(13425, 13452, 13542, 14325, 14352, 14532, 15342, 15432, 31425, 31452, 31542)
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Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2567, 12826, 64770, 329549, 1685981, 8661144, 44634278, 230584632, ...
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 206 rules.

Finding the specification took 2029 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_{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_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{15}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ 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_{5}\! \left(x \right)\\ F_{15}\! \left(x \right) &= x\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= -F_{198}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{15}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{31}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{180}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{36}\! \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_{175}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{43}\! \left(x \right) &= -F_{170}\! \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_{15}\! \left(x \right)}\\ F_{46}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{50}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= -F_{53}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{53}\! \left(x \right) &= \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{15}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{15}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{6}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{15}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{66}\! \left(x \right) &= x^{2} F_{66} \left(x \right)^{2}-2 x F_{66} \left(x \right)^{2}+F_{66}\! \left(x \right) x +2 F_{66}\! \left(x \right)-1\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{15}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{15}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{118}\! \left(x \right) F_{120}\! \left(x \right) F_{15}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{15}\! \left(x \right) F_{66}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{15}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{116}\! \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_{6}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{66}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{108}\! \left(x \right)}\\ F_{94}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{99}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{100}\! \left(x \right) &= -F_{104}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{105}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{110}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{15}\! \left(x \right) F_{6}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{118}\! \left(x \right) &= \frac{F_{119}\! \left(x \right)}{F_{11}\! \left(x \right) F_{15}\! \left(x \right)}\\ F_{119}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{15}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{132}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{15}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= \frac{F_{128}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{130}\! \left(x \right) &= \frac{F_{131}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{131}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{135}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{137}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{138}\! \left(x \right) &= -F_{142}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{142}\! \left(x \right) &= -F_{76}\! \left(x \right)+F_{143}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{118}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{11}\! \left(x \right) F_{118}\! \left(x \right) F_{120}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{15}\! \left(x \right) F_{151}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{151}\! \left(x \right) &= -F_{165}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= \frac{F_{153}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{15}\! \left(x \right) F_{155}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{164}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{120}\! \left(x \right) F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{158}\! \left(x \right) &= \frac{F_{159}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{142}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{163}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{53}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{172}\! \left(x \right) &= -F_{173}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{163}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{11}\! \left(x \right) F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{15}\! \left(x \right) F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{15}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{15}\! \left(x \right) F_{179}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{185}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{188}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{15}\! \left(x \right) F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{195}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{118}\! \left(x \right) F_{42}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{66} \left(x \right)^{2} F_{163}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{15}\! \left(x \right) F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{205}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{67}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{66}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{55}\! \left(x \right) F_{78}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 206 rules.

Finding the specification took 2029 seconds.

This tree is too big to show here. Click to view tree on new page.

Copy 206 equations to clipboard:
\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{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_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{15}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ 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_{5}\! \left(x \right)\\ F_{15}\! \left(x \right) &= x\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= -F_{198}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{15}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{31}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{180}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{36}\! \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_{175}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{43}\! \left(x \right) &= -F_{170}\! \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_{15}\! \left(x \right)}\\ F_{46}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{50}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= -F_{53}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{53}\! \left(x \right) &= \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{15}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{15}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{6}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{15}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{66}\! \left(x \right) &= x^{2} F_{66} \left(x \right)^{2}-2 x F_{66} \left(x \right)^{2}+F_{66}\! \left(x \right) x +2 F_{66}\! \left(x \right)-1\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{15}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{15}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{118}\! \left(x \right) F_{120}\! \left(x \right) F_{15}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{15}\! \left(x \right) F_{66}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{15}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{116}\! \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_{6}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{66}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{108}\! \left(x \right)}\\ F_{94}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{99}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{100}\! \left(x \right) &= -F_{104}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{105}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{110}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{15}\! \left(x \right) F_{6}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{118}\! \left(x \right) &= \frac{F_{119}\! \left(x \right)}{F_{11}\! \left(x \right) F_{15}\! \left(x \right)}\\ F_{119}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{15}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{132}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{15}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= \frac{F_{128}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{130}\! \left(x \right) &= \frac{F_{131}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{131}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{135}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{137}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{138}\! \left(x \right) &= -F_{142}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{142}\! \left(x \right) &= -F_{76}\! \left(x \right)+F_{143}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{118}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{11}\! \left(x \right) F_{118}\! \left(x \right) F_{120}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{15}\! \left(x \right) F_{151}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{151}\! \left(x \right) &= -F_{165}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= \frac{F_{153}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{15}\! \left(x \right) F_{155}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{164}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{120}\! \left(x \right) F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{158}\! \left(x \right) &= \frac{F_{159}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{142}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{163}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{53}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{172}\! \left(x \right) &= -F_{173}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{163}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{11}\! \left(x \right) F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{15}\! \left(x \right) F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{15}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{15}\! \left(x \right) F_{179}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{185}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{188}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{15}\! \left(x \right) F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{195}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{118}\! \left(x \right) F_{42}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{66} \left(x \right)^{2} F_{163}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{15}\! \left(x \right) F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{205}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{67}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{66}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{55}\! \left(x \right) F_{78}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 213 rules.

Finding the specification took 4632 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_{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_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{15}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ 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_{5}\! \left(x \right)\\ F_{15}\! \left(x \right) &= x\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{15}\! \left(x \right) F_{90}\! \left(x \right)}\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{206}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= -F_{205}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{15}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{31}\! \left(x \right) &= -F_{187}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{182}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{36}\! \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_{177}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{43}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= -F_{50}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{49}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{4}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{55}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{4}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= -F_{60}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{15}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{15}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{6}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{15}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{15}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{76}\! \left(x \right) &= \frac{F_{77}\! \left(x \right)}{F_{118}\! \left(x \right)}\\ F_{77}\! \left(x \right) &= -F_{82}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{121}\! \left(x \right) F_{15}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{15}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{131}\! \left(x \right) F_{15}\! \left(x \right) F_{70}\! \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) &= x^{2} F_{90} \left(x \right)^{2}-2 x F_{90} \left(x \right)^{2}+F_{90}\! \left(x \right) x +2 F_{90}\! \left(x \right)-1\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{15}\! \left(x \right) F_{90}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{15}\! \left(x \right) F_{90}\! \left(x \right)}\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{129}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{103}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{6}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{104}\! \left(x \right) &= -F_{90}\! \left(x \right)+F_{105}\! \left(x \right)\\ F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{121}\! \left(x \right)}\\ F_{106}\! \left(x \right) &= -F_{114}\! \left(x \right)+F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= \frac{F_{108}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{110}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= -F_{90}\! \left(x \right)+F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= \frac{F_{113}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{113}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{114}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= \frac{F_{116}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{116}\! \left(x \right) &= F_{110}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{105}\! \left(x \right) F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{118}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{15}\! \left(x \right) F_{6}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{131}\! \left(x \right) &= \frac{F_{132}\! \left(x \right)}{F_{11}\! \left(x \right) F_{15}\! \left(x \right)}\\ F_{132}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{138}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{15}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{136}\! \left(x \right) &= \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{137}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{141}\! \left(x \right) &= -F_{145}\! \left(x \right)+F_{142}\! \left(x \right)\\ F_{142}\! \left(x \right) &= \frac{F_{143}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{145}\! \left(x \right) &= -F_{149}\! \left(x \right)+F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= \frac{F_{147}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{149}\! \left(x \right) &= -F_{87}\! \left(x \right)+F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{15}\! \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_{131}\! \left(x \right) F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{131}\! \left(x \right) F_{70}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{15}\! \left(x \right) F_{159}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{159}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= \frac{F_{161}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{15}\! \left(x \right) F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{171}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{166}\! \left(x \right) &= \frac{F_{167}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{149}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{60}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{15}\! \left(x \right) F_{60}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{11}\! \left(x \right) F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{15}\! \left(x \right) F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{185}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{105}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{105}\! \left(x \right) F_{15}\! \left(x \right) F_{181}\! \left(x \right)\\ F_{187}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= -F_{191}\! \left(x \right)+F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= \frac{F_{190}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{190}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{185}\! \left(x \right)\\ F_{192}\! \left(x \right) &= -F_{201}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{200}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{15}\! \left(x \right) F_{196}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{199}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{131}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{53}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{90} \left(x \right)^{2} F_{15}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{133}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{15}\! \left(x \right) F_{208}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)+F_{212}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{211}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{74}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{80}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{62}\! \left(x \right) F_{89}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 75 rules.

Finding the specification took 2241 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_{18}\! \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) &= x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{18}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x \right)+F_{14}\! \left(x , y\right)\\ F_{13}\! \left(x \right) &= x^{2} F_{13} \left(x \right)^{2}-2 x F_{13} \left(x \right)^{2}+F_{13}\! \left(x \right) x +2 F_{13}\! \left(x \right)-1\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\ F_{15}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= y F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{18}\! \left(x \right) &= x\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x , 1\right)\\ F_{20}\! \left(x , y\right) &= F_{13}\! \left(x \right)+F_{21}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{13}\! \left(x \right) F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= y x\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{18}\! \left(x \right) F_{26}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{18}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{18}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{35}\! \left(x \right) &= -F_{38}\! \left(x \right)-F_{61}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{13}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{18}\! \left(x \right) F_{36}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{18}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x , 1\right)\\ F_{45}\! \left(x , y\right) &= -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}\\ F_{46}\! \left(x , y\right) &= x^{2} F_{46}\! \left(x , y\right)^{2} y^{2}-2 y x F_{46}\! \left(x , y\right)^{2}+x F_{46}\! \left(x , y\right) y +2 F_{46}\! \left(x , y\right)-1\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{18}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{42}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{13}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{13}\! \left(x \right) F_{18}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{18}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{18}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{18}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{13}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{19}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{49}\! \left(x \right)\\ \end{align*}\)