Av(13425, 13452, 13542, 14235, 14253, 14325, 14352, 14523, 14532, 15342, 15423, 15432)
Counting Sequence
1, 1, 2, 6, 24, 108, 517, 2569, 13075, 67630, 353808, 1866263, 9904742, 52813400, 282632385, ...
This specification was found using the strategy pack "Point Placements Req Corrob" and has 211 rules.
Finding the specification took 12340 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 211 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_{21}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{6}\! \left(x \right) &= x F_{6} \left(x \right)^{3}+2 x F_{6} \left(x \right)^{2}+2 F_{6}\! \left(x \right) x +x\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{21}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{203}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{15}\! \left(x \right) &= -F_{171}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= \frac{F_{17}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= x\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{21}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{21}\! \left(x \right) F_{6}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{21}\! \left(x \right) F_{33}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{34}\! \left(x \right) &= x F_{34} \left(x \right)^{3}-x F_{34} \left(x \right)^{2}+x F_{34}\! \left(x \right)+1\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{21}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{21}\! \left(x \right) F_{42}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{21}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{34}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{21}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{156}\! \left(x \right) F_{21}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{21}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{34}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{21}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{34}\! \left(x \right)}\\
F_{64}\! \left(x \right) &= -F_{147}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= -F_{146}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{69}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{34} \left(x \right)^{2}\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{21}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= \frac{F_{78}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= -F_{142}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{84}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= \frac{F_{83}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{83}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{21}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{2}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= -F_{94}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= \frac{F_{93}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{93}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{21}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{107}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{106}\! \left(x \right) F_{110}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{110}\! \left(x \right) &= \frac{F_{111}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{111}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{110}\! \left(x \right) F_{114}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{4}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{21}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{21}\! \left(x \right) F_{34}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{125}\! \left(x \right) &= -F_{128}\! \left(x \right)+F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{127}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{130}\! \left(x \right) &= \frac{F_{131}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{131}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{2}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{138}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{139}\! \left(x \right) &= -F_{140}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{110}\! \left(x \right) F_{145}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= -F_{149}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{150}\! \left(x \right) &= \frac{F_{151}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{6}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{47}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{156}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{21}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{121}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{0}\! \left(x \right) F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= -F_{196}\! \left(x \right)+F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= \frac{F_{181}\! \left(x \right)}{F_{21}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= -F_{156}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= -F_{190}\! \left(x \right)+F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= -F_{188}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= \frac{F_{187}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{187}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{156}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{106}\! \left(x \right) F_{193}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{193}\! \left(x \right) &= \frac{F_{194}\! \left(x \right)}{F_{21}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{194}\! \left(x \right) &= F_{190}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{2}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{196}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right) F_{202}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{201}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{179}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)+F_{208}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{5}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{0}\! \left(x \right) F_{99}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 207 rules.
Finding the specification took 4289 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 207 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_{21}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{6}\! \left(x \right) &= x F_{6} \left(x \right)^{3}+2 x F_{6} \left(x \right)^{2}+2 F_{6}\! \left(x \right) x +x\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{21}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{199}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{15}\! \left(x \right) &= -F_{167}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= \frac{F_{17}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= x\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{21}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{21}\! \left(x \right) F_{6}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{21}\! \left(x \right) F_{33}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{34}\! \left(x \right) &= x F_{34} \left(x \right)^{3}-x F_{34} \left(x \right)^{2}+x F_{34}\! \left(x \right)+1\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{21}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{21}\! \left(x \right) F_{42}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{21}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{34}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{21}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{21}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{158}\! \left(x \right) F_{21}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{21}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{34}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{21}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{34}\! \left(x \right)}\\
F_{68}\! \left(x \right) &= -F_{152}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= -F_{151}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{73}\! \left(x \right) &= -F_{77}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{34} \left(x \right)^{2}\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{21}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= \frac{F_{82}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= -F_{147}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{87}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{21}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{2}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{102}\! \left(x \right) &= \frac{F_{103}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{112}\! \left(x \right) F_{116}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{117}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{116}\! \left(x \right) F_{120}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{4}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{21}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{21}\! \left(x \right) F_{34}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{132}\! \left(x \right) &= -F_{140}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= -F_{136}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{138}\! \left(x \right) &= \frac{F_{139}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{139}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{105}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{116}\! \left(x \right) F_{150}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= -F_{154}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{6}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{47}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{158}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{127}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{130}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{0}\! \left(x \right) F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= -F_{192}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{176}\! \left(x \right) &= \frac{F_{177}\! \left(x \right)}{F_{21}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= -F_{191}\! \left(x \right)+F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= -F_{158}\! \left(x \right)+F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= -F_{186}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= -F_{184}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= \frac{F_{183}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{183}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{158}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{112}\! \left(x \right) F_{189}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{189}\! \left(x \right) &= \frac{F_{190}\! \left(x \right)}{F_{21}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{190}\! \left(x \right) &= F_{186}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{2}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{192}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right) F_{198}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{197}\! \left(x \right) &= -F_{168}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{5}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{0}\! \left(x \right) F_{105}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 157 rules.
Finding the specification took 37890 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 157 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_{4}\! \left(x \right) F_{41}\! \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 F_{6} \left(x \right)^{3}+2 x F_{6} \left(x \right)^{2}+2 F_{6}\! \left(x \right) x +x\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{41}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{15}\! \left(x \right) &= -F_{55}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= \frac{F_{17}\! \left(x \right)}{F_{41}\! \left(x \right)}\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{0}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x , 1\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= x F_{25}\! \left(x , y\right)^{3} y -x F_{25}\! \left(x , y\right)^{2} y +x F_{25}\! \left(x , y\right) y +1\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{41}\! \left(x \right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right) F_{41}\! \left(x \right)\\
F_{32}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{22}\! \left(y x \right)\\
F_{38}\! \left(x , y\right) &= y F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{32}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= x\\
F_{42}\! \left(x , y\right) &= y x\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{29}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{4}\! \left(x \right) F_{41}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x , 1\right)\\
F_{51}\! \left(x , y\right) &= -\frac{-F_{37}\! \left(x , y\right) y +F_{37}\! \left(x , 1\right)}{-1+y}\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{22}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{4}\! \left(x \right) F_{41}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{59}\! \left(x \right) &= x F_{59} \left(x \right)^{3}-x F_{59} \left(x \right)^{2}+x F_{59}\! \left(x \right)+1\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x , 1\right)\\
F_{62}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{59}\! \left(x \right) F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{41}\! \left(x \right) F_{66}\! \left(x , y\right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{41}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{0}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x , 1\right)\\
F_{76}\! \left(x , y\right) &= -\frac{y \left(F_{62}\! \left(x , 1\right)-F_{62}\! \left(x , y\right)\right)}{-1+y}\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{41}\! \left(x \right) F_{79}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{59}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x , 1\right)\\
F_{83}\! \left(x , y\right) &= -\frac{-F_{84}\! \left(x , y\right) y +F_{84}\! \left(x , 1\right)}{-1+y}\\
F_{84}\! \left(x , y\right) &= F_{59}\! \left(x \right)+F_{62}\! \left(x , y\right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{41}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{5}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{113}\! \left(x \right) F_{41}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{41}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{41}\! \left(x \right) F_{50}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{22}\! \left(x \right) F_{41}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{104}\! \left(x \right) &= -F_{112}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= \frac{F_{107}\! \left(x \right)}{F_{41}\! \left(x \right)}\\
F_{107}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{110}\! \left(x \right) &= \frac{F_{111}\! \left(x \right)}{F_{41}\! \left(x \right)}\\
F_{111}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{113}\! \left(x \right) &= \frac{F_{114}\! \left(x \right)}{F_{41}\! \left(x \right)}\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= \frac{F_{116}\! \left(x \right)}{F_{41}\! \left(x \right)}\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= -F_{146}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= -F_{121}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{41}\! \left(x \right)}\\
F_{120}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{123}\! \left(x \right) &= \frac{F_{124}\! \left(x \right)}{F_{41}\! \left(x \right)}\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{2}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{113}\! \left(x \right) F_{132}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{22}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x , 1\right)\\
F_{142}\! \left(x , y\right) &= -\frac{-y F_{25}\! \left(x , y\right)+F_{25}\! \left(x , 1\right)}{-1+y}\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{141}\! \left(x \right) F_{145}\! \left(x \right) F_{22}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x , 1\right)\\
F_{148}\! \left(x , y\right) &= -\frac{y \left(F_{149}\! \left(x , 1\right)-F_{149}\! \left(x , y\right)\right)}{-1+y}\\
F_{149}\! \left(x , y\right) &= x F_{149}\! \left(x , y\right)^{3} y +2 x F_{149}\! \left(x , y\right)^{2} y +2 x F_{149}\! \left(x , y\right) y +y x\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{23}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{141}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{0}\! \left(x \right) F_{139}\! \left(x \right)\\
\end{align*}\)