Av(13452, 13524, 13542, 14352, 31452, 31524, 31542, 35124, 35142, 35214)
Counting Sequence
1, 1, 2, 6, 24, 110, 531, 2626, 13192, 67074, 344350, 1781898, 9281658, 48617801, 255896339, ...
This specification was found using the strategy pack "Point Placements Req Corrob" and has 151 rules.
Finding the specification took 2807 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_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{12}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{10}\! \left(x \right) &= \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{11}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{18}\! \left(x \right) &= -F_{146}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= \frac{F_{20}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{12}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{0}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{12}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{12}\! \left(x \right) F_{38}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{38}\! \left(x \right)}\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{2}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{12}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{12}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{12}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{38}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{53}\! \left(x \right) &= x^{2} F_{53} \left(x \right)^{3}-x^{2} F_{53} \left(x \right)^{2}+x F_{53} \left(x \right)^{2}+1\\
F_{54}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{12}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{12}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{12}\! \left(x \right) F_{59}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{53} \left(x \right)^{2} F_{12}\! \left(x \right)\\
F_{65}\! \left(x \right) &= -F_{59}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{12}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= -F_{76}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{12}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{75}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{76}\! \left(x \right) &= -F_{77}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{77}\! \left(x \right) &= -F_{80}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{79}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{87}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= \frac{F_{83}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= -F_{86}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{86}\! \left(x \right) &= x^{2} F_{86} \left(x \right)^{3}+2 x^{2} F_{86} \left(x \right)^{2}+x^{2} F_{86}\! \left(x \right)+x F_{86} \left(x \right)^{2}+2 x F_{86}\! \left(x \right)+x\\
F_{87}\! \left(x \right) &= -F_{91}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= \frac{F_{89}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{12}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{9}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{101}\! \left(x \right) F_{12}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{0}\! \left(x \right) F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{53}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{54}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{109}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{116}\! \left(x \right) &= -F_{132}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= -F_{120}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= \frac{F_{119}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{119}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{12}\! \left(x \right) F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{125}\! \left(x \right) &= \frac{F_{126}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{126}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{0}\! \left(x \right) F_{129}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{12}\! \left(x \right) F_{125}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{12}\! \left(x \right) F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{12}\! \left(x \right) F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{138}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{16}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{53}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{10}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{12}\! \left(x \right) F_{143}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{143}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{65}\! \left(x \right)}\\
F_{144}\! \left(x \right) &= -F_{145}\! \left(x \right)+F_{101}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{34}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{146}\! \left(x \right) &= -F_{149}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= \frac{F_{148}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{148}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{139}\! \left(x \right) F_{54}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 162 rules.
Finding the specification took 1587 seconds.
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Copy 162 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_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{12}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{10}\! \left(x \right) &= \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{11}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{18}\! \left(x \right) &= -F_{157}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= \frac{F_{20}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{0}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{12}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{12}\! \left(x \right) F_{37}\! \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_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{2}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{12}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{12}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{12}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{37}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \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) &= x^{2} F_{52} \left(x \right)^{3}-x^{2} F_{52} \left(x \right)^{2}+x F_{52} \left(x \right)^{2}+1\\
F_{53}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{12}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{12}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{12}\! \left(x \right) F_{58}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{52} \left(x \right)^{2} F_{12}\! \left(x \right)\\
F_{64}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{12}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{12}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{78}\! \left(x \right) &= -F_{79}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{79}\! \left(x \right) &= -F_{82}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{97}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{12}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{96}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{97}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{98}\! \left(x \right) &= -F_{101}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= \frac{F_{100}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{100}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{104}\! \left(x \right) &= \frac{F_{105}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{111}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{111}\! \left(x \right) &= \frac{F_{112}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{4}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{0}\! \left(x \right) F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{12}\! \left(x \right) F_{121}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{52}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{53}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{104}\! \left(x \right) F_{12}\! \left(x \right) F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= x^{2} F_{126} \left(x \right)^{3}+2 x^{2} F_{126} \left(x \right)^{2}+x^{2} F_{126}\! \left(x \right)+x F_{126} \left(x \right)^{2}+2 x F_{126}\! \left(x \right)+x\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{119}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{129}\! \left(x \right) &= -F_{143}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= \frac{F_{132}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{132}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{12}\! \left(x \right) F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{138}\! \left(x \right) &= \frac{F_{139}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{139}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{0}\! \left(x \right) F_{142}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{12}\! \left(x \right) F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{12}\! \left(x \right) F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{16}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{52}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{10}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{12}\! \left(x \right) F_{154}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{154}\! \left(x \right) &= \frac{F_{155}\! \left(x \right)}{F_{64}\! \left(x \right)}\\
F_{155}\! \left(x \right) &= -F_{156}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{33}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{157}\! \left(x \right) &= -F_{160}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= \frac{F_{159}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{159}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{150}\! \left(x \right) F_{53}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 69 rules.
Finding the specification took 861 seconds.
Copy 69 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{0}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{16}\! \left(x \right) &= \frac{F_{17}\! \left(x \right)}{F_{11}\! \left(x \right) F_{31}\! \left(x \right)}\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{20}\! \left(x \right) &= \frac{F_{21}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{21}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{11}\! \left(x \right) F_{20}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{25}\! \left(x \right) &= x^{2} F_{25} \left(x \right)^{3}-x^{2} F_{25} \left(x \right)^{2}+x F_{25} \left(x \right)^{2}+1\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{11}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x , 1\right)\\
F_{29}\! \left(x , y\right) &= -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}\\
F_{30}\! \left(x , y\right) &= y^{2} x^{2} F_{30}\! \left(x , y\right)^{3}-x^{2} F_{30}\! \left(x , y\right)^{2} y^{2}+y x F_{30}\! \left(x , y\right)^{2}+1\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{11}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{11}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{11}\! \left(x \right) F_{32}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x , 1\right)\\
F_{43}\! \left(x , y\right) &= -\frac{-F_{44}\! \left(x , y\right) y +F_{44}\! \left(x , 1\right)}{-1+y}\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= y x\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{48}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{46}\! \left(x , y\right) F_{48}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{43}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x , 1\right)\\
F_{58}\! \left(x , y\right) &= F_{48}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= x^{2} F_{59}\! \left(x , y\right)^{3} y^{2}+2 x^{2} F_{59}\! \left(x , y\right)^{2} y^{2}+x^{2} F_{59}\! \left(x , y\right) y^{2}+x F_{59}\! \left(x , y\right)^{2} y +2 x F_{59}\! \left(x , y\right) y +y x\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{0}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{11}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x , 1\right)\\
F_{68}\! \left(x , y\right) &= -\frac{-y F_{57}\! \left(x , y\right)+F_{57}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)