Av(12435, 12453, 12543, 21435, 21453, 21543, 24135, 24153, 24513, 25143, 25413)
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Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2556, 12639, 62783, 312552, 1557651, 7766984, 38739716, 193254560, ...
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 146 rules.

Finding the specification took 2054 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_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= x^{2} F_{5} \left(x \right)^{2}+2 x^{2} F_{5}\! \left(x \right)+4 x F_{5} \left(x \right)^{2}+x^{2}-13 x F_{5}\! \left(x \right)-F_{5} \left(x \right)^{2}+8 x +4 F_{5}\! \left(x \right)-2\\ F_{6}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{15}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{12} \left(x \right)^{2} F_{15}\! \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_{9}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{12} \left(x \right)^{2} F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= -F_{145}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= -F_{115}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= \frac{F_{26}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{29}\! \left(x \right) &= x F_{29} \left(x \right)^{4}+x^{2} F_{29} \left(x \right)^{2}+3 x F_{29} \left(x \right)^{3}+2 x^{2} F_{29}\! \left(x \right)+x F_{29} \left(x \right)^{2}-F_{29} \left(x \right)^{3}+x^{2}-F_{29}\! \left(x \right) x +F_{29}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{15}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{29}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{15}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= -F_{49}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{44}\! \left(x \right) &= x^{2} F_{44} \left(x \right)^{2}+4 x^{2} F_{44}\! \left(x \right)+4 x F_{44} \left(x \right)^{2}+4 x^{2}-5 x F_{44}\! \left(x \right)-F_{44} \left(x \right)^{2}-x +2 F_{44}\! \left(x \right)\\ F_{45}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{48}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{49}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{2}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{55}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{103}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{15}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{15}\! \left(x \right) F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= x F_{68} \left(x \right)^{4}+x^{2} F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3} x -2 x F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3}+2 F_{68}\! \left(x \right) x +3 F_{68} \left(x \right)^{2}-2 F_{68}\! \left(x \right)+1\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{15}\! \left(x \right) F_{68}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{12}\! \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_{15}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{12}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{68}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{12}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{15}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{55}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{68}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{15}\! \left(x \right) F_{73}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{15}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{12}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{12}\! \left(x \right) F_{68}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{103}\! \left(x \right) &= \frac{F_{104}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{104}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{107}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{110}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{15}\! \left(x \right) F_{54}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{80}\! \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_{18}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{12}\! \left(x \right) F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{117}\! \left(x \right) F_{129}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{129}\! \left(x \right) &= \frac{F_{130}\! \left(x \right)}{F_{0}\! \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_{15}\! \left(x \right)}\\ F_{132}\! \left(x \right) &= F_{35}\! \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_{15}\! \left(x \right)}\\ F_{135}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{129}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{54}\! \left(x \right) F_{68}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{12}\! \left(x \right) F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{142}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{129}\! \left(x \right) F_{144}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{116}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{0}\! \left(x \right) F_{12}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 195 rules.

Finding the specification took 5671 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}+4 x^{2} F_{6}\! \left(x \right)+4 x F_{6} \left(x \right)^{2}+4 x^{2}-5 x F_{6}\! \left(x \right)-F_{6} \left(x \right)^{2}-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_{21}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{12} \left(x \right)^{2} F_{15}\! \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_{9}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{12} \left(x \right)^{2} F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{24}\! \left(x \right) &= x F_{24} \left(x \right)^{4}+x^{2} F_{24} \left(x \right)^{2}+3 x F_{24} \left(x \right)^{3}+2 x^{2} F_{24}\! \left(x \right)+x F_{24} \left(x \right)^{2}-F_{24} \left(x \right)^{3}+x^{2}-F_{24}\! \left(x \right) x +F_{24}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{15}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{12}\! \left(x \right) F_{23}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{23}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= x F_{30} \left(x \right)^{4}+x^{2} F_{30} \left(x \right)^{2}-F_{30} \left(x \right)^{3} x -2 x F_{30} \left(x \right)^{2}-F_{30} \left(x \right)^{3}+2 F_{30}\! \left(x \right) x +3 F_{30} \left(x \right)^{2}-2 F_{30}\! \left(x \right)+1\\ F_{31}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{126}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= -F_{193}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{15}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{24}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{15}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{52}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{53}\! \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_{0}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{57}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{2}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{15}\! \left(x \right) F_{24}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{15}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{12}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{63}\! \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_{82}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{82}\! \left(x \right) &= \frac{F_{83}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{83}\! \left(x \right) &= -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{85}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{86}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{88}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{2}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{12}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{15}\! \left(x \right) F_{76}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{30}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{66}\! \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) &= \frac{F_{101}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= \frac{F_{103}\! \left(x \right)}{F_{182}\! \left(x \right)}\\ F_{103}\! \left(x \right) &= -F_{189}\! \left(x \right)+F_{104}\! \left(x \right)\\ F_{104}\! \left(x \right) &= \frac{F_{105}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{107}\! \left(x \right) &= -F_{168}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{109}\! \left(x \right) &= -F_{156}\! \left(x \right)+F_{110}\! \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_{113}\! \left(x \right)+F_{129}\! \left(x \right)\\ F_{113}\! \left(x \right) &= \frac{F_{114}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{15}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{12}\! \left(x \right) F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{124}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{130}\! \left(x \right) &= -F_{165}\! \left(x \right)+F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= \frac{F_{132}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{156}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{145}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{140}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{15}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{15}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{126}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{12}\! \left(x \right) F_{138}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{126}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{150}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{158}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{159}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{15}\! \left(x \right) F_{161}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{12}\! \left(x \right) F_{158}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{12}\! \left(x \right) F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{168}\! \left(x \right) &= x^{2} F_{168} \left(x \right)^{2}+2 x^{2} F_{168}\! \left(x \right)+4 x F_{168} \left(x \right)^{2}+x^{2}-13 x F_{168}\! \left(x \right)-F_{168} \left(x \right)^{2}+8 x +4 F_{168}\! \left(x \right)-2\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{15}\! \left(x \right) F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right) F_{174}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{15}\! \left(x \right) F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{15}\! \left(x \right) F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{185}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{184}\! \left(x \right) &= 0\\ F_{185}\! \left(x \right) &= F_{15}\! \left(x \right) F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{15}\! \left(x \right) F_{180}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{102}\! \left(x \right) F_{180}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{173}\! \left(x \right) F_{190}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{192}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{15}\! \left(x \right) F_{182}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{66}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 146 rules.

Finding the specification took 2054 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_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= x^{2} F_{5} \left(x \right)^{2}+2 x^{2} F_{5}\! \left(x \right)+4 x F_{5} \left(x \right)^{2}+x^{2}-13 x F_{5}\! \left(x \right)-F_{5} \left(x \right)^{2}+8 x +4 F_{5}\! \left(x \right)-2\\ F_{6}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{15}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{12} \left(x \right)^{2} F_{15}\! \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_{9}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{12} \left(x \right)^{2} F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= -F_{145}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= -F_{115}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= \frac{F_{26}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{29}\! \left(x \right) &= x F_{29} \left(x \right)^{4}+x^{2} F_{29} \left(x \right)^{2}+3 x F_{29} \left(x \right)^{3}+2 x^{2} F_{29}\! \left(x \right)+x F_{29} \left(x \right)^{2}-F_{29} \left(x \right)^{3}+x^{2}-F_{29}\! \left(x \right) x +F_{29}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{15}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{29}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{15}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= -F_{49}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{44}\! \left(x \right) &= x^{2} F_{44} \left(x \right)^{2}+4 x^{2} F_{44}\! \left(x \right)+4 x F_{44} \left(x \right)^{2}+4 x^{2}-5 x F_{44}\! \left(x \right)-F_{44} \left(x \right)^{2}-x +2 F_{44}\! \left(x \right)\\ F_{45}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{48}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{49}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{2}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{55}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{103}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{15}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{15}\! \left(x \right) F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= x F_{68} \left(x \right)^{4}+x^{2} F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3} x -2 x F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3}+2 F_{68}\! \left(x \right) x +3 F_{68} \left(x \right)^{2}-2 F_{68}\! \left(x \right)+1\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{15}\! \left(x \right) F_{68}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{12}\! \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_{15}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{12}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{68}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{12}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{15}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{55}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{68}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{15}\! \left(x \right) F_{73}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{15}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{12}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{12}\! \left(x \right) F_{68}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{103}\! \left(x \right) &= \frac{F_{104}\! \left(x \right)}{F_{15}\! \left(x \right)}\\ F_{104}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{107}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{110}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{15}\! \left(x \right) F_{54}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{80}\! \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_{18}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{12}\! \left(x \right) F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{117}\! \left(x \right) F_{129}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{129}\! \left(x \right) &= \frac{F_{130}\! \left(x \right)}{F_{0}\! \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_{15}\! \left(x \right)}\\ F_{132}\! \left(x \right) &= F_{35}\! \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_{15}\! \left(x \right)}\\ F_{135}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{129}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{54}\! \left(x \right) F_{68}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{12}\! \left(x \right) F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{142}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{129}\! \left(x \right) F_{144}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{116}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{0}\! \left(x \right) F_{12}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 68 rules.

Finding the specification took 3032 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_{19}\! \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_{19}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= \frac{F_{8}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{8}\! \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) &= x F_{10} \left(x \right)^{4}+x^{2} F_{10} \left(x \right)^{2}+3 x F_{10} \left(x \right)^{3}+2 x^{2} F_{10}\! \left(x \right)+x F_{10} \left(x \right)^{2}-F_{10} \left(x \right)^{3}+x^{2}-F_{10}\! \left(x \right) x +F_{10}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{16}\! \left(x \right) &= -F_{20}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{19}\! \left(x \right) &= x\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{19}\! \left(x \right) F_{23}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x , 1\right)\\ F_{24}\! \left(x , y\right) &= -\frac{-F_{25}\! \left(x , y\right) y +F_{25}\! \left(x , 1\right)}{-1+y}\\ F_{25}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\ F_{27}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)^{2} F_{28}\! \left(x , y\right)\\ F_{28}\! \left(x , y\right) &= y x\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{19}\! \left(x \right) F_{31}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{31}\! \left(x \right) &= -F_{65}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{19}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{36}\! \left(x \right) &= -F_{57}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= -F_{41}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{0}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= -F_{44}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{44}\! \left(x \right) &= x F_{44} \left(x \right)^{4}+x^{2} F_{44} \left(x \right)^{2}-F_{44} \left(x \right)^{3} x -2 x F_{44} \left(x \right)^{2}-F_{44} \left(x \right)^{3}+2 F_{44}\! \left(x \right) x +3 F_{44} \left(x \right)^{2}-2 F_{44}\! \left(x \right)+1\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{19}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x , 1\right)\\ F_{48}\! \left(x , y\right) &= -\frac{-F_{49}\! \left(x , y\right) y +F_{49}\! \left(x , 1\right)}{-1+y}\\ F_{50}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{52}\! \left(x , y\right) &= F_{31}\! \left(x \right) F_{53}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= F_{15}\! \left(y x \right)\\ F_{55}\! \left(x , y\right) &= F_{31}\! \left(x \right) F_{56}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= x^{2} F_{56}\! \left(x , y\right)^{2} y^{2}+x F_{56}\! \left(x , y\right)^{4} y +2 x^{2} F_{56}\! \left(x , y\right) y^{2}+3 x F_{56}\! \left(x , y\right)^{3} y +x^{2} y^{2}+x F_{56}\! \left(x , y\right)^{2} y -x F_{56}\! \left(x , y\right) y -F_{56}\! \left(x , y\right)^{3}+F_{56}\! \left(x , y\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) &= \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right) F_{19}\! \left(x \right)}\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{10}\! \left(x \right) F_{19}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{15}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x , 1\right)\\ F_{67}\! \left(x , y\right) &= -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}\\ \end{align*}\)