Av(13425, 13452, 13542, 31425, 31452, 31542, 35142)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3121, 17265, 97174, 553228, 3174692, 18322053, 106189146, 617416861, ...
This specification was found using the strategy pack "Point Placements Req Corrob" and has 124 rules.
Finding the specification took 6435 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_{4}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 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_{10}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= x\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{14} \left(x \right)^{2} F_{9}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{18}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= -F_{122}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{14}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{65}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{14}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{64}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= -F_{48}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= \frac{F_{41}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{43}\! \left(x \right) x +F_{43} \left(x \right)^{2}+x\\
F_{44}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{47}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{48}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{50}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{38}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{58}\! \left(x \right) &= 0\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{52}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{14}\! \left(x \right) F_{68}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{86}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= -F_{83}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= \frac{F_{72}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{14}\! \left(x \right) F_{75}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{31}\! \left(x \right) F_{78}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= \frac{F_{82}\! \left(x \right)}{F_{31}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{82}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{31}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{14}\! \left(x \right) F_{86}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{20}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{9}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{9}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{98}\! \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_{9}\! \left(x \right)}\\
F_{100}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{4}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{108}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{114}\! \left(x \right) &= \frac{F_{115}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{115}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right) F_{14}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{78}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{114}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{114}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 123 rules.
Finding the specification took 3134 seconds.
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Copy 123 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_{9}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 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_{10}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= x\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{14} \left(x \right)^{2} F_{9}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{18}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= -F_{121}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{14}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{64}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{14}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{63}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= \frac{F_{41}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{45}\! \left(x \right) &= -F_{50}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= -F_{49}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{49}\! \left(x \right) x +F_{49} \left(x \right)^{2}+x\\
F_{50}\! \left(x \right) &= F_{38}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{57}\! \left(x \right) &= 0\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{51}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{14}\! \left(x \right) F_{67}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{85}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= -F_{82}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{14}\! \left(x \right) F_{74}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{31}\! \left(x \right) F_{77}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{77}\! \left(x \right) &= \frac{F_{78}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{31}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{31}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{14}\! \left(x \right) F_{85}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{20}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{9}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{9}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{99}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{107}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{113}\! \left(x \right) &= \frac{F_{114}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{114}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{14}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{77}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{113}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{113}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 56 rules.
Finding the specification took 3153 seconds.
Copy 56 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_{34}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+4 x^{2} F_{7}\! \left(x , y\right) y^{2}+4 y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -5 x F_{7}\! \left(x , y\right) y -y x -F_{7}\! \left(x , y\right)^{2}+2 F_{7}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{34}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\
F_{19}\! \left(x , y\right) &= y x\\
F_{20}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)^{2} F_{19}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , 1, y\right)\\
F_{25}\! \left(x , y , z\right) &= F_{26}\! \left(x , y z , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{0}\! \left(x \right) F_{27}\! \left(x , y , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{28}\! \left(x , y , z\right)+F_{43}\! \left(x , y , z\right)\\
F_{28}\! \left(x , y , z\right) &= F_{29}\! \left(x \right) F_{35}\! \left(x , y , z\right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x , 1\right)\\
F_{30}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{34}\! \left(x \right)\\
F_{33}\! \left(x , y\right) &= -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}\\
F_{34}\! \left(x \right) &= x\\
F_{36}\! \left(x , y , z\right) &= F_{20}\! \left(x , y\right)+F_{35}\! \left(x , y , z\right)\\
F_{36}\! \left(x , y , z\right) &= F_{37}\! \left(x , z\right)+F_{38}\! \left(x , y , z\right)\\
F_{37}\! \left(x , y\right) &= x^{2} F_{37}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{37}\! \left(x , y\right) y^{2}+y^{2} x^{2}+4 x F_{37}\! \left(x , y\right)^{2} y -13 x F_{37}\! \left(x , y\right) y +8 y x -F_{37}\! \left(x , y\right)^{2}+4 F_{37}\! \left(x , y\right)-2\\
F_{38}\! \left(x , y , z\right) &= F_{39}\! \left(x , y , z\right)\\
F_{39}\! \left(x , y , z\right) &= F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{40}\! \left(x , y , z\right)\\
F_{40}\! \left(x , y , z\right) &= F_{36}\! \left(x , y , z\right)+F_{41}\! \left(x , y , z\right)\\
F_{41}\! \left(x , y , z\right) &= F_{42}\! \left(x , y , z\right) F_{7}\! \left(x , z\right)\\
F_{42}\! \left(x , y , z\right) &= \frac{y F_{20}\! \left(x , y\right)-F_{20}\! \left(x , z\right) z}{-z +y}\\
F_{43}\! \left(x , y , z\right) &= F_{44}\! \left(x , z\right) F_{55}\! \left(x , y , z\right)\\
F_{45}\! \left(x , y\right) &= F_{29}\! \left(x \right)+F_{44}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , 1, y\right)\\
F_{47}\! \left(x , y , z\right) &= F_{46}\! \left(x , y z , z\right)\\
F_{47}\! \left(x , y , z\right) &= F_{48}\! \left(x , y , z\right)+F_{49}\! \left(x , y , z\right)\\
F_{48}\! \left(x , y , z\right) &= F_{36}\! \left(x , y z , z\right)\\
F_{49}\! \left(x , y , z\right) &= F_{50}\! \left(x , y , z\right)\\
F_{50}\! \left(x , y , z\right) &= F_{34}\! \left(x \right) F_{51}\! \left(x , y , z\right)\\
F_{51}\! \left(x , y , z\right) &= F_{52}\! \left(x , y , z\right)+F_{54}\! \left(x , y , z\right)\\
F_{52}\! \left(x , y , z\right) &= F_{20}\! \left(x , z\right) F_{53}\! \left(x , y , z\right)\\
F_{53}\! \left(x , y , z\right) &= \frac{y z F_{47}\! \left(x , y , z\right)-F_{47}\! \left(x , \frac{1}{z}, z\right)}{y z -1}\\
F_{54}\! \left(x , y , z\right) &= F_{27}\! \left(x , y z , z\right)\\
F_{55}\! \left(x , y , z\right) &= \frac{z \left(F_{21}\! \left(x , y\right)-F_{21}\! \left(x , z\right)\right)}{-z +y}\\
\end{align*}\)