Av(13524, 13542, 31524, 31542, 35124, 35142, 35214)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3124, 17330, 98038, 562364, 3259267, 19040394, 111936899, 661453238, ...
This specification was found using the strategy pack "Point Placements Req Corrob" and has 91 rules.
Finding the specification took 1411 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_{32}\! \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_{32}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= -F_{90}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{22}\! \left(x \right) &= \frac{F_{23}\! \left(x \right)}{F_{38}\! \left(x \right)}\\
F_{23}\! \left(x \right) &= -F_{17}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{2}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{32}\! \left(x \right) &= x\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{0}\! \left(x \right) F_{32}\! \left(x \right) F_{35}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{0}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{38}\! \left(x \right) x +F_{38} \left(x \right)^{2}-2 F_{38}\! \left(x \right)+2\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{37} \left(x \right)^{2} F_{32}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{32}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{2}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= -F_{70}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{51} \left(x \right)^{2} F_{32}\! \left(x \right)\\
F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{35}\! \left(x \right)}\\
F_{55}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{32}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{0}\! \left(x \right) F_{32}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{65}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{32}\! \left(x \right) F_{51}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{50}\! \left(x \right) F_{68}\! \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) &= \frac{F_{73}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= -F_{82}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= \frac{F_{78}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{87}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= -F_{86}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{86}\! \left(x \right) x +F_{86} \left(x \right)^{2}+x\\
F_{87}\! \left(x \right) &= F_{2}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{75}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{26}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 92 rules.
Finding the specification took 844 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_{32}\! \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_{32}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= -F_{91}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{22}\! \left(x \right) &= \frac{F_{23}\! \left(x \right)}{F_{38}\! \left(x \right)}\\
F_{23}\! \left(x \right) &= -F_{17}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{2}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{32}\! \left(x \right) &= x\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{0}\! \left(x \right) F_{32}\! \left(x \right) F_{35}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{0}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{38}\! \left(x \right) x +F_{38} \left(x \right)^{2}-2 F_{38}\! \left(x \right)+2\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{37} \left(x \right)^{2} F_{32}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{32}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{2}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= -F_{70}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{51} \left(x \right)^{2} F_{32}\! \left(x \right)\\
F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{35}\! \left(x \right)}\\
F_{55}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{32}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{0}\! \left(x \right) F_{32}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{65}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{32}\! \left(x \right) F_{51}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{50}\! \left(x \right) F_{68}\! \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) &= \frac{F_{73}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= -F_{85}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= \frac{F_{78}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{80}\! \left(x \right) x +F_{80} \left(x \right)^{2}+x\\
F_{81}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{84}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{85}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{87}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{2}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{75}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{26}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 103 rules.
Finding the specification took 615 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_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{12}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{28}\! \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_{12}\! \left(x \right)}\\
F_{21}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x , 1\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= x F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , y\right)^{2}-2 F_{24}\! \left(x , y\right)+2\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)^{2} F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= y x\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{97}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{12}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= \frac{F_{37}\! \left(x \right)}{F_{61}\! \left(x \right)}\\
F_{37}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= -F_{44}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{60}\! \left(x \right)}\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{64}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{59}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{12}\! \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) &= \frac{F_{58}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{58}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{0}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{61}\! \left(x \right) x +F_{61} \left(x \right)^{2}-2 F_{61}\! \left(x \right)+2\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{22} \left(x \right)^{2} F_{12}\! \left(x \right)\\
F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= -F_{74}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{12}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{2}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{88}\! \left(x \right)}\\
F_{79}\! \left(x \right) &= -F_{87}\! \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_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{83}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{4}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x , 1\right)\\
F_{89}\! \left(x , y\right) &= -\frac{-F_{90}\! \left(x , y\right) y +F_{90}\! \left(x , 1\right)}{-1+y}\\
F_{90}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right) F_{23}\! \left(x , y\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) &= F_{96}\! \left(x , 1\right)\\
F_{96}\! \left(x , y\right) &= -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{12}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x , 1\right)\\
F_{102}\! \left(x , y\right) &= -\frac{-y F_{23}\! \left(x , y\right)+F_{23}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)