Av(12453, 12543, 15243, 21453, 21543, 24153, 24513, 25143, 25413, 51243, 52143, 52413)
Counting Sequence
1, 1, 2, 6, 24, 108, 512, 2492, 12309, 61340, 307402, 1546284, 7798059, 39398169, 199317340, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 90 rules.
Finding the specification took 1838 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_{27}\! \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_{27}\! \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_{2}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x , 1\right)\\
F_{12}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= x^{2} F_{13}\! \left(x , y\right)^{2} y^{2}+x F_{13}\! \left(x , y\right)^{4} y +2 x^{2} F_{13}\! \left(x , y\right) y^{2}+3 x F_{13}\! \left(x , y\right)^{3} y +x^{2} y^{2}+x F_{13}\! \left(x , y\right)^{2} y -x F_{13}\! \left(x , y\right) y -F_{13}\! \left(x , y\right)^{3}+F_{13}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= y x\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{16}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{23}\! \left(x \right) F_{27}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{27}\! \left(x \right) &= x\\
F_{28}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{28} \left(x \right)^{2} F_{27}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{2}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{33}\! \left(x \right) &= x F_{33} \left(x \right)^{4}+x^{2} F_{33} \left(x \right)^{2}-F_{33} \left(x \right)^{3} x -2 x F_{33} \left(x \right)^{2}-F_{33} \left(x \right)^{3}+2 F_{33}\! \left(x \right) x +3 F_{33} \left(x \right)^{2}-2 F_{33}\! \left(x \right)+1\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{27}\! \left(x \right) F_{28}\! \left(x \right) F_{32}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{28}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{42}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{20}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{2}\! \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{y \left(F_{49}\! \left(x , 1\right)-F_{49}\! \left(x , y\right)\right)}{-1+y}\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{33}\! \left(x \right) F_{51}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{33}\! \left(x \right)+F_{49}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)\\
F_{55}\! \left(x \right) &= F_{37}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x , 1\right)\\
F_{57}\! \left(x , y\right) &= -\frac{y \left(F_{53}\! \left(x , 1\right)-F_{53}\! \left(x , y\right)\right)}{-1+y}\\
F_{58}\! \left(x \right) &= F_{28}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{28}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{43}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{27}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{69}\! \left(x \right) &= x^{2} F_{69} \left(x \right)^{2}+2 x^{2} F_{69}\! \left(x \right)+4 x F_{69} \left(x \right)^{2}+x^{2}-13 x F_{69}\! \left(x \right)-F_{69} \left(x \right)^{2}+8 x +4 F_{69}\! \left(x \right)-2\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{27}\! \left(x \right) F_{28}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{73}\! \left(x \right) &= x^{2} F_{73} \left(x \right)^{2}+4 x^{2} F_{73}\! \left(x \right)+4 x F_{73} \left(x \right)^{2}+4 x^{2}-5 x F_{73}\! \left(x \right)-F_{73} \left(x \right)^{2}-x +2 F_{73}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x , 1\right)\\
F_{75}\! \left(x , y\right) &= -\frac{-F_{52}\! \left(x , y\right) y +F_{52}\! \left(x , 1\right)}{-1+y}\\
F_{76}\! \left(x \right) &= F_{74}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= -F_{84}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= \frac{F_{83}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{83}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{84}\! \left(x \right) &= x F_{84} \left(x \right)^{4}+x^{2} F_{84} \left(x \right)^{2}+3 x F_{84} \left(x \right)^{3}+2 x^{2} F_{84}\! \left(x \right)+x F_{84} \left(x \right)^{2}-F_{84} \left(x \right)^{3}+x^{2}-F_{84}\! \left(x \right) x +F_{84}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{2}\! \left(x \right) F_{27}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x , 1\right)\\
F_{88}\! \left(x , y\right) &= -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}\\
F_{11}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 135 rules.
Finding the specification took 3267 seconds.
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Copy 135 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{16}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{19}\! \left(x \right) &= x F_{19} \left(x \right)^{4}+x^{2} F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3} x -2 x F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3}+2 F_{19}\! \left(x \right) x +3 F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+1\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{33}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{33}\! \left(x \right) &= x F_{33} \left(x \right)^{4}+x^{2} F_{33} \left(x \right)^{2}+3 x F_{33} \left(x \right)^{3}+2 x^{2} F_{33}\! \left(x \right)+x F_{33} \left(x \right)^{2}-F_{33} \left(x \right)^{3}+x^{2}-F_{33}\! \left(x \right) x +F_{33}\! \left(x \right)\\
F_{34}\! \left(x \right) &= -F_{37}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{36}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{38}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{11}\! \left(x \right) F_{42}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{19}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{19}\! \left(x \right) F_{49}\! \left(x \right) F_{51}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{51}\! \left(x \right) &= x^{2} F_{51} \left(x \right)^{2}+4 x^{2} F_{51}\! \left(x \right)+4 x F_{51} \left(x \right)^{2}+4 x^{2}-5 x F_{51}\! \left(x \right)-F_{51} \left(x \right)^{2}-x +2 F_{51}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{49} \left(x \right)^{2} F_{11}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{11}\! \left(x \right) F_{64}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{11}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{64}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{11}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{11}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{11}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{11}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{49}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{19}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{11}\! \left(x \right) F_{49}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{52}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{19}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{11}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{11}\! \left(x \right) F_{49}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{11}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{105}\! \left(x \right) F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{11}\! \left(x \right) F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{33}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{11}\! \left(x \right) F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{120}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{49}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{19}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{11}\! \left(x \right) F_{133}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{133}\! \left(x \right) &= \frac{F_{134}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{134}\! \left(x \right) &= F_{128}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 135 rules.
Finding the specification took 3267 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_{11}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{16}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{19}\! \left(x \right) &= x F_{19} \left(x \right)^{4}+x^{2} F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3} x -2 x F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3}+2 F_{19}\! \left(x \right) x +3 F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+1\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{33}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{33}\! \left(x \right) &= x F_{33} \left(x \right)^{4}+x^{2} F_{33} \left(x \right)^{2}+3 x F_{33} \left(x \right)^{3}+2 x^{2} F_{33}\! \left(x \right)+x F_{33} \left(x \right)^{2}-F_{33} \left(x \right)^{3}+x^{2}-F_{33}\! \left(x \right) x +F_{33}\! \left(x \right)\\
F_{34}\! \left(x \right) &= -F_{37}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{36}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{38}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{11}\! \left(x \right) F_{42}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{19}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{19}\! \left(x \right) F_{49}\! \left(x \right) F_{51}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{51}\! \left(x \right) &= x^{2} F_{51} \left(x \right)^{2}+4 x^{2} F_{51}\! \left(x \right)+4 x F_{51} \left(x \right)^{2}+4 x^{2}-5 x F_{51}\! \left(x \right)-F_{51} \left(x \right)^{2}-x +2 F_{51}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{49} \left(x \right)^{2} F_{11}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{11}\! \left(x \right) F_{64}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{11}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{64}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{11}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{11}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{11}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{11}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{49}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{19}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{11}\! \left(x \right) F_{49}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{52}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{19}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{11}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{11}\! \left(x \right) F_{49}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{11}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{105}\! \left(x \right) F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{11}\! \left(x \right) F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{33}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{11}\! \left(x \right) F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{120}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{49}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{19}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{11}\! \left(x \right) F_{133}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{133}\! \left(x \right) &= \frac{F_{134}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{134}\! \left(x \right) &= F_{128}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 137 rules.
Finding the specification took 1759 seconds.
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Copy 137 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{16}\! \left(x \right) &= -F_{60}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{19}\! \left(x \right) &= x F_{19} \left(x \right)^{4}+x^{2} F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3} x -2 x F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3}+2 F_{19}\! \left(x \right) x +3 F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+1\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{33}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{19}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{33}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= x F_{37} \left(x \right)^{4}+x^{2} F_{37} \left(x \right)^{2}+3 x F_{37} \left(x \right)^{3}+2 x^{2} F_{37}\! \left(x \right)+x F_{37} \left(x \right)^{2}-F_{37} \left(x \right)^{3}+x^{2}-F_{37}\! \left(x \right) x +F_{37}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{39}\! \left(x \right) &= -F_{46}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= \frac{F_{41}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{11}\! \left(x \right) F_{43}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{37}\! \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 \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{19}\! \left(x \right) F_{50}\! \left(x \right) F_{52}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{52}\! \left(x \right) &= x^{2} F_{52} \left(x \right)^{2}+4 x^{2} F_{52}\! \left(x \right)+4 x F_{52} \left(x \right)^{2}+4 x^{2}-5 x F_{52}\! \left(x \right)-F_{52} \left(x \right)^{2}-x +2 F_{52}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{50} \left(x \right)^{2} F_{11}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{57}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{59}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{11}\! \left(x \right) F_{66}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{11}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{66}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{11}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{11}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{11}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{11}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{50}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{19}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{53}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{19}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{11}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{107}\! \left(x \right) F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{11}\! \left(x \right) F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{37}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{11}\! \left(x \right) F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{50}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{19}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{11}\! \left(x \right) F_{134}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{129}\! \left(x \right)\\
\end{align*}\)