Av(12354, 12453, 13254, 13452, 14253, 14352, 15243, 15342, 23154, 24153, 25143)
Generating Function
\(\displaystyle \frac{-\sqrt{6 x -1}\, \left(2 x -1\right)^{\frac{3}{2}}+6 x^{3}-10 x^{2}+2 x +1}{2 x \left(3 x -2\right)^{2}}\)
Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2574, 12964, 66426, 345300, 1816976, 9660732, 51825093, 280168474, ...
Implicit Equation for the Generating Function
\(\displaystyle x \left(3 x -2\right)^{2} F \left(x
\right)^{2}+\left(-6 x^{3}+10 x^{2}-2 x -1\right) F \! \left(x \right)+x^{3}-2 x^{2}-x +1 = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a{\left(n + 3 \right)} = \frac{18 \left(n + 1\right) a{\left(n \right)}}{n + 4} - \frac{3 \left(8 n + 13\right) a{\left(n + 1 \right)}}{n + 4} + \frac{\left(19 n + 51\right) a{\left(n + 2 \right)}}{2 \left(n + 4\right)}, \quad n \geq 4\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a{\left(n + 3 \right)} = \frac{18 \left(n + 1\right) a{\left(n \right)}}{n + 4} - \frac{3 \left(8 n + 13\right) a{\left(n + 1 \right)}}{n + 4} + \frac{\left(19 n + 51\right) a{\left(n + 2 \right)}}{2 \left(n + 4\right)}, \quad n \geq 4\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 427 rules.
Finding the specification took 19432 seconds.
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Copy 427 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_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{16}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= x\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{22}\! \left(x \right) &= 0\\
F_{23}\! \left(x \right) &= F_{16}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{16}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{16}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{32}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{16}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{16}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{16}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{16}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{403}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{13}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{16}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{282}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{2}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{162}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= -F_{253}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{13}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= -F_{162}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{12}\! \left(x \right) F_{16}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{68}\! \left(x \right) &= -F_{158}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{16}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{80}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{16}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{16}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{10}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{16}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{92}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{14}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{16}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{16}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{16}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)+F_{103}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{16}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{106}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{115}\! \left(x \right)+F_{117}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{111}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{122}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{16}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{126}\! \left(x \right)+F_{127}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{106}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{133}\! \left(x \right)+F_{134}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{129}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{139}\! \left(x \right)+F_{140}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{16}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{145}\! \left(x \right)+F_{146}\! \left(x \right)+F_{148}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{112}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{135}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{157}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{121}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{150}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{163}\! \left(x \right) &= -F_{252}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= \frac{F_{165}\! \left(x \right)}{F_{16}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{16}\! \left(x \right) F_{168}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{168}\! \left(x \right) &= \frac{F_{169}\! \left(x \right)}{F_{16}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{157}\! \left(x \right) F_{16}\! \left(x \right) F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{16}\! \left(x \right) F_{173}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{16}\! \left(x \right) F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{16}\! \left(x \right) F_{181}\! \left(x \right) F_{250}\! \left(x \right)\\
F_{181}\! \left(x \right) &= \frac{F_{182}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= -F_{65}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= -F_{170}\! \left(x \right)+F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= \frac{F_{186}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{16}\! \left(x \right) F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{16}\! \left(x \right) F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{162}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{20}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{200}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{119}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{121}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{202}\! \left(x \right) &= -F_{205}\! \left(x \right)+F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= \frac{F_{204}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{204}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{16}\! \left(x \right) F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{232}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{157}\! \left(x \right) F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{209}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{230}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{16}\! \left(x \right) F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= -F_{220}\! \left(x \right)+F_{218}\! \left(x \right)\\
F_{218}\! \left(x \right) &= \frac{F_{219}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{219}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{16}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{221}\! \left(x \right)+F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{16}\! \left(x \right) F_{227}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{16}\! \left(x \right) F_{18}\! \left(x \right) F_{227}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{16}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{227}\! \left(x \right) F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{16}\! \left(x \right) F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)+F_{247}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{215}\! \left(x \right) F_{250}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{13}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{253}\! \left(x \right) &= -F_{254}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{162}\! \left(x \right) F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= -F_{44}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{16}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= -F_{260}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{261}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{20} \left(x \right)^{2} F_{16}\! \left(x \right) F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= \frac{F_{263}\! \left(x \right)}{F_{233}\! \left(x \right)}\\
F_{263}\! \left(x \right) &= -F_{279}\! \left(x \right)+F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= \frac{F_{265}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{16}\! \left(x \right) F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{277}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{270}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{270}\! \left(x \right) &= \frac{F_{271}\! \left(x \right)}{F_{16}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{271}\! \left(x \right) &= F_{171}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{16}\! \left(x \right) F_{274}\! \left(x \right)\\
F_{274}\! \left(x \right) &= \frac{F_{275}\! \left(x \right)}{F_{16}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{16}\! \left(x \right) F_{250}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{157}\! \left(x \right) F_{278}\! \left(x \right)\\
F_{278}\! \left(x \right) &= -F_{269}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{157}\! \left(x \right) F_{280}\! \left(x \right)\\
F_{280}\! \left(x \right) &= \frac{F_{281}\! \left(x \right)}{F_{16}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{281}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{16}\! \left(x \right) F_{284}\! \left(x \right)\\
F_{284}\! \left(x \right) &= \frac{F_{285}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{285}\! \left(x \right) &= F_{286}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{16}\! \left(x \right) F_{287}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{402}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{269}\! \left(x \right) F_{289}\! \left(x \right)\\
F_{289}\! \left(x \right) &= \frac{F_{290}\! \left(x \right)}{F_{16}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)+F_{400}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)+F_{302}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{16}\! \left(x \right) F_{295}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{296}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{293}\! \left(x \right)+F_{297}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{16}\! \left(x \right) F_{299}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{300}\! \left(x \right)+F_{301}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{297}\! \left(x \right)\\
F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{16}\! \left(x \right) F_{304}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{305}\! \left(x \right)+F_{395}\! \left(x \right)\\
F_{305}\! \left(x \right) &= -F_{313}\! \left(x \right)+F_{306}\! \left(x \right)\\
F_{306}\! \left(x \right) &= \frac{F_{307}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{307}\! \left(x \right) &= F_{308}\! \left(x \right)\\
F_{308}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{309}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)\\
F_{310}\! \left(x \right) &= F_{16}\! \left(x \right) F_{311}\! \left(x \right)\\
F_{311}\! \left(x \right) &= \frac{F_{312}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{312}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)\\
F_{314}\! \left(x \right) &= F_{16}\! \left(x \right) F_{315}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{394}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{317}\! \left(x \right)+F_{318}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{309}\! \left(x \right)\\
F_{318}\! \left(x \right) &= F_{319}\! \left(x \right)\\
F_{319}\! \left(x \right) &= F_{16}\! \left(x \right) F_{320}\! \left(x \right)\\
F_{320}\! \left(x \right) &= \frac{F_{321}\! \left(x \right)}{F_{0}\! \left(x \right) F_{121}\! \left(x \right)}\\
F_{321}\! \left(x \right) &= -F_{389}\! \left(x \right)+F_{322}\! \left(x \right)\\
F_{322}\! \left(x \right) &= \frac{F_{323}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{323}\! \left(x \right) &= F_{324}\! \left(x \right)\\
F_{324}\! \left(x \right) &= -F_{388}\! \left(x \right)+F_{325}\! \left(x \right)\\
F_{325}\! \left(x \right) &= \frac{F_{326}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{326}\! \left(x \right) &= F_{327}\! \left(x \right)\\
F_{327}\! \left(x \right) &= -F_{387}\! \left(x \right)+F_{328}\! \left(x \right)\\
F_{328}\! \left(x \right) &= -F_{386}\! \left(x \right)+F_{329}\! \left(x \right)\\
F_{329}\! \left(x \right) &= -F_{330}\! \left(x \right)+F_{311}\! \left(x \right)\\
F_{330}\! \left(x \right) &= F_{331}\! \left(x \right)+F_{378}\! \left(x \right)\\
F_{331}\! \left(x \right) &= F_{309}\! \left(x \right)+F_{332}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{333}\! \left(x \right)\\
F_{333}\! \left(x \right) &= F_{16}\! \left(x \right) F_{334}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{335}\! \left(x \right)+F_{338}\! \left(x \right)\\
F_{335}\! \left(x \right) &= F_{309}\! \left(x \right) F_{336}\! \left(x \right)\\
F_{336}\! \left(x \right) &= \frac{F_{337}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{337}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{338}\! \left(x \right) &= F_{339}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{16}\! \left(x \right) F_{340}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{341}\! \left(x \right)+F_{345}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{289}\! \left(x \right) F_{342}\! \left(x \right)\\
F_{342}\! \left(x \right) &= \frac{F_{343}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{343}\! \left(x \right) &= F_{344}\! \left(x \right)\\
F_{344}\! \left(x \right) &= -F_{74}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{346}\! \left(x \right) F_{368}\! \left(x \right)\\
F_{346}\! \left(x \right) &= \frac{F_{347}\! \left(x \right)}{F_{157}\! \left(x \right)}\\
F_{347}\! \left(x \right) &= -F_{367}\! \left(x \right)+F_{348}\! \left(x \right)\\
F_{348}\! \left(x \right) &= \frac{F_{349}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{349}\! \left(x \right) &= F_{350}\! \left(x \right)\\
F_{350}\! \left(x \right) &= -F_{365}\! \left(x \right)+F_{351}\! \left(x \right)\\
F_{351}\! \left(x \right) &= \frac{F_{352}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{352}\! \left(x \right) &= F_{353}\! \left(x \right)\\
F_{353}\! \left(x \right) &= -F_{356}\! \left(x \right)+F_{354}\! \left(x \right)\\
F_{354}\! \left(x \right) &= \frac{F_{355}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{355}\! \left(x \right) &= F_{188}\! \left(x \right)\\
F_{356}\! \left(x \right) &= -F_{359}\! \left(x \right)+F_{357}\! \left(x \right)\\
F_{357}\! \left(x \right) &= \frac{F_{358}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{358}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{359}\! \left(x \right) &= F_{360}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{360}\! \left(x \right) &= -F_{363}\! \left(x \right)+F_{361}\! \left(x \right)\\
F_{361}\! \left(x \right) &= \frac{F_{362}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{362}\! \left(x \right) &= F_{308}\! \left(x \right)\\
F_{363}\! \left(x \right) &= F_{364}\! \left(x \right)\\
F_{364}\! \left(x \right) &= F_{16}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{365}\! \left(x \right) &= \frac{F_{366}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{366}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{367}\! \left(x \right) &= F_{342}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{368}\! \left(x \right) &= \frac{F_{369}\! \left(x \right)}{F_{150}\! \left(x \right)}\\
F_{369}\! \left(x \right) &= -F_{385}\! \left(x \right)+F_{370}\! \left(x \right)\\
F_{370}\! \left(x \right) &= \frac{F_{371}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{371}\! \left(x \right) &= F_{372}\! \left(x \right)\\
F_{372}\! \left(x \right) &= F_{373}\! \left(x \right)+F_{378}\! \left(x \right)\\
F_{373}\! \left(x \right) &= F_{327}\! \left(x \right)+F_{374}\! \left(x \right)\\
F_{374}\! \left(x \right) &= F_{375}\! \left(x \right)\\
F_{375}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{376}\! \left(x \right)\\
F_{376}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{377}\! \left(x \right)\\
F_{377}\! \left(x \right) &= F_{0}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{378}\! \left(x \right) &= F_{379}\! \left(x \right)\\
F_{379}\! \left(x \right) &= F_{16}\! \left(x \right) F_{380}\! \left(x \right)\\
F_{380}\! \left(x \right) &= F_{381}\! \left(x \right)+F_{384}\! \left(x \right)\\
F_{381}\! \left(x \right) &= F_{382}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{382}\! \left(x \right) &= \frac{F_{383}\! \left(x \right)}{F_{16}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{383}\! \left(x \right) &= F_{291}\! \left(x \right)\\
F_{384}\! \left(x \right) &= F_{152}\! \left(x \right) F_{368}\! \left(x \right)\\
F_{385}\! \left(x \right) &= F_{382}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{386}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{374}\! \left(x \right)\\
F_{387}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{388}\! \left(x \right) &= F_{317}\! \left(x \right) F_{374}\! \left(x \right)\\
F_{389}\! \left(x \right) &= F_{20}\! \left(x \right) F_{390}\! \left(x \right)\\
F_{390}\! \left(x \right) &= \frac{F_{391}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{391}\! \left(x \right) &= F_{392}\! \left(x \right)\\
F_{392}\! \left(x \right) &= -F_{393}\! \left(x \right)+F_{306}\! \left(x \right)\\
F_{393}\! \left(x \right) &= F_{2}\! \left(x \right) F_{317}\! \left(x \right)\\
F_{394}\! \left(x \right) &= F_{305}\! \left(x \right)\\
F_{395}\! \left(x \right) &= F_{396}\! \left(x \right)\\
F_{396}\! \left(x \right) &= F_{16}\! \left(x \right) F_{397}\! \left(x \right)\\
F_{397}\! \left(x \right) &= F_{398}\! \left(x \right)+F_{399}\! \left(x \right)\\
F_{398}\! \left(x \right) &= F_{20}\! \left(x \right) F_{315}\! \left(x \right)\\
F_{399}\! \left(x \right) &= F_{121}\! \left(x \right) F_{316}\! \left(x \right)\\
F_{400}\! \left(x \right) &= F_{401}\! \left(x \right)\\
F_{401}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{292}\! \left(x \right)\\
F_{402}\! \left(x \right) &= F_{278}\! \left(x \right) F_{368}\! \left(x \right)\\
F_{403}\! \left(x \right) &= F_{404}\! \left(x \right)\\
F_{404}\! \left(x \right) &= F_{16}\! \left(x \right) F_{405}\! \left(x \right)\\
F_{405}\! \left(x \right) &= F_{406}\! \left(x \right)+F_{422}\! \left(x \right)\\
F_{406}\! \left(x \right) &= \frac{F_{407}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)\\
F_{408}\! \left(x \right) &= -F_{8}\! \left(x \right)+F_{409}\! \left(x \right)\\
F_{409}\! \left(x \right) &= F_{410}\! \left(x \right)+F_{420}\! \left(x \right)\\
F_{410}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{411}\! \left(x \right)\\
F_{411}\! \left(x \right) &= F_{412}\! \left(x \right)\\
F_{412}\! \left(x \right) &= F_{16}\! \left(x \right) F_{413}\! \left(x \right)\\
F_{413}\! \left(x \right) &= F_{256}\! \left(x \right)+F_{414}\! \left(x \right)\\
F_{414}\! \left(x \right) &= -F_{415}\! \left(x \right)+F_{260}\! \left(x \right)\\
F_{415}\! \left(x \right) &= -F_{166}\! \left(x \right)+F_{416}\! \left(x \right)\\
F_{416}\! \left(x \right) &= F_{417}\! \left(x \right)\\
F_{417}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{418}\! \left(x \right)\\
F_{418}\! \left(x \right) &= F_{278}\! \left(x \right)+F_{419}\! \left(x \right)\\
F_{419}\! \left(x \right) &= F_{20}\! \left(x \right) F_{269}\! \left(x \right)\\
F_{420}\! \left(x \right) &= F_{421}\! \left(x \right)\\
F_{421}\! \left(x \right) &= F_{16}\! \left(x \right) F_{280}\! \left(x \right)\\
F_{422}\! \left(x \right) &= F_{423}\! \left(x \right)\\
F_{423}\! \left(x \right) &= F_{16}\! \left(x \right) F_{424}\! \left(x \right)\\
F_{424}\! \left(x \right) &= F_{425}\! \left(x \right)+F_{426}\! \left(x \right)\\
F_{425}\! \left(x \right) &= F_{20}\! \left(x \right) F_{280}\! \left(x \right)\\
F_{426}\! \left(x \right) &= F_{121}\! \left(x \right) F_{262}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 409 rules.
Finding the specification took 6548 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_{139}\! \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_{15}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{11}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= -F_{20}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{37} \left(x \right)^{2} F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= \frac{F_{23}\! \left(x \right)}{F_{153}\! \left(x \right)}\\
F_{23}\! \left(x \right) &= -F_{150}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{11}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{11}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{11}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{11}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{11}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{50}\! \left(x \right) &= 0\\
F_{51}\! \left(x \right) &= F_{11}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{11}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{11}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{11}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{62}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{11}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{11}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{11}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{11}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{11}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{11}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{11}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{11}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{11}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{50}\! \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_{11}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{95}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{11}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{11}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{102}\! \left(x \right)+F_{50}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{11}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{11}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{108}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{11}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{112}\! \left(x \right)+F_{113}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{11}\! \left(x \right) F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{11}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{11}\! \left(x \right) F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{119}\! \left(x \right)+F_{120}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{11}\! \left(x \right) F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{11}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{11}\! \left(x \right) F_{115}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{125}\! \left(x \right)+F_{126}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{11}\! \left(x \right) F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{11}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{11}\! \left(x \right) F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{131}\! \left(x \right)+F_{132}\! \left(x \right)+F_{134}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{11}\! \left(x \right) F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{11}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{11}\! \left(x \right) F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{11}\! \left(x \right) F_{121}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{11}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{11}\! \left(x \right) F_{141}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{141}\! \left(x \right) &= \frac{F_{142}\! \left(x \right)}{F_{11}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{11}\! \left(x \right) F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{147}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{151}\! \left(x \right) &= \frac{F_{152}\! \left(x \right)}{F_{11}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{152}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{154}\! \left(x \right) &= -F_{155}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{155}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= -F_{398}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{394}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{159}\! \left(x \right) &= \frac{F_{160}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{166}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{2}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{11}\! \left(x \right) F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{170}\! \left(x \right) &= \frac{F_{171}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= \frac{F_{173}\! \left(x \right)}{F_{212}\! \left(x \right)}\\
F_{173}\! \left(x \right) &= -F_{209}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{11}\! \left(x \right) F_{179}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{181}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{182}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= \frac{F_{184}\! \left(x \right)}{F_{37}\! \left(x \right)}\\
F_{184}\! \left(x \right) &= -F_{202}\! \left(x \right)+F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= \frac{F_{186}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{11}\! \left(x \right) F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{11}\! \left(x \right) F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{107}\! \left(x \right) F_{190}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{195}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{180}\! \left(x \right) F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{205}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{206}\! \left(x \right) &= -F_{207}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{209}\! \left(x \right) &= -F_{210}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right) F_{212}\! \left(x \right)\\
F_{211}\! \left(x \right) &= -F_{164}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{11}\! \left(x \right) F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= \frac{F_{216}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{11}\! \left(x \right) F_{218}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{393}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{220}\! \left(x \right) &= \frac{F_{221}\! \left(x \right)}{F_{11}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{391}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{233}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{11}\! \left(x \right) F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{227}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{11}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{232}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{228}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{11}\! \left(x \right) F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{385}\! \left(x \right)\\
F_{236}\! \left(x \right) &= -F_{248}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= \frac{F_{238}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{11}\! \left(x \right) F_{244}\! \left(x \right)\\
F_{244}\! \left(x \right) &= \frac{F_{245}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{11}\! \left(x \right) F_{250}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)+F_{252}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{11}\! \left(x \right) F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= \frac{F_{256}\! \left(x \right)}{F_{0}\! \left(x \right) F_{107}\! \left(x \right)}\\
F_{256}\! \left(x \right) &= -F_{380}\! \left(x \right)+F_{257}\! \left(x \right)\\
F_{257}\! \left(x \right) &= \frac{F_{258}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= -F_{379}\! \left(x \right)+F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= \frac{F_{261}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= -F_{375}\! \left(x \right)+F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= -F_{374}\! \left(x \right)+F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= -F_{265}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{366}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{11}\! \left(x \right) F_{269}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{270}\! \left(x \right)+F_{273}\! \left(x \right)\\
F_{270}\! \left(x \right) &= F_{242}\! \left(x \right) F_{271}\! \left(x \right)\\
F_{271}\! \left(x \right) &= \frac{F_{272}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{272}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{11}\! \left(x \right) F_{275}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{280}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{220}\! \left(x \right) F_{277}\! \left(x \right)\\
F_{277}\! \left(x \right) &= \frac{F_{278}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= -F_{190}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{281}\! \left(x \right) F_{361}\! \left(x \right)\\
F_{281}\! \left(x \right) &= \frac{F_{282}\! \left(x \right)}{F_{40}\! \left(x \right)}\\
F_{282}\! \left(x \right) &= -F_{360}\! \left(x \right)+F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= \frac{F_{284}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\
F_{285}\! \left(x \right) &= -F_{358}\! \left(x \right)+F_{286}\! \left(x \right)\\
F_{286}\! \left(x \right) &= \frac{F_{287}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)\\
F_{288}\! \left(x \right) &= -F_{349}\! \left(x \right)+F_{289}\! \left(x \right)\\
F_{289}\! \left(x \right) &= \frac{F_{290}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{11}\! \left(x \right) F_{293}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)+F_{305}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{296}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{291}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{11}\! \left(x \right) F_{298}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right)+F_{302}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{300}\! \left(x \right)+F_{301}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{205}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{177}\! \left(x \right) F_{203}\! \left(x \right)\\
F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{304}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{38}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{182}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{305}\! \left(x \right) &= F_{306}\! \left(x \right)+F_{337}\! \left(x \right)\\
F_{306}\! \left(x \right) &= -F_{309}\! \left(x \right)+F_{307}\! \left(x \right)\\
F_{307}\! \left(x \right) &= \frac{F_{308}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{308}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)\\
F_{310}\! \left(x \right) &= F_{11}\! \left(x \right) F_{311}\! \left(x \right)\\
F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{336}\! \left(x \right)\\
F_{312}\! \left(x \right) &= F_{313}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)+F_{317}\! \left(x \right)\\
F_{314}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{11}\! \left(x \right) F_{313}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{318}\! \left(x \right)+F_{334}\! \left(x \right)\\
F_{318}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{319}\! \left(x \right)\\
F_{319}\! \left(x \right) &= F_{320}\! \left(x \right)\\
F_{320}\! \left(x \right) &= F_{11}\! \left(x \right) F_{321}\! \left(x \right)\\
F_{321}\! \left(x \right) &= -F_{324}\! \left(x \right)+F_{322}\! \left(x \right)\\
F_{322}\! \left(x \right) &= \frac{F_{323}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{323}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{324}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{325}\! \left(x \right)\\
F_{325}\! \left(x \right) &= F_{326}\! \left(x \right)\\
F_{326}\! \left(x \right) &= F_{11}\! \left(x \right) F_{327}\! \left(x \right)\\
F_{327}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{328}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{329}\! \left(x \right)+F_{332}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{330}\! \left(x \right)\\
F_{330}\! \left(x \right) &= F_{11}\! \left(x \right) F_{331}\! \left(x \right)\\
F_{331}\! \left(x \right) &= F_{328}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{333}\! \left(x \right)\\
F_{333}\! \left(x \right) &= F_{11}\! \left(x \right) F_{329}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{335}\! \left(x \right)\\
F_{335}\! \left(x \right) &= F_{11}\! \left(x \right) F_{327}\! \left(x \right)\\
F_{336}\! \left(x \right) &= F_{153}\! \left(x \right) F_{331}\! \left(x \right)\\
F_{337}\! \left(x \right) &= F_{338}\! \left(x \right)\\
F_{338}\! \left(x \right) &= F_{11}\! \left(x \right) F_{339}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{340}\! \left(x \right)+F_{348}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{246}\! \left(x \right) F_{341}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{342}\! \left(x \right)+F_{345}\! \left(x \right)\\
F_{342}\! \left(x \right) &= F_{343}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{343}\! \left(x \right) &= F_{344}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{344}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{346}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{346}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{347}\! \left(x \right)\\
F_{347}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{348}\! \left(x \right) &= F_{319}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{349}\! \left(x \right) &= -F_{352}\! \left(x \right)+F_{350}\! \left(x \right)\\
F_{350}\! \left(x \right) &= \frac{F_{351}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{351}\! \left(x \right) &= F_{295}\! \left(x \right)\\
F_{352}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{353}\! \left(x \right) &= -F_{356}\! \left(x \right)+F_{354}\! \left(x \right)\\
F_{354}\! \left(x \right) &= \frac{F_{355}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{355}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{356}\! \left(x \right) &= F_{357}\! \left(x \right)\\
F_{357}\! \left(x \right) &= F_{11}\! \left(x \right) F_{185}\! \left(x \right)\\
F_{358}\! \left(x \right) &= \frac{F_{359}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{359}\! \left(x \right) &= F_{306}\! \left(x \right)\\
F_{360}\! \left(x \right) &= F_{277}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{361}\! \left(x \right) &= \frac{F_{362}\! \left(x \right)}{F_{195}\! \left(x \right)}\\
F_{362}\! \left(x \right) &= -F_{373}\! \left(x \right)+F_{363}\! \left(x \right)\\
F_{363}\! \left(x \right) &= \frac{F_{364}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{364}\! \left(x \right) &= F_{365}\! \left(x \right)\\
F_{365}\! \left(x \right) &= F_{263}\! \left(x \right)+F_{366}\! \left(x \right)\\
F_{366}\! \left(x \right) &= F_{367}\! \left(x \right)\\
F_{367}\! \left(x \right) &= F_{11}\! \left(x \right) F_{368}\! \left(x \right)\\
F_{368}\! \left(x \right) &= F_{369}\! \left(x \right)+F_{372}\! \left(x \right)\\
F_{369}\! \left(x \right) &= F_{191}\! \left(x \right) F_{370}\! \left(x \right)\\
F_{370}\! \left(x \right) &= \frac{F_{371}\! \left(x \right)}{F_{11}\! \left(x \right) F_{37}\! \left(x \right)}\\
F_{371}\! \left(x \right) &= F_{222}\! \left(x \right)\\
F_{372}\! \left(x \right) &= F_{197}\! \left(x \right) F_{361}\! \left(x \right)\\
F_{373}\! \left(x \right) &= F_{190}\! \left(x \right) F_{370}\! \left(x \right)\\
F_{374}\! \left(x \right) &= F_{0} \left(x \right)^{2}\\
F_{375}\! \left(x \right) &= F_{376}\! \left(x \right)\\
F_{376}\! \left(x \right) &= F_{11}\! \left(x \right) F_{37}\! \left(x \right) F_{377}\! \left(x \right)\\
F_{377}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{378}\! \left(x \right)\\
F_{378}\! \left(x \right) &= F_{0}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{379}\! \left(x \right) &= F_{241}\! \left(x \right) F_{375}\! \left(x \right)\\
F_{380}\! \left(x \right) &= F_{37}\! \left(x \right) F_{381}\! \left(x \right)\\
F_{381}\! \left(x \right) &= \frac{F_{382}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{382}\! \left(x \right) &= F_{383}\! \left(x \right)\\
F_{383}\! \left(x \right) &= -F_{384}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{384}\! \left(x \right) &= F_{2}\! \left(x \right) F_{241}\! \left(x \right)\\
F_{385}\! \left(x \right) &= F_{386}\! \left(x \right)\\
F_{386}\! \left(x \right) &= F_{11}\! \left(x \right) F_{387}\! \left(x \right)\\
F_{387}\! \left(x \right) &= F_{388}\! \left(x \right)+F_{389}\! \left(x \right)\\
F_{388}\! \left(x \right) &= F_{250}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{389}\! \left(x \right) &= F_{107}\! \left(x \right) F_{390}\! \left(x \right)\\
F_{390}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{391}\! \left(x \right) &= F_{392}\! \left(x \right)\\
F_{392}\! \left(x \right) &= F_{11}\! \left(x \right) F_{370}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{393}\! \left(x \right) &= F_{136}\! \left(x \right) F_{361}\! \left(x \right)\\
F_{394}\! \left(x \right) &= F_{395}\! \left(x \right)\\
F_{395}\! \left(x \right) &= F_{11}\! \left(x \right) F_{37}\! \left(x \right) F_{396}\! \left(x \right)\\
F_{396}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{397}\! \left(x \right)\\
F_{397}\! \left(x \right) &= F_{29}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{398}\! \left(x \right) &= -F_{402}\! \left(x \right)+F_{399}\! \left(x \right)\\
F_{399}\! \left(x \right) &= \frac{F_{400}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{400}\! \left(x \right) &= F_{401}\! \left(x \right)\\
F_{401}\! \left(x \right) &= F_{11}\! \left(x \right) F_{157}\! \left(x \right)\\
F_{402}\! \left(x \right) &= F_{403}\! \left(x \right)\\
F_{403}\! \left(x \right) &= -F_{139}\! \left(x \right)+F_{404}\! \left(x \right)\\
F_{404}\! \left(x \right) &= \frac{F_{405}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{405}\! \left(x \right) &= F_{406}\! \left(x \right)\\
F_{406}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{407}\! \left(x \right)\\
F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)\\
F_{408}\! \left(x \right) &= F_{11}\! \left(x \right) F_{399}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "All The Strategies 2 Tracked Fusion Tracked Component Fusion Symmetries" and has 103 rules.
Finding the specification took 13333 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_{5}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{0} \left(x \right)^{2}\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{27}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{101}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x , 1\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{68}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= y F_{26}\! \left(x \right)\\
F_{26}\! \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_{23}\! \left(x , 1\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{66}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= y F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{27}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= -F_{41}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{27}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{40}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{27}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{27}\! \left(x \right)}\\
F_{45}\! \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_{57}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{27}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{52}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{52}\! \left(x \right) &= 0\\
F_{53}\! \left(x \right) &= F_{27}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{27}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{27}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{46}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{27}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{0}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{66}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= y x\\
F_{68}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{27}\! \left(x \right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{27}\! \left(x \right) F_{71}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{27}\! \left(x \right) F_{71}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{72}\! \left(x , y\right)+F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{66}\! \left(x , y\right) F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{66}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= y F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{27}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{27}\! \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_{1}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{27}\! \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_{27}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{91}\! \left(x , y\right) &= y^{2} F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{27}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{27}\! \left(x \right) F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{96}\! \left(x , y\right)+F_{97}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{23}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{98}\! \left(x , y\right) F_{99}\! \left(x \right)\\
F_{23}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{99}\! \left(x \right) &= -F_{36}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{2}\! \left(x \right)\\
\end{align*}\)