Av(13254, 13524, 31254, 31524, 32154, 32514, 35124, 35214)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3028, 16690, 94229, 541722, 3158594, 18625214, 110838544, 664625680, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 251 rules.
Finding the specification took 33492 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{12}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{0}\! \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_{7}\! \left(x \right)\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{180}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \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_{35}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= y x\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{17}\! \left(x \right)+F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{247}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{84}\! \left(x \right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)+F_{41}\! \left(x \right)\\
F_{40}\! \left(x , y\right) &= -\frac{-F_{21}\! \left(x , y\right) y +F_{21}\! \left(x , 1\right)}{-1+y}\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x , 1\right)\\
F_{43}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{43}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x \right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{52}\! \left(x \right) &= 0\\
F_{53}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{50}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{49}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= y F_{61}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{52}\! \left(x \right)+F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{65}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{73}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{73}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{78}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{80}\! \left(x , y\right) F_{84}\! \left(x \right)\\
F_{80}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= y F_{83}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= -\frac{-F_{71}\! \left(x , y\right) y +F_{71}\! \left(x , 1\right)}{-1+y}\\
F_{84}\! \left(x \right) &= x^{4} F_{84} \left(x \right)^{3}+5 x^{3} F_{84} \left(x \right)^{2}-11 x^{2} F_{84} \left(x \right)^{2}+3 x^{2} F_{84}\! \left(x \right)+10 x F_{84}\! \left(x \right)-9 x +1\\
F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{87}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{87}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{84}\! \left(x \right) F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{25}\! \left(x , y\right) F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{96}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{97}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{97}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{99}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{99}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{102}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)\\
F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)+F_{227}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{226}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{219}\! \left(x , y\right)\\
F_{113}\! \left(x , y\right) &= F_{114}\! \left(x , y\right) F_{2}\! \left(x \right)\\
F_{115}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{117}\! \left(x , y\right)\\
F_{116}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{116}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)\\
F_{118}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{159}\! \left(x , y\right)\\
F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{123}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{122}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{124}\! \left(x \right)+F_{148}\! \left(x , y\right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{12}\! \left(x \right) F_{127}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x , 1\right)\\
F_{129}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{139}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)+F_{84}\! \left(x \right)\\
F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)\\
F_{133}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{134}\! \left(x , y\right)\\
F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)+F_{137}\! \left(x , y\right)\\
F_{135}\! \left(x , y\right) &= F_{136}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{136}\! \left(x \right) &= F_{124}\! \left(x \right)\\
F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{129}\! \left(x , y\right) &= F_{136}\! \left(x \right)+F_{138}\! \left(x , y\right)\\
F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)+F_{142}\! \left(x , y\right)\\
F_{140}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= x^{4} F_{141} \left(x \right)^{3}+3 x^{4} F_{141} \left(x \right)^{2}+3 x^{4} F_{141}\! \left(x \right)+5 x^{3} F_{141} \left(x \right)^{2}+x^{4}+10 x^{3} F_{141}\! \left(x \right)-11 x^{2} F_{141} \left(x \right)^{2}+5 x^{3}-19 x^{2} F_{141}\! \left(x \right)-8 x^{2}+10 x F_{141}\! \left(x \right)+x\\
F_{142}\! \left(x , y\right) &= F_{143}\! \left(x , y\right)\\
F_{143}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{144}\! \left(x , y\right)\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)+F_{146}\! \left(x , y\right)\\
F_{145}\! \left(x , y\right) &= F_{129}\! \left(x , y\right) F_{140}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right) F_{84}\! \left(x \right)\\
F_{147}\! \left(x , y\right) &= -\frac{-F_{138}\! \left(x , y\right)+F_{138}\! \left(x , 1\right)}{-1+y}\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)\\
F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right) F_{157}\! \left(x , y\right)\\
F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{151}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)\\
F_{154}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)+F_{156}\! \left(x , y\right)\\
F_{155}\! \left(x , y\right) &= F_{154}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{155}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{84}\! \left(x \right)\\
F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)\\
F_{158}\! \left(x , y\right) &= y x\\
F_{159}\! \left(x , y\right) &= F_{160}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{160}\! \left(x , y\right) &= y F_{161}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{161}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{163}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)+F_{218}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{163}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)\\
F_{166}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{167}\! \left(x , y\right)\\
F_{167}\! \left(x , y\right) &= F_{168}\! \left(x , y\right)+F_{169}\! \left(x , y\right)\\
F_{168}\! \left(x , y\right) &= F_{129}\! \left(x , y\right) F_{65}\! \left(x , y\right)\\
F_{169}\! \left(x , y\right) &= F_{170}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{170}\! \left(x , y\right) &= F_{171}\! \left(x , y\right)+F_{172}\! \left(x , y\right)\\
F_{171}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)+F_{65}\! \left(x , y\right)\\
F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)\\
F_{173}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{174}\! \left(x , y\right)\\
F_{174}\! \left(x , y\right) &= F_{175}\! \left(x , y\right)+F_{183}\! \left(x , y\right)\\
F_{175}\! \left(x , y\right) &= F_{176}\! \left(x , y\right)+F_{177}\! \left(x , y\right)\\
F_{176}\! \left(x , y\right) &= F_{129}\! \left(x , y\right) F_{171}\! \left(x , y\right)\\
F_{177}\! \left(x , y\right) &= F_{147}\! \left(x , y\right) F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{12}\! \left(x \right) F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x , 1\right)\\
F_{181}\! \left(x , y\right) &= -\frac{-F_{182}\! \left(x , y\right) y +F_{182}\! \left(x , 1\right)}{-1+y}\\
F_{182}\! \left(x , y\right) &= y^{4} x^{4} F_{182}\! \left(x , y\right)^{3}+5 x^{3} F_{182}\! \left(x , y\right)^{2} y^{3}-11 y^{2} x^{2} F_{182}\! \left(x , y\right)^{2}+3 x^{2} F_{182}\! \left(x , y\right) y^{2}+10 x F_{182}\! \left(x , y\right) y -9 y x +1\\
F_{183}\! \left(x , y\right) &= F_{184}\! \left(x , y\right)+F_{185}\! \left(x , y\right)\\
F_{184}\! \left(x , y\right) &= F_{130}\! \left(x , y\right) F_{170}\! \left(x , y\right)\\
F_{185}\! \left(x , y\right) &= F_{186}\! \left(x , y\right) F_{84}\! \left(x \right)\\
F_{186}\! \left(x , y\right) &= -\frac{-F_{187}\! \left(x , y\right)+F_{187}\! \left(x , 1\right)}{-1+y}\\
F_{170}\! \left(x , y\right) &= F_{187}\! \left(x , y\right)+F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= -F_{217}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= \frac{F_{190}\! \left(x \right)}{F_{12}\! \left(x \right) F_{200}\! \left(x \right)}\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{12}\! \left(x \right) F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{136}\! \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_{1}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{12}\! \left(x \right) F_{194}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{12}\! \left(x \right) F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{201}\! \left(x \right) &= -F_{211}\! \left(x \right)+F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= \frac{F_{203}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{141}\! \left(x \right) F_{195}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{12}\! \left(x \right) F_{200}\! \left(x \right) F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x , 1\right)\\
F_{209}\! \left(x , y\right) &= -\frac{-y F_{210}\! \left(x , y\right)+F_{210}\! \left(x , 1\right)}{-1+y}\\
F_{210}\! \left(x , y\right) &= x^{4} F_{210}\! \left(x , y\right)^{3} y^{4}+3 x^{4} F_{210}\! \left(x , y\right)^{2} y^{4}+3 x^{4} F_{210}\! \left(x , y\right) y^{4}+y^{4} x^{4}+5 x^{3} F_{210}\! \left(x , y\right)^{2} y^{3}+10 x^{3} F_{210}\! \left(x , y\right) y^{3}+5 x^{3} y^{3}-11 x^{2} F_{210}\! \left(x , y\right)^{2} y^{2}-19 x^{2} F_{210}\! \left(x , y\right) y^{2}-8 y^{2} x^{2}+10 x F_{210}\! \left(x , y\right) y +y x\\
F_{211}\! \left(x \right) &= F_{136}\! \left(x \right) F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)+F_{215}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{200}\! \left(x \right) F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{12}\! \left(x \right) F_{198}\! \left(x \right) F_{200}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{136}\! \left(x \right) F_{200}\! \left(x \right)\\
F_{218}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{65}\! \left(x , y\right)\\
F_{219}\! \left(x , y\right) &= F_{220}\! \left(x , y\right)\\
F_{220}\! \left(x , y\right) &= F_{221}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{221}\! \left(x , y\right) &= F_{222}\! \left(x , y\right)+F_{223}\! \left(x , y\right)\\
F_{222}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\
F_{223}\! \left(x , y\right) &= F_{160}\! \left(x , y\right) F_{224}\! \left(x , y\right)\\
F_{224}\! \left(x , y\right) &= F_{225}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{225}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{25}\! \left(x , y\right)\\
F_{226}\! \left(x , y\right) &= F_{124}\! \left(x \right) F_{55}\! \left(x , y\right)\\
F_{227}\! \left(x , y\right) &= F_{228}\! \left(x , y\right)\\
F_{228}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{180}\! \left(x \right) F_{229}\! \left(x , y\right)\\
F_{230}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{229}\! \left(x , y\right) F_{84}\! \left(x \right)\\
F_{230}\! \left(x , y\right) &= F_{231}\! \left(x , y\right)\\
F_{231}\! \left(x , y\right) &= F_{232}\! \left(x \right)+F_{234}\! \left(x , y\right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{234}\! \left(x , y\right) &= F_{235}\! \left(x , y\right)\\
F_{236}\! \left(x , y\right) &= F_{235}\! \left(x , y\right)+F_{237}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{236}\! \left(x , y\right)+F_{7}\! \left(x \right)\\
F_{237}\! \left(x , y\right) &= F_{238}\! \left(x , y\right)+F_{241}\! \left(x , y\right)\\
F_{238}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{239}\! \left(x , y\right)\\
F_{239}\! \left(x , y\right) &= F_{240}\! \left(x , y\right)\\
F_{240}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{236}\! \left(x , y\right)\\
F_{241}\! \left(x , y\right) &= F_{242}\! \left(x , y\right)\\
F_{242}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{243}\! \left(x , y\right)\\
F_{243}\! \left(x , y\right) &= F_{244}\! \left(x , y\right)+F_{245}\! \left(x , y\right)\\
F_{244}\! \left(x , y\right) &= F_{238}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{245}\! \left(x , y\right) &= F_{246}\! \left(x , y\right)\\
F_{246}\! \left(x , y\right) &= F_{154}\! \left(x , y\right) F_{95}\! \left(x , y\right)\\
F_{247}\! \left(x , y\right) &= F_{131}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{12}\! \left(x \right) F_{250}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{41}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 249 rules.
Finding the specification took 33492 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{12}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{0}\! \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_{7}\! \left(x \right)\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{178}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \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_{35}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= y x\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{17}\! \left(x \right)+F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{245}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{82}\! \left(x \right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)+F_{41}\! \left(x \right)\\
F_{40}\! \left(x , y\right) &= -\frac{-F_{21}\! \left(x , y\right) y +F_{21}\! \left(x , 1\right)}{-1+y}\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x , 1\right)\\
F_{43}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{43}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{73}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= y F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x \right)+F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{53}\! \left(x \right) &= 0\\
F_{54}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{52}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{49}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= y F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{66}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{69}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{71}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{71}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{78}\! \left(x , y\right) F_{82}\! \left(x \right)\\
F_{78}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= y F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= -\frac{-F_{69}\! \left(x , y\right) y +F_{69}\! \left(x , 1\right)}{-1+y}\\
F_{82}\! \left(x \right) &= x^{4} F_{82} \left(x \right)^{3}+5 x^{3} F_{82} \left(x \right)^{2}-11 x^{2} F_{82} \left(x \right)^{2}+3 x^{2} F_{82}\! \left(x \right)+10 x F_{82}\! \left(x \right)-9 x +1\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{85}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{82}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{25}\! \left(x , y\right) F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{95}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{95}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{97}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{97}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{98}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{100}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)+F_{225}\! \left(x , y\right)\\
F_{108}\! \left(x , y\right) &= F_{107}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)+F_{224}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{217}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right) F_{2}\! \left(x \right)\\
F_{113}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)+F_{115}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{113}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{114}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right)\\
F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{157}\! \left(x , y\right)\\
F_{118}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{121}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{120}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{122}\! \left(x \right)+F_{146}\! \left(x , y\right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{12}\! \left(x \right) F_{125}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x , 1\right)\\
F_{127}\! \left(x , y\right) &= F_{128}\! \left(x , y\right)+F_{137}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{82}\! \left(x \right)\\
F_{129}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)\\
F_{131}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{132}\! \left(x , y\right)\\
F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{135}\! \left(x , y\right)\\
F_{133}\! \left(x , y\right) &= F_{134}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{134}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{127}\! \left(x , y\right) &= F_{134}\! \left(x \right)+F_{136}\! \left(x , y\right)\\
F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{140}\! \left(x , y\right)\\
F_{138}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= x^{4} F_{139} \left(x \right)^{3}+3 x^{4} F_{139} \left(x \right)^{2}+3 x^{4} F_{139}\! \left(x \right)+5 x^{3} F_{139} \left(x \right)^{2}+x^{4}+10 x^{3} F_{139}\! \left(x \right)-11 x^{2} F_{139} \left(x \right)^{2}+5 x^{3}-19 x^{2} F_{139}\! \left(x \right)-8 x^{2}+10 x F_{139}\! \left(x \right)+x\\
F_{140}\! \left(x , y\right) &= F_{141}\! \left(x , y\right)\\
F_{141}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{142}\! \left(x , y\right)\\
F_{142}\! \left(x , y\right) &= F_{143}\! \left(x , y\right)+F_{144}\! \left(x , y\right)\\
F_{143}\! \left(x , y\right) &= F_{127}\! \left(x , y\right) F_{138}\! \left(x , y\right)\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right) F_{82}\! \left(x \right)\\
F_{145}\! \left(x , y\right) &= -\frac{-F_{136}\! \left(x , y\right)+F_{136}\! \left(x , 1\right)}{-1+y}\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{148}\! \left(x , y\right) F_{155}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)\\
F_{150}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{149}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)+F_{154}\! \left(x , y\right)\\
F_{153}\! \left(x , y\right) &= F_{152}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{153}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)\\
F_{154}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{82}\! \left(x \right)\\
F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= y x\\
F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{158}\! \left(x , y\right) &= y F_{159}\! \left(x , y\right)\\
F_{160}\! \left(x , y\right) &= F_{159}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{161}\! \left(x , y\right) &= F_{160}\! \left(x , y\right)+F_{216}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{161}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right)\\
F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{165}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{167}\! \left(x , y\right)\\
F_{166}\! \left(x , y\right) &= F_{127}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{167}\! \left(x , y\right) &= F_{168}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{168}\! \left(x , y\right) &= F_{169}\! \left(x , y\right)+F_{170}\! \left(x , y\right)\\
F_{169}\! \left(x , y\right) &= F_{163}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{170}\! \left(x , y\right) &= F_{171}\! \left(x , y\right)\\
F_{171}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{172}\! \left(x , y\right)\\
F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)+F_{181}\! \left(x , y\right)\\
F_{173}\! \left(x , y\right) &= F_{174}\! \left(x , y\right)+F_{175}\! \left(x , y\right)\\
F_{174}\! \left(x , y\right) &= F_{127}\! \left(x , y\right) F_{169}\! \left(x , y\right)\\
F_{175}\! \left(x , y\right) &= F_{145}\! \left(x , y\right) F_{176}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{12}\! \left(x \right) F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x , 1\right)\\
F_{179}\! \left(x , y\right) &= -\frac{-F_{180}\! \left(x , y\right) y +F_{180}\! \left(x , 1\right)}{-1+y}\\
F_{180}\! \left(x , y\right) &= y^{4} x^{4} F_{180}\! \left(x , y\right)^{3}+5 x^{3} F_{180}\! \left(x , y\right)^{2} y^{3}-11 y^{2} x^{2} F_{180}\! \left(x , y\right)^{2}+3 x^{2} F_{180}\! \left(x , y\right) y^{2}+10 x F_{180}\! \left(x , y\right) y -9 y x +1\\
F_{181}\! \left(x , y\right) &= F_{182}\! \left(x , y\right)+F_{183}\! \left(x , y\right)\\
F_{182}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{168}\! \left(x , y\right)\\
F_{183}\! \left(x , y\right) &= F_{184}\! \left(x , y\right) F_{82}\! \left(x \right)\\
F_{184}\! \left(x , y\right) &= -\frac{-F_{185}\! \left(x , y\right)+F_{185}\! \left(x , 1\right)}{-1+y}\\
F_{168}\! \left(x , y\right) &= F_{185}\! \left(x , y\right)+F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= -F_{215}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{12}\! \left(x \right) F_{198}\! \left(x \right)}\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{12}\! \left(x \right) F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{199}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{134}\! \left(x \right) F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{12}\! \left(x \right) F_{192}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{12}\! \left(x \right) F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{199}\! \left(x \right) &= -F_{209}\! \left(x \right)+F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= \frac{F_{201}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{139}\! \left(x \right) F_{193}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{12}\! \left(x \right) F_{198}\! \left(x \right) F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x , 1\right)\\
F_{207}\! \left(x , y\right) &= -\frac{-y F_{208}\! \left(x , y\right)+F_{208}\! \left(x , 1\right)}{-1+y}\\
F_{208}\! \left(x , y\right) &= x^{4} F_{208}\! \left(x , y\right)^{3} y^{4}+3 x^{4} F_{208}\! \left(x , y\right)^{2} y^{4}+3 x^{4} F_{208}\! \left(x , y\right) y^{4}+y^{4} x^{4}+5 x^{3} F_{208}\! \left(x , y\right)^{2} y^{3}+10 x^{3} F_{208}\! \left(x , y\right) y^{3}+5 x^{3} y^{3}-11 x^{2} F_{208}\! \left(x , y\right)^{2} y^{2}-19 x^{2} F_{208}\! \left(x , y\right) y^{2}-8 y^{2} x^{2}+10 x F_{208}\! \left(x , y\right) y +y x\\
F_{209}\! \left(x \right) &= F_{134}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{198}\! \left(x \right) F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{12}\! \left(x \right) F_{196}\! \left(x \right) F_{198}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{134}\! \left(x \right) F_{198}\! \left(x \right)\\
F_{216}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{217}\! \left(x , y\right) &= F_{218}\! \left(x , y\right)\\
F_{218}\! \left(x , y\right) &= F_{219}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{219}\! \left(x , y\right) &= F_{220}\! \left(x , y\right)+F_{221}\! \left(x , y\right)\\
F_{220}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{221}\! \left(x , y\right) &= F_{158}\! \left(x , y\right) F_{222}\! \left(x , y\right)\\
F_{222}\! \left(x , y\right) &= F_{223}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{223}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{25}\! \left(x , y\right)\\
F_{224}\! \left(x , y\right) &= F_{122}\! \left(x \right) F_{57}\! \left(x , y\right)\\
F_{225}\! \left(x , y\right) &= F_{226}\! \left(x , y\right)\\
F_{226}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{178}\! \left(x \right) F_{227}\! \left(x , y\right)\\
F_{228}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{227}\! \left(x , y\right) F_{82}\! \left(x \right)\\
F_{228}\! \left(x , y\right) &= F_{229}\! \left(x , y\right)\\
F_{229}\! \left(x , y\right) &= F_{230}\! \left(x \right)+F_{232}\! \left(x , y\right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{232}\! \left(x , y\right) &= F_{233}\! \left(x , y\right)\\
F_{234}\! \left(x , y\right) &= F_{233}\! \left(x , y\right)+F_{235}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{234}\! \left(x , y\right)+F_{7}\! \left(x \right)\\
F_{235}\! \left(x , y\right) &= F_{236}\! \left(x , y\right)+F_{239}\! \left(x , y\right)\\
F_{236}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{237}\! \left(x , y\right)\\
F_{237}\! \left(x , y\right) &= F_{238}\! \left(x , y\right)\\
F_{238}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{234}\! \left(x , y\right)\\
F_{239}\! \left(x , y\right) &= F_{240}\! \left(x , y\right)\\
F_{240}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{241}\! \left(x , y\right)\\
F_{241}\! \left(x , y\right) &= F_{242}\! \left(x , y\right)+F_{243}\! \left(x , y\right)\\
F_{242}\! \left(x , y\right) &= F_{236}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{243}\! \left(x , y\right) &= F_{244}\! \left(x , y\right)\\
F_{244}\! \left(x , y\right) &= F_{152}\! \left(x , y\right) F_{93}\! \left(x , y\right)\\
F_{245}\! \left(x , y\right) &= F_{129}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{12}\! \left(x \right) F_{248}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{41}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 242 rules.
Finding the specification took 144084 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_{26}\! \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_{26}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x , 1\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{24}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= y x\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= x\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{31}\! \left(x \right)\\
F_{30}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{15}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x , 1\right)\\
F_{35}\! \left(x , y\right) &= -\frac{-F_{36}\! \left(x , y\right) y +F_{36}\! \left(x , 1\right)}{-1+y}\\
F_{36}\! \left(x , y\right) &= y^{4} x^{4} F_{36}\! \left(x , y\right)^{3}+5 x^{3} F_{36}\! \left(x , y\right)^{2} y^{3}-11 y^{2} x^{2} F_{36}\! \left(x , y\right)^{2}+3 x^{2} F_{36}\! \left(x , y\right) y^{2}+10 x F_{36}\! \left(x , y\right) y -9 y x +1\\
F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{240}\! \left(x , y\right)+F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right) F_{86}\! \left(x \right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)+F_{43}\! \left(x \right)\\
F_{42}\! \left(x , y\right) &= -\frac{-F_{16}\! \left(x , y\right) y +F_{16}\! \left(x , 1\right)}{-1+y}\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x , 1\right)\\
F_{45}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{54}\! \left(x \right)+F_{55}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{54}\! \left(x \right) &= 0\\
F_{55}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{51}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= y F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{66}\! \left(x , y\right)+F_{71}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{67}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{26}\! \left(x \right)+F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{54}\! \left(x \right)+F_{69}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{70}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{67}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{75}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{75}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{82}\! \left(x , y\right) F_{86}\! \left(x \right)\\
F_{82}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= y F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= -\frac{-F_{73}\! \left(x , y\right) y +F_{73}\! \left(x , 1\right)}{-1+y}\\
F_{86}\! \left(x \right) &= x^{4} F_{86} \left(x \right)^{3}+5 x^{3} F_{86} \left(x \right)^{2}-11 x^{2} F_{86} \left(x \right)^{2}+3 x^{2} F_{86}\! \left(x \right)+10 x F_{86}\! \left(x \right)-9 x +1\\
F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{89}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{86}\! \left(x \right) F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)+F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{26}\! \left(x \right) F_{96}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{97}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{98}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{99}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{99}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{106}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{106}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{104}\! \left(x , y\right)\\
F_{107}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)\\
F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{223}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{111}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{222}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)+F_{215}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{2}\! \left(x \right)\\
F_{117}\! \left(x , y\right) &= F_{116}\! \left(x , y\right)+F_{119}\! \left(x , y\right)\\
F_{118}\! \left(x , y\right) &= F_{117}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{118}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)\\
F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{158}\! \left(x , y\right)\\
F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{125}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{124}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{49}\! \left(x , y\right)\\
F_{125}\! \left(x , y\right) &= F_{126}\! \left(x \right)+F_{150}\! \left(x , y\right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{26}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x , 1\right)\\
F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{141}\! \left(x , y\right)\\
F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{86}\! \left(x \right)\\
F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)\\
F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{139}\! \left(x , y\right)\\
F_{137}\! \left(x , y\right) &= F_{138}\! \left(x \right) F_{21}\! \left(x , y\right)\\
F_{138}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{131}\! \left(x , y\right) &= F_{138}\! \left(x \right)+F_{140}\! \left(x , y\right)\\
F_{141}\! \left(x , y\right) &= F_{142}\! \left(x , y\right)+F_{144}\! \left(x , y\right)\\
F_{142}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= x^{4} F_{143} \left(x \right)^{3}+3 x^{4} F_{143} \left(x \right)^{2}+3 x^{4} F_{143}\! \left(x \right)+5 x^{3} F_{143} \left(x \right)^{2}+x^{4}+10 x^{3} F_{143}\! \left(x \right)-11 x^{2} F_{143} \left(x \right)^{2}+5 x^{3}-19 x^{2} F_{143}\! \left(x \right)-8 x^{2}+10 x F_{143}\! \left(x \right)+x\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)\\
F_{145}\! \left(x , y\right) &= F_{146}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{148}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{131}\! \left(x , y\right) F_{142}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right) F_{86}\! \left(x \right)\\
F_{149}\! \left(x , y\right) &= -\frac{-F_{140}\! \left(x , y\right)+F_{140}\! \left(x , 1\right)}{-1+y}\\
F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)\\
F_{151}\! \left(x , y\right) &= F_{152}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{153}\! \left(x , y\right) &= F_{152}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{153}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)\\
F_{155}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)+F_{157}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{155}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)\\
F_{157}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{86}\! \left(x \right)\\
F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{159}\! \left(x , y\right) &= y F_{160}\! \left(x , y\right)\\
F_{161}\! \left(x , y\right) &= F_{160}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)+F_{214}\! \left(x , y\right)\\
F_{163}\! \left(x , y\right) &= F_{162}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{166}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)+F_{168}\! \left(x , y\right)\\
F_{167}\! \left(x , y\right) &= F_{131}\! \left(x , y\right) F_{67}\! \left(x , y\right)\\
F_{168}\! \left(x , y\right) &= F_{169}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{169}\! \left(x , y\right) &= F_{170}\! \left(x , y\right)+F_{171}\! \left(x , y\right)\\
F_{170}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{171}\! \left(x , y\right) &= F_{172}\! \left(x , y\right)\\
F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{173}\! \left(x , y\right) &= F_{174}\! \left(x , y\right)+F_{179}\! \left(x , y\right)\\
F_{174}\! \left(x , y\right) &= F_{175}\! \left(x , y\right)+F_{176}\! \left(x , y\right)\\
F_{175}\! \left(x , y\right) &= F_{131}\! \left(x , y\right) F_{170}\! \left(x , y\right)\\
F_{176}\! \left(x , y\right) &= F_{149}\! \left(x , y\right) F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{26}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{179}\! \left(x , y\right) &= F_{180}\! \left(x , y\right)+F_{181}\! \left(x , y\right)\\
F_{180}\! \left(x , y\right) &= F_{132}\! \left(x , y\right) F_{169}\! \left(x , y\right)\\
F_{181}\! \left(x , y\right) &= F_{182}\! \left(x , y\right) F_{86}\! \left(x \right)\\
F_{182}\! \left(x , y\right) &= -\frac{-F_{183}\! \left(x , y\right)+F_{183}\! \left(x , 1\right)}{-1+y}\\
F_{169}\! \left(x , y\right) &= F_{183}\! \left(x , y\right)+F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= -F_{213}\! \left(x \right)+F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= \frac{F_{186}\! \left(x \right)}{F_{196}\! \left(x \right) F_{26}\! \left(x \right)}\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{138}\! \left(x \right) F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{190}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{197}\! \left(x \right) &= -F_{207}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= \frac{F_{199}\! \left(x \right)}{F_{26}\! \left(x \right)}\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{202}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{143}\! \left(x \right) F_{191}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{196}\! \left(x \right) F_{204}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x , 1\right)\\
F_{205}\! \left(x , y\right) &= -\frac{-y F_{206}\! \left(x , y\right)+F_{206}\! \left(x , 1\right)}{-1+y}\\
F_{206}\! \left(x , y\right) &= x^{4} F_{206}\! \left(x , y\right)^{3} y^{4}+3 x^{4} F_{206}\! \left(x , y\right)^{2} y^{4}+3 x^{4} F_{206}\! \left(x , y\right) y^{4}+x^{4} y^{4}+5 x^{3} F_{206}\! \left(x , y\right)^{2} y^{3}+10 x^{3} F_{206}\! \left(x , y\right) y^{3}+5 x^{3} y^{3}-11 x^{2} F_{206}\! \left(x , y\right)^{2} y^{2}-19 x^{2} F_{206}\! \left(x , y\right) y^{2}-8 y^{2} x^{2}+10 x F_{206}\! \left(x , y\right) y +y x\\
F_{207}\! \left(x \right) &= F_{138}\! \left(x \right) F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)+F_{211}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{196}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{194}\! \left(x \right) F_{196}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{138}\! \left(x \right) F_{196}\! \left(x \right)\\
F_{214}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{67}\! \left(x , y\right)\\
F_{215}\! \left(x , y\right) &= F_{216}\! \left(x , y\right)\\
F_{216}\! \left(x , y\right) &= F_{217}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{217}\! \left(x , y\right) &= F_{218}\! \left(x , y\right)+F_{219}\! \left(x , y\right)\\
F_{218}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{219}\! \left(x , y\right) &= F_{159}\! \left(x , y\right) F_{220}\! \left(x , y\right)\\
F_{220}\! \left(x , y\right) &= F_{221}\! \left(x , y\right)+F_{24}\! \left(x , y\right)\\
F_{221}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{222}\! \left(x , y\right) &= F_{126}\! \left(x \right) F_{57}\! \left(x , y\right)\\
F_{223}\! \left(x , y\right) &= F_{224}\! \left(x , y\right)\\
F_{224}\! \left(x , y\right) &= F_{225}\! \left(x , y\right) F_{26}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{225}\! \left(x , y\right) &= F_{226}\! \left(x , y\right)\\
F_{226}\! \left(x , y\right) &= F_{15}\! \left(x \right)+F_{227}\! \left(x , y\right)\\
F_{227}\! \left(x , y\right) &= F_{228}\! \left(x , y\right)\\
F_{229}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{228}\! \left(x , y\right)\\
F_{230}\! \left(x , y\right) &= F_{229}\! \left(x , y\right) F_{26}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{230}\! \left(x , y\right) &= F_{231}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{231}\! \left(x , y\right)+F_{232}\! \left(x , y\right)\\
F_{232}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{233}\! \left(x , y\right)\\
F_{233}\! \left(x , y\right) &= F_{234}\! \left(x , y\right)\\
F_{234}\! \left(x , y\right) &= F_{235}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{235}\! \left(x , y\right) &= F_{236}\! \left(x , y\right)+F_{238}\! \left(x , y\right)\\
F_{236}\! \left(x , y\right) &= F_{237}\! \left(x , y\right)+F_{31}\! \left(x \right)\\
F_{237}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{238}\! \left(x , y\right) &= F_{239}\! \left(x , y\right)\\
F_{239}\! \left(x , y\right) &= F_{155}\! \left(x , y\right) F_{97}\! \left(x , y\right)\\
F_{240}\! \left(x , y\right) &= F_{133}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{241}\! \left(x \right) &= F_{15}\! \left(x \right) F_{177}\! \left(x \right)\\
\end{align*}\)