Av(13524, 13542, 14523, 14532, 15423, 15432, 132645, 132654, 351624, 351642, 361524, 361542, 3541726, 3541762, 4671325, 4671352, 4761325, 4761352, 46581327, 46581372)
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Counting Sequence
1, 1, 2, 6, 24, 114, 592, 3216, 17904, 101198, 578208, 3332136, 19343408, 113017332, 664168160, ...

This specification was found using the strategy pack "Point And Row And Col Placements Tracked Fusion Req Corrob" and has 185 rules.

Found on July 11, 2021.

Finding the specification took 588414 seconds.

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Copy 185 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_{33}\! \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_{33}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\ F_{8}\! \left(x , y\right) &= F_{181}\! \left(x , y\right)+F_{183}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{180}\! \left(x , y\right)\\ F_{15}\! \left(x \right) &= 0\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{4}\! \left(x \right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{178}\! \left(x , y\right)+F_{19}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{22}\! \left(x , y\right) &= F_{176}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{174}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{172}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)\\ F_{26}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x , 1\right)\\ F_{30}\! \left(x , y\right) &= F_{31}\! \left(x \right)+F_{34}\! \left(x , y\right)\\ F_{31}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{29}\! \left(x \right) F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= x\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\ F_{35}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{31}\! \left(x \right) F_{36}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= y x\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{31}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x , 1\right)\\ F_{42}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{33}\! \left(x \right) F_{40}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\ F_{55}\! \left(x \right) &= F_{33}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{33}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{33}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= -F_{15}\! \left(x \right)-F_{76}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{33}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{59}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x , 1\right)\\ F_{75}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x , 1\right)\\ F_{77}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{78}\! \left(x , y\right)\\ F_{78}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{79}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)+F_{84}\! \left(x , y\right)\\ F_{83}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\ F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)\\ F_{86}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{87}\! \left(x , y\right)\\ F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\ F_{88}\! \left(x , y\right) &= -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}\\ F_{89}\! \left(x , y\right) &= F_{19}\! \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_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{83}\! \left(x , y\right)\\ F_{92}\! \left(x , y\right) &= F_{93}\! \left(x , y\right)\\ F_{93}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right) F_{94}\! \left(x , y\right)\\ F_{94}\! \left(x , y\right) &= F_{95}\! \left(x , y\right)+F_{99}\! \left(x , y\right)\\ F_{95}\! \left(x , y\right) &= F_{41}\! \left(x \right) F_{96}\! \left(x , y\right)\\ F_{97}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{96}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\ F_{98}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\ F_{100}\! \left(x , y\right) &= -\frac{y \left(F_{101}\! \left(x , 1\right)-F_{101}\! \left(x , y\right)\right)}{-1+y}\\ F_{102}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{29}\! \left(x \right)\\ F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{29}\! \left(x \right)\\ F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)\\ F_{104}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{106}\! \left(x , y\right) &= -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}\\ F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)\\ F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{110}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{111}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{159}\! \left(x , y\right)+F_{161}\! \left(x , y\right)\\ F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)+F_{151}\! \left(x , y\right)\\ F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{113}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)\\ F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{116}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)\\ F_{118}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{149}\! \left(x , y\right)\\ F_{119}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)\\ F_{121}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{144}\! \left(x , y\right)\\ F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{142}\! \left(x , y\right)\\ F_{122}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{123}\! \left(x , y\right)\\ F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)\\ F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{126}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)+F_{140}\! \left(x , y\right)\\ F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)+F_{138}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{128}\! \left(x , y\right)\\ F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right) F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)\\ F_{129}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)\\ F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)\\ F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{132}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{133}\! \left(x , y\right)\\ F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\ F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{15}\! \left(x \right)\\ F_{135}\! \left(x , y\right) &= F_{130}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{137}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)\\ F_{138}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)\\ F_{139}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{140}\! \left(x , y\right) &= F_{141}\! \left(x , y\right)\\ F_{141}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{142}\! \left(x , y\right) &= F_{143}\! \left(x , y\right)\\ F_{143}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{144}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{145}\! \left(x , y\right)\\ F_{145}\! \left(x , y\right) &= F_{146}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\ 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_{36}\! \left(x , y\right)\\ F_{148}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{146}\! \left(x , y\right)\\ F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)\\ F_{150}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{151}\! \left(x , y\right) &= F_{152}\! \left(x , y\right)\\ F_{152}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{153}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)+F_{157}\! \left(x , y\right)\\ F_{154}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{155}\! \left(x , y\right)\\ F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)\\ F_{156}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\ F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)\\ F_{158}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{159}\! \left(x , y\right) &= F_{160}\! \left(x , y\right)\\ F_{160}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{161}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)\\ F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)+F_{169}\! \left(x , y\right)\\ F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)+F_{168}\! \left(x , y\right)\\ F_{166}\! \left(x , y\right) &= F_{165}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{166}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)\\ F_{8}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\ F_{168}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)\\ F_{169}\! \left(x , y\right) &= F_{152}\! \left(x , y\right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)\\ F_{173}\! \left(x , y\right) &= F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right) F_{83}\! \left(x , y\right)\\ F_{174}\! \left(x , y\right) &= F_{175}\! \left(x , y\right)\\ F_{175}\! \left(x , y\right) &= F_{31}\! \left(x \right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{176}\! \left(x , y\right) &= F_{177}\! \left(x , y\right)\\ F_{177}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{178}\! \left(x , y\right) &= F_{179}\! \left(x , y\right)\\ F_{179}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{180}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{181}\! \left(x , y\right) &= F_{182}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{182}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\ F_{183}\! \left(x , y\right) &= F_{184}\! \left(x , y\right)\\ F_{184}\! \left(x , y\right) &= F_{111}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Row And Col Placements Tracked Fusion Req Corrob" and has 185 rules.

Found on July 11, 2021.

Finding the specification took 588414 seconds.

This tree is too big to show here. Click to view tree on new page.

Copy 185 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_{33}\! \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_{33}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\ F_{8}\! \left(x , y\right) &= F_{181}\! \left(x , y\right)+F_{183}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{180}\! \left(x , y\right)\\ F_{15}\! \left(x \right) &= 0\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{4}\! \left(x \right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{178}\! \left(x , y\right)+F_{19}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{22}\! \left(x , y\right) &= F_{176}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{174}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{172}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)\\ F_{26}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x , 1\right)\\ F_{30}\! \left(x , y\right) &= F_{31}\! \left(x \right)+F_{34}\! \left(x , y\right)\\ F_{31}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{29}\! \left(x \right) F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= x\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\ F_{35}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{31}\! \left(x \right) F_{36}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= y x\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{31}\! \left(x \right) F_{33}\! \left(x \right) F_{40}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x , 1\right)\\ F_{42}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{33}\! \left(x \right) F_{40}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\ F_{55}\! \left(x \right) &= F_{33}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{33}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{33}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= -F_{15}\! \left(x \right)-F_{76}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{33}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{59}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x , 1\right)\\ F_{75}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x , 1\right)\\ F_{77}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{78}\! \left(x , y\right)\\ F_{78}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{79}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)+F_{84}\! \left(x , y\right)\\ F_{83}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\ F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)\\ F_{86}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{87}\! \left(x , y\right)\\ F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\ F_{88}\! \left(x , y\right) &= -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}\\ F_{89}\! \left(x , y\right) &= F_{19}\! \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_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{83}\! \left(x , y\right)\\ F_{92}\! \left(x , y\right) &= F_{93}\! \left(x , y\right)\\ F_{93}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right) F_{94}\! \left(x , y\right)\\ F_{94}\! \left(x , y\right) &= F_{95}\! \left(x , y\right)+F_{99}\! \left(x , y\right)\\ F_{95}\! \left(x , y\right) &= F_{41}\! \left(x \right) F_{96}\! \left(x , y\right)\\ F_{97}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{96}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\ F_{98}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\ F_{100}\! \left(x , y\right) &= -\frac{y \left(F_{101}\! \left(x , 1\right)-F_{101}\! \left(x , y\right)\right)}{-1+y}\\ F_{102}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{29}\! \left(x \right)\\ F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{29}\! \left(x \right)\\ F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)\\ F_{104}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{106}\! \left(x , y\right) &= -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}\\ F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)\\ F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{110}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{111}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{159}\! \left(x , y\right)+F_{161}\! \left(x , y\right)\\ F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)+F_{151}\! \left(x , y\right)\\ F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{113}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)\\ F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{116}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)\\ F_{118}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{149}\! \left(x , y\right)\\ F_{119}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)\\ F_{121}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{144}\! \left(x , y\right)\\ F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{142}\! \left(x , y\right)\\ F_{122}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{123}\! \left(x , y\right)\\ F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)\\ F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{126}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)+F_{140}\! \left(x , y\right)\\ F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)+F_{138}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{128}\! \left(x , y\right)\\ F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right) F_{26}\! \left(x \right) F_{45}\! \left(x , y\right)\\ F_{129}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)\\ F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)\\ F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{132}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{133}\! \left(x , y\right)\\ F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\ F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{15}\! \left(x \right)\\ F_{135}\! \left(x , y\right) &= F_{130}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{137}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)\\ F_{138}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)\\ F_{139}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{33}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{140}\! \left(x , y\right) &= F_{141}\! \left(x , y\right)\\ F_{141}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{142}\! \left(x , y\right) &= F_{143}\! \left(x , y\right)\\ F_{143}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{144}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{145}\! \left(x , y\right)\\ F_{145}\! \left(x , y\right) &= F_{146}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\ 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_{36}\! \left(x , y\right)\\ F_{148}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{146}\! \left(x , y\right)\\ F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)\\ F_{150}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{151}\! \left(x , y\right) &= F_{152}\! \left(x , y\right)\\ F_{152}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{153}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)+F_{157}\! \left(x , y\right)\\ F_{154}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{155}\! \left(x , y\right)\\ F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)\\ F_{156}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\ F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)\\ F_{158}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{159}\! \left(x , y\right) &= F_{160}\! \left(x , y\right)\\ F_{160}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{161}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)\\ F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)+F_{169}\! \left(x , y\right)\\ F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)+F_{168}\! \left(x , y\right)\\ F_{166}\! \left(x , y\right) &= F_{165}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{166}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)\\ F_{8}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\ F_{168}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)\\ F_{169}\! \left(x , y\right) &= F_{152}\! \left(x , y\right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{33}\! \left(x \right) F_{41}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)\\ F_{173}\! \left(x , y\right) &= F_{29}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right) F_{83}\! \left(x , y\right)\\ F_{174}\! \left(x , y\right) &= F_{175}\! \left(x , y\right)\\ F_{175}\! \left(x , y\right) &= F_{31}\! \left(x \right) F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{176}\! \left(x , y\right) &= F_{177}\! \left(x , y\right)\\ F_{177}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{178}\! \left(x , y\right) &= F_{179}\! \left(x , y\right)\\ F_{179}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{36}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{180}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{181}\! \left(x , y\right) &= F_{182}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{182}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\ F_{183}\! \left(x , y\right) &= F_{184}\! \left(x , y\right)\\ F_{184}\! \left(x , y\right) &= F_{111}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Row And Col Placements Tracked Fusion Req Corrob Not Expanded" and has 186 rules.

Found on January 18, 2022.

Finding the specification took 609287 seconds.

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Copy 186 equations to clipboard:
\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{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_{34}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\ F_{8}\! \left(x , y\right) &= F_{182}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{34}\! \left(x \right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{181}\! \left(x , y\right)\\ F_{15}\! \left(x \right) &= 0\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{34}\! \left(x \right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{4}\! \left(x \right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{179}\! \left(x , y\right)+F_{19}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{34}\! \left(x \right)\\ F_{22}\! \left(x , y\right) &= F_{177}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{84}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{175}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{46}\! \left(x , y\right)\\ F_{26}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x , 1\right)\\ F_{30}\! \left(x , y\right) &= F_{31}\! \left(x \right)+F_{35}\! \left(x , y\right)\\ F_{31}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{31} \left(x \right)^{2} F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= x\\ F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{31}\! \left(x \right) F_{37}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= y x\\ F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{41}\! \left(x \right)}\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{31}\! \left(x \right) F_{34}\! \left(x \right) F_{41}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x , 1\right)\\ F_{43}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{46}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{34}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{34}\! \left(x \right) F_{41}\! \left(x \right)}\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{54}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\ F_{56}\! \left(x \right) &= F_{34}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{34}\! \left(x \right) F_{42}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{34}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{34}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{15}\! \left(x \right)-F_{77}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= -F_{68}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{34}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{60}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{76}\! \left(x , 1\right)\\ F_{76}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x , 1\right)\\ F_{78}\! \left(x , y\right) &= F_{34}\! \left(x \right) F_{79}\! \left(x , y\right)\\ F_{79}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{80}\! \left(x , y\right)+F_{86}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{34}\! \left(x \right) F_{80}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{83}\! \left(x , y\right)\\ F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\ F_{85}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\ F_{86}\! \left(x , y\right) &= F_{87}\! \left(x , y\right)\\ F_{87}\! \left(x , y\right) &= F_{34}\! \left(x \right) F_{88}\! \left(x , y\right)\\ F_{88}\! \left(x , y\right) &= F_{89}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\ F_{89}\! \left(x , y\right) &= -\frac{-y F_{90}\! \left(x , y\right)+F_{90}\! \left(x , 1\right)}{-1+y}\\ F_{90}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\ F_{91}\! \left(x , y\right) &= F_{92}\! \left(x , y\right)\\ F_{92}\! \left(x , y\right) &= F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{42}\! \left(x \right) F_{84}\! \left(x , y\right)\\ F_{93}\! \left(x , y\right) &= F_{94}\! \left(x , y\right)\\ F_{94}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{84}\! \left(x , y\right) F_{95}\! \left(x , y\right)\\ F_{95}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\ F_{96}\! \left(x , y\right) &= F_{42}\! \left(x \right) F_{97}\! \left(x , y\right)\\ F_{98}\! \left(x , y\right) &= F_{34}\! \left(x \right) F_{97}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{98}\! \left(x , y\right)+F_{99}\! \left(x , y\right)\\ F_{99}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\ F_{101}\! \left(x , y\right) &= -\frac{y \left(F_{102}\! \left(x , 1\right)-F_{102}\! \left(x , y\right)\right)}{-1+y}\\ F_{103}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{29}\! \left(x \right)\\ F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{29}\! \left(x \right)\\ F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)\\ F_{105}\! \left(x , y\right) &= F_{103}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right) F_{34}\! \left(x \right)\\ F_{107}\! \left(x , y\right) &= -\frac{-y F_{79}\! \left(x , y\right)+F_{79}\! \left(x , 1\right)}{-1+y}\\ 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_{37}\! \left(x , y\right)\\ F_{111}\! \left(x , y\right) &= F_{110}\! \left(x , y\right) F_{34}\! \left(x \right)\\ F_{112}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\ F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{152}\! \left(x , y\right)\\ F_{113}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)\\ F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{117}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{117}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)\\ F_{119}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{150}\! \left(x , y\right)\\ F_{120}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{34}\! \left(x \right)\\ F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right)\\ F_{122}\! \left(x , y\right) &= F_{121}\! \left(x , y\right)+F_{145}\! \left(x , y\right)\\ F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right)+F_{143}\! \left(x , y\right)\\ F_{123}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{124}\! \left(x , y\right)\\ F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)\\ F_{125}\! \left(x , y\right) &= F_{126}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{126}\! \left(x , y\right)+F_{141}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{128}\! \left(x , y\right)+F_{139}\! \left(x , y\right)\\ F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)\\ F_{129}\! \left(x , y\right) &= F_{130}\! \left(x , y\right) F_{26}\! \left(x \right) F_{46}\! \left(x , y\right)\\ F_{130}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{131}\! \left(x , y\right)\\ F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)\\ F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{133}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{134}\! \left(x , y\right)\\ F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\ F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right)+F_{137}\! \left(x , y\right)+F_{15}\! \left(x \right)\\ F_{136}\! \left(x , y\right) &= F_{131}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{138}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)\\ F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)\\ F_{140}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{34}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{141}\! \left(x , y\right) &= F_{142}\! \left(x , y\right)\\ F_{142}\! \left(x , y\right) &= F_{122}\! \left(x , y\right) F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{143}\! \left(x , y\right) &= F_{144}\! \left(x , y\right)\\ F_{144}\! \left(x , y\right) &= F_{126}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{145}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{146}\! \left(x , y\right)\\ F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{147}\! \left(x , y\right) &= F_{148}\! \left(x , y\right)\\ F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{149}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)+F_{147}\! \left(x , y\right)\\ F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)\\ F_{151}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right)\\ F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)\\ F_{153}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right)\\ F_{154}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)+F_{158}\! \left(x , y\right)\\ F_{155}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{156}\! \left(x , y\right)\\ F_{156}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)\\ F_{157}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\ F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right)\\ F_{159}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{160}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)\\ F_{161}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{84}\! \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_{37}\! \left(x , y\right)\\ F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)+F_{170}\! \left(x , y\right)\\ F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{169}\! \left(x , y\right)\\ F_{167}\! \left(x , y\right) &= F_{166}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{167}\! \left(x , y\right) &= F_{168}\! \left(x , y\right)\\ F_{8}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)+F_{168}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\ F_{169}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)\\ F_{170}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{34}\! \left(x \right) F_{42}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{173}\! \left(x , y\right) &= F_{174}\! \left(x , y\right)\\ F_{174}\! \left(x , y\right) &= F_{29}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right) F_{84}\! \left(x , y\right)\\ F_{175}\! \left(x , y\right) &= F_{176}\! \left(x , y\right)\\ F_{176}\! \left(x , y\right) &= F_{31}\! \left(x \right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{84}\! \left(x , y\right)\\ F_{177}\! \left(x , y\right) &= F_{178}\! \left(x , y\right)\\ F_{178}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{84}\! \left(x , y\right)\\ F_{179}\! \left(x , y\right) &= F_{180}\! \left(x , y\right)\\ F_{180}\! \left(x , y\right) &= F_{103}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{84}\! \left(x , y\right)\\ F_{181}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{182}\! \left(x , y\right) &= F_{183}\! \left(x , y\right) F_{34}\! \left(x \right)\\ F_{183}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\ F_{184}\! \left(x , y\right) &= F_{185}\! \left(x , y\right)\\ F_{185}\! \left(x , y\right) &= F_{112}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ \end{align*}\)