Av(12453, 12534, 12543, 13452, 13524, 13542, 14352, 14523, 14532, 15342, 15423, 15432)
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Counting Sequence
1, 1, 2, 6, 24, 108, 517, 2575, 13200, 69180, 368993, 1996473, 10930943, 60449347, 337157867, ...
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Implicit Equation for the Generating Function
\(\displaystyle x \left(x -1\right) \left(x^{3}-4 x +4\right) F \left(x \right)^{3}+x \left(x -2\right) \left(x^{2}+2 x -4\right) F \left(x \right)^{2}+\left(2 x^{3}+2 x^{2}-9 x +1\right) F \! \left(x \right)+x^{2}+4 x -1 = 0\)
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Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 108\)
\(\displaystyle a(6) = 517\)
\(\displaystyle a(7) = 2575\)
\(\displaystyle a(8) = 13200\)
\(\displaystyle a(9) = 69180\)
\(\displaystyle a(10) = 368993\)
\(\displaystyle a(11) = 1996473\)
\(\displaystyle a(12) = 10930943\)
\(\displaystyle a(13) = 60449347\)
\(\displaystyle a{\left(n + 14 \right)} = \frac{115 \left(n + 1\right) \left(n + 2\right) a{\left(n \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(n + 2\right) \left(1423 n + 4282\right) a{\left(n + 1 \right)}}{32 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(28 n^{2} + 750 n + 5021\right) a{\left(n + 13 \right)}}{\left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(164 n^{2} + 4062 n + 25141\right) a{\left(n + 12 \right)}}{\left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(2476 n^{2} + 55623 n + 312290\right) a{\left(n + 11 \right)}}{4 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(3394 n^{2} - 25695 n - 193075\right) a{\left(n + 4 \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(3760 n^{2} + 31869 n + 61220\right) a{\left(n + 2 \right)}}{32 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(4079 n^{2} + 74955 n + 225772\right) a{\left(n + 3 \right)}}{32 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(6542 n^{2} + 116811 n + 520669\right) a{\left(n + 9 \right)}}{2 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(6698 n^{2} + 134763 n + 677467\right) a{\left(n + 10 \right)}}{4 \left(n + 14\right) \left(2 n + 29\right)} + \frac{3 \left(6812 n^{2} + 43254 n + 30927\right) a{\left(n + 5 \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(35837 n^{2} + 475692 n + 1561051\right) a{\left(n + 7 \right)}}{8 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(36497 n^{2} + 570276 n + 2219602\right) a{\left(n + 8 \right)}}{8 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(48206 n^{2} + 505551 n + 1258654\right) a{\left(n + 6 \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)}, \quad n \geq 14\)
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This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 332 rules.

Finding the specification took 21027 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_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\ F_{10}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{9}\! \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_{34}\! \left(x , y\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= y x\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{14}\! \left(x , y\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_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{24}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\ F_{25}\! \left(x \right) &= 0\\ F_{26}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\ F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\ F_{28}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{24}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{30}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)\\ F_{31}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\ F_{32}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{33}\! \left(x , y\right)\\ F_{33}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\ F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= -\frac{y \left(F_{11}\! \left(x , 1\right)-F_{11}\! \left(x , y\right)\right)}{-1+y}\\ F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\ F_{39}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{40}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y , 1\right)\\ F_{41}\! \left(x , y , z\right) &= -\frac{-F_{42}\! \left(x , y z \right) z +F_{42}\! \left(x , y\right)}{z -1}\\ F_{43}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{42}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{44}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{331}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{55}\! \left(x , y\right) &= F_{327}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\ F_{57}\! \left(x , y\right) &= F_{325}\! \left(x , y\right)+F_{58}\! \left(x , y\right)\\ F_{58}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{59}\! \left(x , y\right)\\ F_{60}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)+F_{59}\! \left(x , y\right)\\ F_{61}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{60}\! \left(x , y\right)\\ F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= F_{324}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{64}\! \left(x , y\right) &= -\frac{-F_{63}\! \left(x , y\right) y +F_{63}\! \left(x , 1\right)}{-1+y}\\ F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\ F_{65}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{66}\! \left(x , y\right)\\ F_{66}\! \left(x , y\right) &= -\frac{-F_{44}\! \left(x , y\right) y +F_{44}\! \left(x , 1\right)}{-1+y}\\ F_{68}\! \left(x , y\right) &= F_{322}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\ F_{69}\! \left(x , y\right) &= F_{321}\! \left(x , y\right)+F_{68}\! \left(x , y\right)\\ F_{69}\! \left(x , y\right) &= -\frac{-y F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)}{-1+y}\\ F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{72}\! \left(x , y\right)\\ F_{73}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{72}\! \left(x , y\right)\\ F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)\\ F_{74}\! \left(x , y\right) &= F_{319}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\ F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\ F_{77}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)\\ F_{79}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{80}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{281}\! \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) &= F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= F_{85}\! \left(x , y\right)\\ F_{86}\! \left(x , y\right) &= -\frac{-F_{85}\! \left(x , y\right) y +F_{85}\! \left(x , 1\right)}{-1+y}\\ F_{86}\! \left(x , y\right) &= F_{87}\! \left(x , y\right)\\ F_{87}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{88}\! \left(x , y\right)\\ F_{89}\! \left(x , y\right) &= F_{280}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\ F_{90}\! \left(x , y\right) &= F_{244}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\ F_{91}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{90}\! \left(x , y\right)\\ F_{91}\! \left(x , y\right) &= F_{92}\! \left(x , y\right)\\ F_{92}\! \left(x , y\right) &= -\frac{-F_{93}\! \left(x , y\right)+F_{93}\! \left(x , 1\right)}{-1+y}\\ F_{94}\! \left(x , y\right) &= F_{197}\! \left(x \right)+F_{93}\! \left(x , y\right)\\ F_{95}\! \left(x , y\right) &= F_{196}\! \left(x , y\right)+F_{94}\! \left(x , y\right)\\ F_{96}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{95}\! \left(x , y\right)\\ F_{96}\! \left(x , y\right) &= F_{97}\! \left(x , y\right)\\ F_{97}\! \left(x , y\right) &= F_{194}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\ F_{99}\! \left(x , y\right) &= F_{106}\! \left(x \right)+F_{98}\! \left(x , y\right)\\ F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{101}\! \left(x , y\right)\\ F_{100}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{44}\! \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_{4}\! \left(x \right)\\ F_{103}\! \left(x , y\right) &= -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}\\ F_{104}\! \left(x , y\right) &= F_{105}\! \left(x \right)+F_{97}\! \left(x , y\right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{106}\! \left(x \right) &= \frac{F_{107}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{107}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{108}\! \left(x \right) &= -F_{113}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= \frac{F_{110}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{106}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{115}\! \left(x \right) &= \frac{F_{116}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{120}\! \left(x \right) &= -F_{193}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{121}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= \frac{F_{123}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{98}\! \left(x , 1\right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{140}\! \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_{4}\! \left(x \right)\\ F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\ F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)\\ F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right)+F_{139}\! \left(x , y\right)\\ F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{138}\! \left(x , y\right)\\ F_{137}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\ F_{138}\! \left(x , y\right) &= y F_{70}\! \left(x , y\right)\\ F_{139}\! \left(x , y\right) &= F_{69}\! \left(x , y\right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{142}\! \left(x \right) &= \frac{F_{143}\! \left(x \right)}{F_{174}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{153}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{0}\! \left(x \right) F_{106}\! \left(x \right) F_{150}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{151}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{150}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= -F_{155}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{161}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{0}\! \left(x \right) F_{159}\! \left(x \right)\\ F_{159}\! \left(x \right) &= \frac{F_{160}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{160}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{149}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{168}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x , 1\right)\\ F_{166}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)\\ F_{167}\! \left(x , y\right) &= F_{142}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x , 1\right)\\ F_{169}\! \left(x , y\right) &= y F_{170}\! \left(x , y\right)\\ F_{170}\! \left(x , y\right) &= F_{171}\! \left(x , y\right)\\ F_{171}\! \left(x , y\right) &= F_{142}\! \left(x \right) F_{172}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{173}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{100}\! \left(x , 1\right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x , 1\right)\\ F_{179}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{180}\! \left(x , y\right)\\ F_{180}\! \left(x , y\right) &= F_{181}\! \left(x , y\right)\\ F_{181}\! \left(x , y\right) &= F_{182}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{182}\! \left(x , y\right) &= -\frac{-y F_{179}\! \left(x , y\right)+F_{179}\! \left(x , 1\right)}{-1+y}\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{142}\! \left(x \right) F_{178}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= -F_{190}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{122}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{190}\! \left(x \right) &= -F_{176}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= \frac{F_{192}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{192}\! \left(x \right) &= F_{124}\! \left(x \right)\\ F_{193}\! \left(x \right) &= -F_{190}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{194}\! \left(x , y\right) &= y F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= -F_{125}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{196}\! \left(x , y\right) &= y F_{74}\! \left(x , y\right)\\ F_{197}\! \left(x \right) &= -F_{201}\! \left(x \right)+F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{242}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{201}\! \left(x \right) &= -F_{234}\! \left(x \right)+F_{202}\! \left(x \right)\\ F_{203}\! \left(x , y\right) &= F_{202}\! \left(x \right)+F_{225}\! \left(x , y\right)\\ F_{204}\! \left(x , y\right) &= F_{203}\! \left(x , y\right)+F_{224}\! \left(x , y\right)\\ F_{205}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{204}\! \left(x , y\right)\\ F_{205}\! \left(x , y\right) &= F_{206}\! \left(x , y\right)\\ F_{207}\! \left(x , y\right) &= F_{206}\! \left(x , y\right)+F_{213}\! \left(x , y\right)\\ F_{207}\! \left(x , y\right) &= F_{208}\! \left(x , y\right)\\ F_{208}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{209}\! \left(x , y\right)\\ F_{209}\! \left(x , y\right) &= F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)\\ F_{210}\! \left(x , y\right) &= F_{120}\! \left(x \right)+F_{211}\! \left(x , y\right)\\ F_{211}\! \left(x , y\right) &= y F_{193}\! \left(x \right)\\ F_{212}\! \left(x , y\right) &= F_{211}\! \left(x , y\right)\\ F_{213}\! \left(x , y\right) &= F_{214}\! \left(x , y\right)\\ F_{214}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{215}\! \left(x , y\right)\\ F_{215}\! \left(x , y\right) &= F_{216}\! \left(x , y\right)+F_{223}\! \left(x , y\right)\\ F_{216}\! \left(x , y\right) &= F_{200}\! \left(x \right)+F_{217}\! \left(x , y\right)\\ F_{217}\! \left(x , y\right) &= y F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{221}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{200}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{193}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{223}\! \left(x , y\right) &= F_{217}\! \left(x , y\right)\\ F_{224}\! \left(x , y\right) &= F_{225}\! \left(x , y\right)\\ F_{225}\! \left(x , y\right) &= y F_{226}\! \left(x \right)\\ F_{226}\! \left(x \right) &= -F_{227}\! \left(x \right)+F_{185}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{229}\! \left(x \right) &= \frac{F_{230}\! \left(x \right)}{F_{159}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\ F_{231}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{232}\! \left(x \right)\\ F_{232}\! \left(x \right) &= \frac{F_{233}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{233}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{234}\! \left(x \right) &= -F_{240}\! \left(x \right)+F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= -F_{239}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{236}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{237}\! \left(x \right)\\ F_{237}\! \left(x \right) &= \frac{F_{238}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{238}\! \left(x \right) &= F_{124}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{196}\! \left(x , 1\right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x , 1\right)\\ F_{94}\! \left(x , y\right) &= F_{241}\! \left(x , y\right)+F_{242}\! \left(x \right)\\ F_{242}\! \left(x \right) &= \frac{F_{243}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{243}\! \left(x \right) &= F_{195}\! \left(x \right)\\ F_{244}\! \left(x , y\right) &= F_{245}\! \left(x , y\right)\\ F_{245}\! \left(x , y\right) &= -\frac{-y F_{246}\! \left(x , y\right)+F_{246}\! \left(x , 1\right)}{-1+y}\\ F_{247}\! \left(x , y\right) &= F_{246}\! \left(x , y\right)+F_{278}\! \left(x , y\right)\\ F_{248}\! \left(x , y\right) &= F_{247}\! \left(x , y\right)+F_{253}\! \left(x , y\right)\\ F_{249}\! \left(x , y\right) &= F_{150}\! \left(x \right) F_{248}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{249}\! \left(x , y\right) &= F_{250}\! \left(x , y\right)\\ F_{70}\! \left(x , y\right) &= F_{250}\! \left(x , y\right)+F_{251}\! \left(x , y\right)\\ F_{251}\! \left(x , y\right) &= F_{252}\! \left(x , y\right)\\ F_{252}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{150}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{254}\! \left(x , y\right) &= F_{253}\! \left(x , y\right)+F_{256}\! \left(x , y\right)\\ F_{255}\! \left(x , y\right) &= F_{254}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{255}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)\\ F_{256}\! \left(x , y\right) &= F_{257}\! \left(x , y\right)+F_{278}\! \left(x , y\right)\\ F_{257}\! \left(x , y\right) &= F_{172}\! \left(x , y\right)+F_{258}\! \left(x , y\right)\\ F_{258}\! \left(x , y\right) &= F_{259}\! \left(x , y\right)\\ F_{259}\! \left(x , y\right) &= F_{260}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{261}\! \left(x , y\right) &= F_{260}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{261}\! \left(x , y\right) &= F_{262}\! \left(x , y\right)\\ F_{263}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{262}\! \left(x , y\right)\\ F_{263}\! \left(x , y\right) &= F_{264}\! \left(x , y\right)\\ F_{264}\! \left(x , y\right) &= F_{265}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{265}\! \left(x , y\right) &= F_{266}\! \left(x , y\right)+F_{268}\! \left(x , y\right)\\ F_{267}\! \left(x , y\right) &= F_{266}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{267}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)\\ F_{268}\! \left(x , y\right) &= y F_{269}\! \left(x , y\right)\\ F_{269}\! \left(x , y\right) &= F_{270}\! \left(x , y\right)\\ F_{270}\! \left(x , y\right) &= F_{271}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{272}\! \left(x , y\right) &= F_{271}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{272}\! \left(x , y\right) &= F_{273}\! \left(x , y\right)\\ F_{273}\! \left(x , y\right) &= F_{274}\! \left(x , y\right)+F_{276}\! \left(x , y\right)\\ F_{274}\! \left(x , y\right) &= F_{275}\! \left(x , y\right)\\ F_{275}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{178}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{276}\! \left(x , y\right) &= F_{277}\! \left(x , y\right)\\ F_{277}\! \left(x , y\right) &= F_{178}\! \left(x \right) F_{4}\! \left(x \right) F_{80}\! \left(x , y\right)\\ F_{278}\! \left(x , y\right) &= F_{279}\! \left(x , y\right)\\ F_{279}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{74}\! \left(x , y\right)\\ F_{280}\! \left(x , y\right) &= y F_{246}\! \left(x , y\right)\\ F_{281}\! \left(x , y\right) &= F_{282}\! \left(x , y\right)+F_{316}\! \left(x , y\right)\\ F_{283}\! \left(x , y\right) &= F_{282}\! \left(x , y\right)+F_{287}\! \left(x , y\right)\\ F_{284}\! \left(x , y\right) &= F_{283}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{284}\! \left(x , y\right) &= F_{285}\! \left(x , y\right)\\ F_{285}\! \left(x , y\right) &= F_{286}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{286}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\ F_{287}\! \left(x , y\right) &= F_{288}\! \left(x , y\right)\\ F_{288}\! \left(x , y\right) &= F_{289}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{290}\! \left(x , y\right) &= F_{263}\! \left(x , y\right)+F_{289}\! \left(x , y\right)\\ F_{290}\! \left(x , y\right) &= F_{291}\! \left(x \right)+F_{292}\! \left(x , y\right)\\ F_{291}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{293}\! \left(x , y\right) &= F_{292}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{293}\! \left(x , y\right) &= F_{294}\! \left(x , y\right)\\ F_{295}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{294}\! \left(x , y\right)\\ F_{296}\! \left(x , y\right) &= F_{295}\! \left(x , y\right)+F_{298}\! \left(x , y\right)\\ F_{297}\! \left(x , y\right) &= F_{296}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{297}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\ F_{299}\! \left(x , y\right) &= F_{298}\! \left(x , y\right)+F_{314}\! \left(x , y\right)\\ F_{299}\! \left(x , y\right) &= F_{300}\! \left(x , y\right)+F_{313}\! \left(x , y\right)\\ F_{300}\! \left(x , y\right) &= F_{106}\! \left(x \right)+F_{301}\! \left(x , y\right)\\ F_{301}\! \left(x , y\right) &= F_{302}\! \left(x , y\right)\\ F_{302}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{303}\! \left(x , y\right)\\ F_{303}\! \left(x , y\right) &= F_{304}\! \left(x , 1, y\right)\\ F_{304}\! \left(x , y , z\right) &= -\frac{-F_{305}\! \left(x , y z \right) y +F_{305}\! \left(x , z\right)}{-1+y}\\ F_{305}\! \left(x , y\right) &= F_{200}\! \left(x \right)+F_{306}\! \left(x , y\right)\\ F_{306}\! \left(x , y\right) &= F_{307}\! \left(x , y\right)\\ F_{307}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{308}\! \left(x , y\right)\\ F_{308}\! \left(x , y\right) &= F_{309}\! \left(x , y\right)+F_{310}\! \left(x , y\right)\\ F_{309}\! \left(x , y\right) &= F_{229}\! \left(x \right)+F_{306}\! \left(x , y\right)\\ F_{310}\! \left(x , y\right) &= y F_{311}\! \left(x , y\right)\\ F_{311}\! \left(x , y\right) &= F_{312}\! \left(x , y\right)\\ F_{312}\! \left(x , y\right) &= F_{309}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{296}\! \left(x , y\right) &= F_{301}\! \left(x , y\right)+F_{313}\! \left(x , y\right)\\ F_{314}\! \left(x , y\right) &= F_{315}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\ F_{315}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x , y\right)\\ F_{316}\! \left(x , y\right) &= F_{317}\! \left(x , y\right)\\ F_{317}\! \left(x , y\right) &= F_{318}\! \left(x , y\right)\\ F_{318}\! \left(x , y\right) &= F_{269}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{319}\! \left(x , y\right) &= F_{320}\! \left(x , y\right)\\ F_{320}\! \left(x , y\right) &= F_{273}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{321}\! \left(x , y\right) &= -\frac{-F_{317}\! \left(x , y\right) y +F_{317}\! \left(x , 1\right)}{-1+y}\\ F_{322}\! \left(x , y\right) &= F_{323}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{323}\! \left(x , y\right) &= -\frac{-F_{100}\! \left(x , y\right) y +F_{100}\! \left(x , 1\right)}{-1+y}\\ F_{324}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{44}\! \left(x , y\right)\\ F_{325}\! \left(x , y\right) &= F_{326}\! \left(x , 1, y\right)\\ F_{326}\! \left(x , y , z\right) &= -\frac{y \left(F_{93}\! \left(x , z\right)-F_{93}\! \left(x , y z \right)\right)}{-1+y}\\ F_{327}\! \left(x , y\right) &= F_{328}\! \left(x , y\right)\\ F_{328}\! \left(x , y\right) &= y F_{329}\! \left(x , y\right)\\ F_{329}\! \left(x , y\right) &= F_{330}\! \left(x , 1, y\right)\\ F_{330}\! \left(x , y , z\right) &= -\frac{-F_{70}\! \left(x , y z \right) y +F_{70}\! \left(x , z\right)}{-1+y}\\ F_{331}\! \left(x , y\right) &= y F_{62}\! \left(x , y\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 175 rules.

Finding the specification took 22139 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_{25}\! \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_{25}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{24}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{25}\! \left(x \right) &= x\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{25}\! \left(x \right) F_{28}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= -F_{161}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{25}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{25}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{47}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{48}\! \left(x \right) &= -F_{102}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{25}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{57}\! \left(x \right) &= -F_{20}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{59}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= -F_{21}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{25}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{0}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{25}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{25}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{25}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{25}\! \left(x \right) F_{29}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{25}\! \left(x \right) F_{82}\! \left(x \right)}\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= -F_{81}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{25}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{25}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{23}\! \left(x \right) F_{25}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{25}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{17}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{17}\! \left(x \right) F_{25}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{25}\! \left(x \right) F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{100}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{25}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{146}\! \left(x \right)\\ F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= -F_{140}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{0}\! \left(x \right) F_{111}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{114}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{115}\! \left(x \right) &= -F_{134}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{117}\! \left(x \right) &= -F_{125}\! \left(x \right)+F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= \frac{F_{119}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{125}\! \left(x \right) &= -F_{128}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{127}\! \left(x \right) &= F_{120}\! \left(x \right)\\ F_{128}\! \left(x \right) &= \frac{F_{129}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{129}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{130}\! \left(x \right) &= -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= \frac{F_{132}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{132}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{133}\! \left(x \right) &= -F_{74}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= \frac{F_{137}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{137}\! \left(x \right) &= F_{93}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{140}\! \left(x \right) &= -F_{141}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{144}\! \left(x \right) &= \frac{F_{145}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{145}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{146}\! \left(x \right) &= \frac{F_{147}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{152}\! \left(x \right) &= \frac{F_{153}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{153}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{158}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{159}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right) F_{25}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{166}\! \left(x \right) &= -F_{169}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= \frac{F_{168}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{168}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{171}\! \left(x \right) &= \frac{F_{172}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{172}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{152}\! \left(x \right) F_{25}\! \left(x \right) F_{28}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 174 rules.

Finding the specification took 77253 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_{25}\! \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_{25}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{24}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{25}\! \left(x \right) &= x\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{25}\! \left(x \right) F_{28}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= -F_{160}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{25}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{25}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{46}\! \left(x \right) &= \frac{F_{47}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{47}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{48}\! \left(x \right) &= -F_{102}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{25}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{57}\! \left(x \right) &= -F_{20}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{59}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= -F_{21}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{25}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{0}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{25}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{25}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{25}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{25}\! \left(x \right) F_{29}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{25}\! \left(x \right) F_{82}\! \left(x \right)}\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= -F_{81}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{25}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{25}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{23}\! \left(x \right) F_{25}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{25}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{17}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{17}\! \left(x \right) F_{25}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{25}\! \left(x \right) F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{100}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{25}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{145}\! \left(x \right)\\ F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= -F_{139}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{0}\! \left(x \right) F_{111}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{114}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{115}\! \left(x \right) &= -F_{133}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= -F_{129}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{117}\! \left(x \right) &= -F_{125}\! \left(x \right)+F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= \frac{F_{119}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{125}\! \left(x \right) &= -F_{128}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{127}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{128}\! \left(x \right) &= -F_{74}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{129}\! \left(x \right) &= -F_{131}\! \left(x \right)+F_{130}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{131}\! \left(x \right) &= \frac{F_{132}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{132}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{134}\! \left(x \right) &= -F_{137}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= \frac{F_{136}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{136}\! \left(x \right) &= F_{93}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{20}\! \left(x \right) F_{25}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{139}\! \left(x \right) &= -F_{140}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{143}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{144}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{145}\! \left(x \right) &= \frac{F_{146}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= -F_{137}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{151}\! \left(x \right) &= \frac{F_{152}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{152}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{161}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right) F_{25}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{165}\! \left(x \right) &= -F_{168}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= \frac{F_{167}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{167}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{170}\! \left(x \right) &= \frac{F_{171}\! \left(x \right)}{F_{25}\! \left(x \right)}\\ F_{171}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{151}\! \left(x \right) F_{25}\! \left(x \right) F_{28}\! \left(x \right)\\ \end{align*}\)