Av(12435, 12453, 12543, 14235, 14253, 21435, 21453, 21543)
Generating Function
\(\displaystyle \frac{\left(-10 x^{6}+36 x^{5}-75 x^{4}+72 x^{3}-11 x^{2}-13 x +2\right) \sqrt{5 x^{2}-6 x +1}-20 x^{7}+64 x^{6}-69 x^{5}-115 x^{4}+481 x^{3}-544 x^{2}+237 x -28}{10 x^{7}-92 x^{6}+340 x^{5}-742 x^{4}+980 x^{3}-712 x^{2}+244 x -26}\)
Counting Sequence
1, 1, 2, 6, 24, 112, 562, 2920, 15453, 82664, 445237, 2409175, 13078298, 71162538, 387887162, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(5 x^{7}-46 x^{6}+170 x^{5}-371 x^{4}+490 x^{3}-356 x^{2}+122 x -13\right) F \left(x
\right)^{2}+\left(20 x^{7}-64 x^{6}+69 x^{5}+115 x^{4}-481 x^{3}+544 x^{2}-237 x +28\right) F \! \left(x \right)-5 x^{7}+36 x^{6}-76 x^{5}+79 x^{4}+63 x^{3}-186 x^{2}+113 x -15 = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 562\)
\(\displaystyle a(7) = 2920\)
\(\displaystyle a(8) = 15453\)
\(\displaystyle a(9) = 82664\)
\(\displaystyle a(10) = 445237\)
\(\displaystyle a(11) = 2409175\)
\(\displaystyle a(12) = 13078298\)
\(\displaystyle a(13) = 71162538\)
\(\displaystyle a(14) = 387887162\)
\(\displaystyle a{\left(n + 15 \right)} = - \frac{125 n a{\left(n \right)}}{13 \left(n + 15\right)} + \frac{125 \left(14 n + 9\right) a{\left(n + 1 \right)}}{13 \left(n + 15\right)} - \frac{135 \left(167 n + 238\right) a{\left(n + 2 \right)}}{26 \left(n + 15\right)} + \frac{\left(569 n + 7963\right) a{\left(n + 14 \right)}}{26 \left(n + 15\right)} - \frac{\left(4763 n + 62710\right) a{\left(n + 13 \right)}}{26 \left(n + 15\right)} + \frac{\left(18325 n + 233723\right) a{\left(n + 12 \right)}}{26 \left(n + 15\right)} - \frac{\left(24192 n + 361381\right) a{\left(n + 11 \right)}}{26 \left(n + 15\right)} - \frac{\left(58205 n + 231164\right) a{\left(n + 10 \right)}}{26 \left(n + 15\right)} + \frac{\left(91226 n + 205731\right) a{\left(n + 3 \right)}}{26 \left(n + 15\right)} + \frac{\left(156979 n + 1015156\right) a{\left(n + 9 \right)}}{13 \left(n + 15\right)} - \frac{\left(257436 n + 798085\right) a{\left(n + 4 \right)}}{26 \left(n + 15\right)} + \frac{\left(528408 n + 2083711\right) a{\left(n + 5 \right)}}{26 \left(n + 15\right)} - \frac{\left(665831 n + 4123511\right) a{\left(n + 8 \right)}}{26 \left(n + 15\right)} - \frac{\left(798409 n + 3805825\right) a{\left(n + 6 \right)}}{26 \left(n + 15\right)} + \frac{\left(875671 n + 4851500\right) a{\left(n + 7 \right)}}{26 \left(n + 15\right)}, \quad n \geq 15\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 562\)
\(\displaystyle a(7) = 2920\)
\(\displaystyle a(8) = 15453\)
\(\displaystyle a(9) = 82664\)
\(\displaystyle a(10) = 445237\)
\(\displaystyle a(11) = 2409175\)
\(\displaystyle a(12) = 13078298\)
\(\displaystyle a(13) = 71162538\)
\(\displaystyle a(14) = 387887162\)
\(\displaystyle a{\left(n + 15 \right)} = - \frac{125 n a{\left(n \right)}}{13 \left(n + 15\right)} + \frac{125 \left(14 n + 9\right) a{\left(n + 1 \right)}}{13 \left(n + 15\right)} - \frac{135 \left(167 n + 238\right) a{\left(n + 2 \right)}}{26 \left(n + 15\right)} + \frac{\left(569 n + 7963\right) a{\left(n + 14 \right)}}{26 \left(n + 15\right)} - \frac{\left(4763 n + 62710\right) a{\left(n + 13 \right)}}{26 \left(n + 15\right)} + \frac{\left(18325 n + 233723\right) a{\left(n + 12 \right)}}{26 \left(n + 15\right)} - \frac{\left(24192 n + 361381\right) a{\left(n + 11 \right)}}{26 \left(n + 15\right)} - \frac{\left(58205 n + 231164\right) a{\left(n + 10 \right)}}{26 \left(n + 15\right)} + \frac{\left(91226 n + 205731\right) a{\left(n + 3 \right)}}{26 \left(n + 15\right)} + \frac{\left(156979 n + 1015156\right) a{\left(n + 9 \right)}}{13 \left(n + 15\right)} - \frac{\left(257436 n + 798085\right) a{\left(n + 4 \right)}}{26 \left(n + 15\right)} + \frac{\left(528408 n + 2083711\right) a{\left(n + 5 \right)}}{26 \left(n + 15\right)} - \frac{\left(665831 n + 4123511\right) a{\left(n + 8 \right)}}{26 \left(n + 15\right)} - \frac{\left(798409 n + 3805825\right) a{\left(n + 6 \right)}}{26 \left(n + 15\right)} + \frac{\left(875671 n + 4851500\right) a{\left(n + 7 \right)}}{26 \left(n + 15\right)}, \quad n \geq 15\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 258 rules.
Finding the specification took 41698 seconds.
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Copy 258 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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \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_{18}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{18}\! \left(x \right) &= x\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{18}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{18}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{18}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{18}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{36}\! \left(x \right) &= \frac{F_{37}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{37}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{40}\! \left(x \right) &= -F_{46}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{45}\! \left(x \right) &= x^{2} F_{45} \left(x \right)^{2}-2 x F_{45} \left(x \right)^{2}+x F_{45}\! \left(x \right)+2 F_{45}\! \left(x \right)-1\\
F_{46}\! \left(x \right) &= F_{2}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{18}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{36}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{45}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{25}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{18}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{59}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{18}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{64}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{18}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= \frac{F_{72}\! \left(x \right)}{F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)}\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= -F_{252}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{182}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= -F_{203}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= -F_{200}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{18}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{18}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{18}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{18}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)+F_{106}\! \left(x \right)\\
F_{101}\! \left(x \right) &= 0\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{120}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{129}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{133}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{131}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{18}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{137}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{121}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{141}\! \left(x \right)+F_{143}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{135}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{124}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= 2 F_{101}\! \left(x \right)+F_{157}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= 2 F_{101}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{152}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{179}\! \left(x \right) &= \frac{F_{180}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{182}\! \left(x \right) &= x^{2} F_{182} \left(x \right)^{2}+2 x^{2} F_{182}\! \left(x \right)-2 x F_{182} \left(x \right)^{2}+x^{2}-3 x F_{182}\! \left(x \right)-x +2 F_{182}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{18}\! \left(x \right) F_{185}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{18}\! \left(x \right) F_{188}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{119}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{36}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{200}\! \left(x \right) &= \frac{F_{201}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{174}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{173}\! \left(x \right) F_{207}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{18}\! \left(x \right) F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{232}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{212}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{18}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{18}\! \left(x \right) F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{138}\! \left(x \right) F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{221}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{18}\! \left(x \right) F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{216}\! \left(x \right)+F_{218}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{18}\! \left(x \right) F_{217}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{227}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{18}\! \left(x \right) F_{220}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{123}\! \left(x \right) F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{18}\! \left(x \right) F_{210}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{18}\! \left(x \right) F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{18}\! \left(x \right) F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{223}\! \left(x \right) F_{232}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{217}\! \left(x \right) F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{18}\! \left(x \right) F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{250}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{236}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{246}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{253}\! \left(x \right) &= -F_{256}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= \frac{F_{255}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{255}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{256}\! \left(x \right) &= \frac{F_{257}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{257}\! \left(x \right) &= F_{202}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 258 rules.
Finding the specification took 41698 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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \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_{18}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{18}\! \left(x \right) &= x\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{18}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{18}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{18}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{18}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{36}\! \left(x \right) &= \frac{F_{37}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{37}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{40}\! \left(x \right) &= -F_{46}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{45}\! \left(x \right) &= x^{2} F_{45} \left(x \right)^{2}-2 x F_{45} \left(x \right)^{2}+F_{45}\! \left(x \right) x +2 F_{45}\! \left(x \right)-1\\
F_{46}\! \left(x \right) &= F_{2}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{18}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{36}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{45}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{25}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{18}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{59}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{18}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{64}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{18}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= \frac{F_{72}\! \left(x \right)}{F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)}\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= -F_{252}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{182}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= -F_{203}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= -F_{200}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{18}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{18}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{18}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{18}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)+F_{106}\! \left(x \right)\\
F_{101}\! \left(x \right) &= 0\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{120}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{129}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{133}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{131}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{18}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{137}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{121}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{141}\! \left(x \right)+F_{143}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{135}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{124}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= 2 F_{101}\! \left(x \right)+F_{157}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= 2 F_{101}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{152}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{179}\! \left(x \right) &= \frac{F_{180}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{182}\! \left(x \right) &= x^{2} F_{182} \left(x \right)^{2}+2 x^{2} F_{182}\! \left(x \right)-2 x F_{182} \left(x \right)^{2}+x^{2}-3 x F_{182}\! \left(x \right)-x +2 F_{182}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{18}\! \left(x \right) F_{185}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{18}\! \left(x \right) F_{188}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{119}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{131}\! \left(x \right) F_{173}\! \left(x \right) F_{36}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{200}\! \left(x \right) &= \frac{F_{201}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{174}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{173}\! \left(x \right) F_{87}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{173}\! \left(x \right) F_{207}\! \left(x \right) F_{87}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{18}\! \left(x \right) F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{232}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{212}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{18}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{18}\! \left(x \right) F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{138}\! \left(x \right) F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{221}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{18}\! \left(x \right) F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{216}\! \left(x \right)+F_{218}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{18}\! \left(x \right) F_{217}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{227}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{18}\! \left(x \right) F_{220}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{123}\! \left(x \right) F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{18}\! \left(x \right) F_{210}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{18}\! \left(x \right) F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{18}\! \left(x \right) F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{223}\! \left(x \right) F_{232}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{217}\! \left(x \right) F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{18}\! \left(x \right) F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{250}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{236}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{246}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{253}\! \left(x \right) &= -F_{256}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= \frac{F_{255}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{255}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{256}\! \left(x \right) &= \frac{F_{257}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{257}\! \left(x \right) &= F_{202}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 262 rules.
Finding the specification took 15644 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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \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_{18}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{18}\! \left(x \right) &= x\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{18}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{18}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{18}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{18}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{28}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= x^{2} F_{36} \left(x \right)^{2}-2 x F_{36} \left(x \right)^{2}+F_{36}\! \left(x \right) x +2 F_{36}\! \left(x \right)-1\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{18}\! \left(x \right) F_{24}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{18}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{18}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{18}\! \left(x \right) F_{58}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{18}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{41}\! \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_{65}\! \left(x \right) &= F_{18}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{18}\! \left(x \right) F_{70}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{18}\! \left(x \right) F_{36}\! \left(x \right)}\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{18}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{18}\! \left(x \right) F_{55}\! \left(x \right)}\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{18}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{18}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right)}\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{256}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{221}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{195}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= -F_{219}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= -F_{216}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{18}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{114}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{118}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{117}\! \left(x \right) &= 0\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{126}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{138}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{136}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{142}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{144}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{112}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{150}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{18}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{154}\! \left(x \right)+F_{156}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{148}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{137}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{165}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= 2 F_{117}\! \left(x \right)+F_{170}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{161}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= 2 F_{117}\! \left(x \right)+F_{178}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{18}\! \left(x \right) F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{18}\! \left(x \right) F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{214}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{114}\! \left(x \right) F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{199}\! \left(x \right)\\
F_{192}\! \left(x \right) &= \frac{F_{193}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{195}\! \left(x \right) &= x^{2} F_{195} \left(x \right)^{2}+2 x^{2} F_{195}\! \left(x \right)-2 x F_{195} \left(x \right)^{2}+x^{2}-3 x F_{195}\! \left(x \right)-x +2 F_{195}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{102}\! \left(x \right) F_{18}\! \left(x \right) F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{103}\! \left(x \right) F_{18}\! \left(x \right) F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{18}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{135}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{216}\! \left(x \right) &= \frac{F_{217}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{18}\! \left(x \right) F_{187}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{103}\! \left(x \right) F_{112}\! \left(x \right) F_{186}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{18}\! \left(x \right) F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{236}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{18}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{18}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{232}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{151}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{18}\! \left(x \right) F_{226}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{223}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{18}\! \left(x \right) F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{18}\! \left(x \right) F_{244}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{236}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{255}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{18}\! \left(x \right) F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{228}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{240}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{250}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{210}\! \left(x \right) F_{257}\! \left(x \right)\\
F_{257}\! \left(x \right) &= -F_{260}\! \left(x \right)+F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= \frac{F_{259}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{259}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{260}\! \left(x \right) &= \frac{F_{261}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{261}\! \left(x \right) &= F_{218}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 53 rules.
Finding the specification took 6976 seconds.
Copy 53 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_{20}\! \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_{20}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= \frac{F_{8}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{8}\! \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_{20}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= x^{2} F_{14} \left(x \right)^{2}-2 x F_{14} \left(x \right)^{2}+F_{14}\! \left(x \right) x +2 F_{14}\! \left(x \right)-1\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{20}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x , 1\right)\\
F_{18}\! \left(x , y\right) &= -\frac{-F_{19}\! \left(x , y\right) y +F_{19}\! \left(x , 1\right)}{-1+y}\\
F_{19}\! \left(x , y\right) &= x^{2} F_{19}\! \left(x , y\right)^{2} y^{2}-2 y x F_{19}\! \left(x , y\right)^{2}+x F_{19}\! \left(x , y\right) y +2 F_{19}\! \left(x , y\right)-1\\
F_{20}\! \left(x \right) &= x\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{20}\! \left(x \right) F_{24}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x , 1\right)\\
F_{26}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{31}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= x^{2} F_{30}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{30}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{30}\! \left(x , y\right)^{2} y -3 x F_{30}\! \left(x , y\right) y -y x +2 F_{30}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= y x\\
F_{33}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{20}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x , 1\right)\\
F_{37}\! \left(x , y\right) &= -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{20}\! \left(x \right) F_{40}\! \left(x \right) F_{49}\! \left(x , y\right)\\
F_{40}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{20}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{20}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{38}\! \left(x , 1\right)\\
F_{50}\! \left(x , y\right) &= F_{20}\! \left(x \right) F_{49}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{20}\! \left(x \right) F_{25}\! \left(x , y\right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{32}\! \left(x , 1\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 262 rules.
Finding the specification took 15644 seconds.
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Copy 262 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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \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_{18}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{18}\! \left(x \right) &= x\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{18}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{18}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{18}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{18}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{28}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= x^{2} F_{36} \left(x \right)^{2}-2 x F_{36} \left(x \right)^{2}+F_{36}\! \left(x \right) x +2 F_{36}\! \left(x \right)-1\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{18}\! \left(x \right) F_{24}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{18}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{18}\! \left(x \right) F_{43}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{18}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{18}\! \left(x \right) F_{58}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{18}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{41}\! \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_{65}\! \left(x \right) &= F_{18}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{18}\! \left(x \right) F_{70}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{18}\! \left(x \right) F_{36}\! \left(x \right)}\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{18}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{18}\! \left(x \right) F_{55}\! \left(x \right)}\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{18}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{18}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right)}\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{256}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{221}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{195}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= -F_{219}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= -F_{216}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{18}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{114}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{118}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{117}\! \left(x \right) &= 0\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{126}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{138}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{136}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{142}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{144}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{112}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{150}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{18}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{154}\! \left(x \right)+F_{156}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{148}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{137}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{165}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= 2 F_{117}\! \left(x \right)+F_{170}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{161}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= 2 F_{117}\! \left(x \right)+F_{178}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{18}\! \left(x \right) F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{18}\! \left(x \right) F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{214}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{114}\! \left(x \right) F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{199}\! \left(x \right)\\
F_{192}\! \left(x \right) &= \frac{F_{193}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{195}\! \left(x \right) &= x^{2} F_{195} \left(x \right)^{2}+2 x^{2} F_{195}\! \left(x \right)-2 x F_{195} \left(x \right)^{2}+x^{2}-3 x F_{195}\! \left(x \right)-x +2 F_{195}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{102}\! \left(x \right) F_{18}\! \left(x \right) F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{103}\! \left(x \right) F_{18}\! \left(x \right) F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{18}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{135}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{103}\! \left(x \right) F_{144}\! \left(x \right) F_{186}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{216}\! \left(x \right) &= \frac{F_{217}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{18}\! \left(x \right) F_{187}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{103}\! \left(x \right) F_{112}\! \left(x \right) F_{186}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{186}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{18}\! \left(x \right) F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{236}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{18}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{18}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{232}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{151}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{18}\! \left(x \right) F_{226}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{223}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{18}\! \left(x \right) F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{18}\! \left(x \right) F_{244}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{236}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{255}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{18}\! \left(x \right) F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{228}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{240}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{250}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{210}\! \left(x \right) F_{257}\! \left(x \right)\\
F_{257}\! \left(x \right) &= -F_{260}\! \left(x \right)+F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= \frac{F_{259}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{259}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{260}\! \left(x \right) &= \frac{F_{261}\! \left(x \right)}{F_{18}\! \left(x \right)}\\
F_{261}\! \left(x \right) &= F_{218}\! \left(x \right)\\
\end{align*}\)