Av(1234, 2341)
Generating Function
\(\displaystyle \frac{\left(-13 x^{4}+50 x^{3}-48 x^{2}+17 x -2\right) \sqrt{1-4 x}-20 x^{5}+77 x^{4}-122 x^{3}+78 x^{2}-21 x +2}{8 \left(x^{2}-3 x +1\right) \left(x -\frac{1}{4}\right) x^{3}}\)
Counting Sequence
1, 1, 2, 6, 22, 89, 376, 1611, 6901, 29375, 123996, 518971, 2155145, 8888348, 36442184, ...
Implicit Equation for the Generating Function
\(\displaystyle x^{3} \left(4 x -1\right) \left(x^{2}-3 x +1\right)^{2} F \left(x
\right)^{2}+\left(4 x -1\right) \left(x^{2}-3 x +1\right) \left(5 x^{4}-18 x^{3}+26 x^{2}-13 x +2\right) F \! \left(x \right)+25 x^{6}-144 x^{5}+304 x^{4}-275 x^{3}+120 x^{2}-25 x +2 = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 22\)
\(\displaystyle a \! \left(5\right) = 89\)
\(\displaystyle a \! \left(6\right) = 376\)
\(\displaystyle a \! \left(n +7\right) = \frac{13 \left(3+2 n \right) a \! \left(n \right)}{10+n}-\frac{\left(5292+1055 n \right) a \! \left(3+n \right)}{2 \left(10+n \right)}-\frac{3 \left(320+123 n \right) a \! \left(n +1\right)}{2 \left(10+n \right)}+\frac{\left(3512+933 n \right) a \! \left(n +2\right)}{20+2 n}+\frac{\left(3862+615 n \right) a \! \left(n +4\right)}{20+2 n}-\frac{\left(1454+193 n \right) a \! \left(n +5\right)}{2 \left(10+n \right)}+\frac{\left(272+31 n \right) a \! \left(n +6\right)}{20+2 n}, \quad n \geq 7\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 22\)
\(\displaystyle a \! \left(5\right) = 89\)
\(\displaystyle a \! \left(6\right) = 376\)
\(\displaystyle a \! \left(n +7\right) = \frac{13 \left(3+2 n \right) a \! \left(n \right)}{10+n}-\frac{\left(5292+1055 n \right) a \! \left(3+n \right)}{2 \left(10+n \right)}-\frac{3 \left(320+123 n \right) a \! \left(n +1\right)}{2 \left(10+n \right)}+\frac{\left(3512+933 n \right) a \! \left(n +2\right)}{20+2 n}+\frac{\left(3862+615 n \right) a \! \left(n +4\right)}{20+2 n}-\frac{\left(1454+193 n \right) a \! \left(n +5\right)}{2 \left(10+n \right)}+\frac{\left(272+31 n \right) a \! \left(n +6\right)}{20+2 n}, \quad n \geq 7\)
Heatmap
To create this heatmap, we sampled 1,000,000 permutations of length 300 uniformly at random. The color of the point \((i, j)\) represents how many permutations have value \(j\) at index \(i\) (darker = more).
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Req Corrob Expand Verified" and has 108 rules.
Found on January 20, 2022.Finding the specification took 2240 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_{14}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \left(x , y\right) &= F_{5}\! \left(x \right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x \right) &= x\\
F_{15}\! \left(x , y\right) &= y x\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{14}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{19}\! \left(x \right)+F_{5}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{14}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{21}\! \left(x \right) &= \frac{F_{22}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{22}\! \left(x \right) &= -F_{24}\! \left(x \right)-F_{5}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{26}\! \left(x \right) &= 0\\
F_{27}\! \left(x \right) &= F_{14}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x , 1\right)\\
F_{29}\! \left(x , y\right) &= F_{26}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= -\frac{-y F_{29}\! \left(x , y\right)+F_{29}\! \left(x , 1\right)}{-1+y}\\
F_{32}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{29}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= -\frac{-y F_{37}\! \left(x , y\right)+F_{37}\! \left(x , 1\right)}{-1+y}\\
F_{37}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{38}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{34}\! \left(x , y\right)\\
F_{39}\! \left(x \right) &= F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x , 1\right)\\
F_{44}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{43}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= -\frac{-y F_{45}\! \left(x , y\right)+F_{45}\! \left(x , 1\right)}{-1+y}\\
F_{48}\! \left(x \right) &= F_{14}\! \left(x \right) F_{49}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x , 1\right)\\
F_{51}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{67}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= -\frac{-y F_{55}\! \left(x , y\right)+F_{55}\! \left(x , 1\right)}{-1+y}\\
F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= -\frac{-F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}\\
F_{59}\! \left(x , y\right) &= -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}\\
F_{60}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{66}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= -\frac{-y F_{65}\! \left(x , y\right)+F_{65}\! \left(x , 1\right)}{-1+y}\\
F_{65}\! \left(x , y\right) &= -\frac{-y F_{37}\! \left(x , y\right)+F_{37}\! \left(x , 1\right)}{-1+y}\\
F_{66}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{62}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= -\frac{-y F_{51}\! \left(x , y\right)+F_{51}\! \left(x , 1\right)}{-1+y}\\
F_{69}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= -\frac{-y F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)}{-1+y}\\
F_{73}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{14}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{14}\! \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) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{14}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x , 1\right)\\
F_{81}\! \left(x , y\right) &= -\frac{-y F_{82}\! \left(x , y\right)+F_{82}\! \left(x , 1\right)}{-1+y}\\
F_{83}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{82}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{101}\! \left(x \right)+F_{84}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{73}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}\\
F_{89}\! \left(x , y\right) &= F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{90}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{73}\! \left(x \right) F_{93}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{73}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{97}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{96}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{94}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{99}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}\\
F_{100}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{105}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{89}\! \left(x , 1\right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{85}\! \left(x , 1\right)\\
F_{107}\! \left(x \right) &= F_{106}\! \left(x \right) F_{14}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Req Corrob" and has 258 rules.
Found on January 20, 2022.Finding the specification took 10608 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_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{22}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{10}\! \left(x \right) &= \frac{F_{11}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x , 1\right)\\
F_{14}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{5}\! \left(x \right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= y x\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{22}\! \left(x \right)\\
F_{21}\! \left(x , y\right) &= -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}\\
F_{22}\! \left(x \right) &= x\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{22}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x , 1\right)\\
F_{28}\! \left(x , y\right) &= -\frac{-y F_{29}\! \left(x , y\right)+F_{29}\! \left(x , 1\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y , 1\right)\\
F_{32}\! \left(x , y , z\right) &= F_{33}\! \left(x , y , y z \right)\\
F_{33}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x , y , z\right)+F_{36}\! \left(x , y , z\right)\\
F_{34}\! \left(x , y , z\right) &= F_{18}\! \left(x , y\right) F_{35}\! \left(x , y , z\right)\\
F_{35}\! \left(x , y , z\right) &= \frac{y F_{32}\! \left(x , y , 1\right)-z F_{32}\! \left(x , y , \frac{z}{y}\right)}{-z +y}\\
F_{36}\! \left(x , y , z\right) &= F_{18}\! \left(x , z\right) F_{33}\! \left(x , y , z\right)\\
F_{37}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{22}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x , 1\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x \right)+F_{49}\! \left(x , y\right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{22}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\
F_{50}\! \left(x \right) &= 0\\
F_{51}\! \left(x , y\right) &= F_{22}\! \left(x \right) F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{22}\! \left(x \right) F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)+F_{59}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}\\
F_{59}\! \left(x , y\right) &= F_{45}\! \left(x , y\right) F_{60}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}\\
F_{61}\! \left(x \right) &= F_{46}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{21}\! \left(x , 1\right)\\
F_{63}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{22}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x , 1\right)\\
F_{68}\! \left(x , y\right) &= -\frac{-y F_{69}\! \left(x , y\right)+F_{69}\! \left(x , 1\right)}{-1+y}\\
F_{69}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{22}\! \left(x \right) F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= -\frac{-y F_{69}\! \left(x , y\right)+F_{69}\! \left(x , 1\right)}{-1+y}\\
F_{73}\! \left(x \right) &= \frac{F_{74}\! \left(x \right)}{F_{46}\! \left(x \right)}\\
F_{74}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= -F_{107}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= \frac{F_{77}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= -F_{106}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{22}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= \frac{F_{82}\! \left(x \right)}{F_{46}\! \left(x \right)}\\
F_{82}\! \left(x \right) &= -F_{105}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x , 1\right)\\
F_{84}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{69}\! \left(x , y\right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{88}\! \left(x , y\right) &= F_{46}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{90}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{46}\! \left(x \right)+F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{50}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{90}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{22}\! \left(x \right) F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{96}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{22}\! \left(x \right) F_{97}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{99}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right) F_{90}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= -\frac{-y F_{68}\! \left(x , y\right)+F_{68}\! \left(x , 1\right)}{-1+y}\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{22}\! \left(x \right)\\
F_{104}\! \left(x , y\right) &= -\frac{-y F_{84}\! \left(x , y\right)+F_{84}\! \left(x , 1\right)}{-1+y}\\
F_{105}\! \left(x \right) &= F_{10}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{46} \left(x \right)^{2}\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{46}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{22}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{110}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{116}\! \left(x \right) &= -F_{119}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= \frac{F_{118}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{118}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{89}\! \left(x , 1\right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{110}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{128}\! \left(x \right) &= \frac{F_{129}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{46}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{46}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= -F_{239}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{220}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{144}\! \left(x \right) &= \frac{F_{145}\! \left(x \right)}{F_{22}\! \left(x \right) F_{48}\! \left(x \right)}\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= -F_{149}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= \frac{F_{148}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{148}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{48}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{152}\! \left(x \right) &= \frac{F_{153}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= -F_{43}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= \frac{F_{156}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= -F_{161}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x , 1\right)\\
F_{162}\! \left(x , y\right) &= -\frac{F_{163}\! \left(x , 1\right)-F_{163}\! \left(x , y\right)}{-1+y}\\
F_{163}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= -F_{217}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{179}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{171}\! \left(x \right) &= \frac{F_{172}\! \left(x \right)}{F_{87}\! \left(x \right)}\\
F_{172}\! \left(x \right) &= -F_{178}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{175}\! \left(x \right) &= \frac{F_{176}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{176}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{155}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{179}\! \left(x \right) &= -F_{216}\! \left(x \right)+F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right) F_{22}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{182}\! \left(x \right) &= -F_{212}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= \frac{F_{184}\! \left(x \right)}{F_{22}\! \left(x \right) F_{48}\! \left(x \right)}\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{188}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{48} \left(x \right)^{3} F_{46}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right) F_{22}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{195}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{22}\! \left(x \right) F_{48}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{196}\! \left(x \right) &= -F_{197}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{198}\! \left(x \right) &= -F_{127}\! \left(x \right)+F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{201}\! \left(x \right) &= \frac{F_{202}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= -F_{209}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= \frac{F_{205}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= -F_{110}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= \frac{F_{208}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{208}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{209}\! \left(x \right) &= -F_{125}\! \left(x \right)+F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= \frac{F_{211}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{211}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x , 1\right)\\
F_{213}\! \left(x , y\right) &= -\frac{-y F_{214}\! \left(x , y\right)+F_{214}\! \left(x , 1\right)}{-1+y}\\
F_{215}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{214}\! \left(x , y\right)\\
F_{215}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{216}\! \left(x \right) &= F_{169}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{182}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{223}\! \left(x \right) &= \frac{F_{224}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= -F_{235}\! \left(x \right)+F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= \frac{F_{227}\! \left(x \right)}{F_{46}\! \left(x \right)}\\
F_{227}\! \left(x \right) &= -F_{231}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{228}\! \left(x \right) &= \frac{F_{229}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= -F_{106}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{152}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{157}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{236}\! \left(x \right)\\
F_{239}\! \left(x \right) &= \frac{F_{240}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x , 1\right)\\
F_{243}\! \left(x , y\right) &= -\frac{y \left(F_{163}\! \left(x , 1\right)-F_{163}\! \left(x , y\right)\right)}{-1+y}\\
F_{244}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= \frac{F_{248}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{250}\! \left(x \right)\\
F_{250}\! \left(x \right) &= -F_{253}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= \frac{F_{252}\! \left(x \right)}{F_{22}\! \left(x \right) F_{48}\! \left(x \right)}\\
F_{252}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{225}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{238}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{247}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 377 rules.
Found on April 24, 2021.Finding the specification took 35 seconds.
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Copy 377 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_{21}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{229}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{21}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{216}\! \left(x , y_{0}\right)+F_{218}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{143}\! \left(x , y_{0}\right)+F_{89}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , 1, y_{0}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{12}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{47}\! \left(x , y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x \right)+F_{22}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x \right)\\
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) &= x\\
F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{23}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x , y_{0}\right)\\
F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)\\
F_{27}\! \left(x \right) &= 0\\
F_{28}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{19}\! \left(x \right)+F_{26}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{22}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{19}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x \right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{39}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{27}\! \left(x \right)+F_{43}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{48}\! \left(x , y_{0}\right)\\
F_{48}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{49}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= F_{50}\! \left(x , y_{0}, 1\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}, y_{1}\right)\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{52}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{53}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{0}\right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{1}\right) F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{y_{1} F_{52}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{52}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{59}\! \left(x , y_{1}, y_{2}\right)+F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{41}\! \left(x , y_{0}, y_{2}\right)+F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{62}\! \left(x , y_{0}, y_{1}\right)+F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}\right) &= F_{63}\! \left(x , y_{0}, y_{1}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{64}\! \left(x , y_{0}, y_{1}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)\\
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= 2 F_{27}\! \left(x \right)+F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{1}\right) F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{37}\! \left(x , y_{0}, y_{2}\right)+F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{69}\! \left(x , y_{0}\right) &= F_{70}\! \left(x , y_{0}, 1\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{71}\! \left(x , y_{0}, y_{1}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{56}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{72}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{73}\! \left(x , y_{0}\right)\\
F_{73}\! \left(x , y_{0}\right) &= F_{74}\! \left(x \right)+F_{80}\! \left(x , y_{0}\right)\\
F_{74}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{21}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{21}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{80}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)\\
F_{81}\! \left(x , y_{0}\right) &= F_{82}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)\\
F_{82}\! \left(x , y_{0}\right) &= F_{83}\! \left(x , y_{0}\right)\\
F_{83}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{84}\! \left(x , y_{0}\right)\\
F_{84}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)\\
F_{85}\! \left(x , y_{0}\right) &= 2 F_{27}\! \left(x \right)+F_{86}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)\\
F_{86}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{87}\! \left(x , y_{0}\right)\\
F_{87}\! \left(x , y_{0}\right) &= F_{26}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)\\
F_{88}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{81}\! \left(x , y_{0}\right)\\
F_{89}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{90}\! \left(x , y_{0}\right)\\
F_{90}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{8}\! \left(x , y_{0}\right)+F_{8}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{91}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{92}\! \left(x , y_{0}\right)\\
F_{92}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{140}\! \left(x , y_{0}\right)+F_{142}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)+F_{93}\! \left(x , y_{0}\right)\\
F_{93}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{94}\! \left(x , y_{0}\right)\\
F_{94}\! \left(x , y_{0}\right) &= F_{105}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)\\
F_{95}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}\right)\\
F_{96}\! \left(x , y_{0}\right) &= F_{75}\! \left(x \right)+F_{97}\! \left(x , y_{0}\right)\\
F_{97}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{98}\! \left(x , y_{0}\right) &= F_{99}\! \left(x , y_{0}\right)\\
F_{99}\! \left(x , y_{0}\right) &= F_{100}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{100}\! \left(x , y_{0}\right) &= F_{19}\! \left(x \right)+F_{98}\! \left(x , y_{0}\right)\\
F_{101}\! \left(x , y_{0}\right) &= 2 F_{27}\! \left(x \right)+F_{102}\! \left(x , y_{0}\right)+F_{104}\! \left(x , y_{0}\right)\\
F_{102}\! \left(x , y_{0}\right) &= F_{103}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)\\
F_{104}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{97}\! \left(x , y_{0}\right)\\
F_{105}\! \left(x , y_{0}\right) &= F_{106}\! \left(x , y_{0}\right)+F_{122}\! \left(x , y_{0}\right)\\
F_{106}\! \left(x , y_{0}\right) &= F_{107}\! \left(x \right)+F_{111}\! \left(x , y_{0}\right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{111}\! \left(x , y_{0}\right) &= F_{112}\! \left(x , y_{0}\right)+F_{117}\! \left(x , y_{0}\right)\\
F_{112}\! \left(x , y_{0}\right) &= F_{113}\! \left(x , y_{0}\right)+F_{115}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)\\
F_{113}\! \left(x , y_{0}\right) &= F_{114}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{114}\! \left(x , y_{0}\right) &= F_{112}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)\\
F_{115}\! \left(x , y_{0}\right) &= F_{116}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{116}\! \left(x , y_{0}\right) &= F_{112}\! \left(x , y_{0}\right)+F_{19}\! \left(x \right)\\
F_{117}\! \left(x , y_{0}\right) &= 2 F_{27}\! \left(x \right)+F_{118}\! \left(x , y_{0}\right)+F_{120}\! \left(x , y_{0}\right)\\
F_{118}\! \left(x , y_{0}\right) &= F_{119}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{119}\! \left(x , y_{0}\right) &= F_{117}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{120}\! \left(x , y_{0}\right) &= F_{121}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{121}\! \left(x , y_{0}\right) &= F_{108}\! \left(x \right)+F_{117}\! \left(x , y_{0}\right)\\
F_{122}\! \left(x , y_{0}\right) &= F_{123}\! \left(x \right)+F_{129}\! \left(x , y_{0}\right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{124}\! \left(x \right) &= 2 F_{27}\! \left(x \right)+F_{125}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{129}\! \left(x , y_{0}\right) &= F_{130}\! \left(x , y_{0}\right)+F_{135}\! \left(x , y_{0}\right)\\
F_{130}\! \left(x , y_{0}\right) &= 2 F_{27}\! \left(x \right)+F_{131}\! \left(x , y_{0}\right)+F_{133}\! \left(x , y_{0}\right)\\
F_{131}\! \left(x , y_{0}\right) &= F_{132}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{132}\! \left(x , y_{0}\right) &= F_{130}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{133}\! \left(x , y_{0}\right) &= F_{134}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{134}\! \left(x , y_{0}\right) &= F_{130}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)\\
F_{135}\! \left(x , y_{0}\right) &= 3 F_{27}\! \left(x \right)+F_{136}\! \left(x , y_{0}\right)+F_{138}\! \left(x , y_{0}\right)\\
F_{136}\! \left(x , y_{0}\right) &= F_{137}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{137}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{135}\! \left(x , y_{0}\right)\\
F_{138}\! \left(x , y_{0}\right) &= F_{139}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{139}\! \left(x , y_{0}\right) &= F_{124}\! \left(x \right)+F_{135}\! \left(x , y_{0}\right)\\
F_{140}\! \left(x , y_{0}\right) &= F_{141}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{141}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{92}\! \left(x , y_{0}\right)+F_{92}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{142}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{95}\! \left(x , y_{0}\right)\\
F_{143}\! \left(x , y_{0}\right) &= F_{144}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{144}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{145}\! \left(x , y_{0}\right)+F_{146}\! \left(x , y_{0}\right)+F_{182}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)\\
F_{145}\! \left(x , y_{0}\right) &= F_{144}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{146}\! \left(x , y_{0}\right) &= F_{147}\! \left(x , 1, y_{0}\right)\\
F_{147}\! \left(x , y_{0}, y_{1}\right) &= F_{148}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{148}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{149}\! \left(x , y_{0}, y_{1}\right)+F_{149}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{149}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{147}\! \left(x , y_{0}, y_{1}\right)+F_{150}\! \left(x , y_{0}, y_{1}\right)+F_{151}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{1}\right)\\
F_{150}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{149}\! \left(x , y_{0}, y_{1}\right)\\
F_{151}\! \left(x , y_{0}, y_{1}\right) &= F_{152}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{152}\! \left(x , y_{0}, y_{1}\right) &= F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{73}\! \left(x , y_{1}\right)\\
F_{153}\! \left(x , y_{0}, y_{1}\right) &= F_{154}\! \left(x , y_{0}\right)+F_{161}\! \left(x , y_{0}, y_{1}\right)\\
F_{154}\! \left(x , y_{0}\right) &= F_{155}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)\\
F_{155}\! \left(x , y_{0}\right) &= F_{156}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{156}\! \left(x , y_{0}\right) &= F_{157}\! \left(x , y_{0}\right)+F_{159}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)+F_{88}\! \left(x , y_{0}\right)\\
F_{157}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{158}\! \left(x , y_{0}\right)\\
F_{158}\! \left(x , y_{0}\right) &= F_{156}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)\\
F_{159}\! \left(x , y_{0}\right) &= F_{160}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{160}\! \left(x , y_{0}\right) &= F_{156}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{161}\! \left(x , y_{0}, y_{1}\right) &= F_{162}\! \left(x , y_{0}, y_{1}\right)+F_{167}\! \left(x , y_{0}, y_{1}\right)\\
F_{162}\! \left(x , y_{0}, y_{1}\right) &= F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)\\
F_{163}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{27}\! \left(x \right)+F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{166}\! \left(x , y_{0}, y_{1}\right)\\
F_{164}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{165}\! \left(x , y_{0}, y_{1}\right)\\
F_{165}\! \left(x , y_{0}, y_{1}\right) &= F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{166}\! \left(x , y_{0}, y_{1}\right) &= F_{162}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{167}\! \left(x , y_{0}, y_{1}\right) &= F_{168}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)\\
F_{168}\! \left(x , y_{0}, y_{1}\right) &= F_{169}\! \left(x , y_{0}, y_{1}\right)\\
F_{169}\! \left(x , y_{0}, y_{1}\right) &= F_{170}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{170}\! \left(x , y_{0}, y_{1}\right) &= F_{168}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)\\
F_{171}\! \left(x , y_{0}, y_{1}\right) &= 3 F_{27}\! \left(x \right)+F_{172}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \left(x , y_{0}, y_{1}\right)\\
F_{172}\! \left(x , y_{0}, y_{1}\right) &= F_{173}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{173}\! \left(x , y_{0}, y_{1}\right) &= F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)\\
F_{174}\! \left(x , y_{0}, y_{1}\right) &= F_{175}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{175}\! \left(x , y_{0}, y_{1}\right) &= F_{176}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \left(x , y_{0}, y_{1}\right)\\
F_{176}\! \left(x , y_{0}, y_{1}\right) &= F_{177}\! \left(x , y_{0}, y_{1}\right)\\
F_{177}\! \left(x , y_{0}, y_{1}\right) &= F_{178}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{178}\! \left(x , y_{0}, y_{1}\right) &= F_{176}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}, y_{1}\right)\\
F_{179}\! \left(x , y_{0}, y_{1}\right) &= 3 F_{27}\! \left(x \right)+F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{180}\! \left(x , y_{0}, y_{1}\right)\\
F_{180}\! \left(x , y_{0}, y_{1}\right) &= F_{181}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{181}\! \left(x , y_{0}, y_{1}\right) &= F_{163}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \left(x , y_{0}, y_{1}\right)\\
F_{182}\! \left(x , y_{0}\right) &= F_{183}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{183}\! \left(x , y_{0}\right) &= F_{184}\! \left(x , y_{0}\right)+F_{73}\! \left(x , y_{0}\right)\\
F_{184}\! \left(x , y_{0}\right) &= F_{185}\! \left(x \right)+F_{200}\! \left(x , y_{0}\right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{190}\! \left(x \right)+F_{192}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{197}\! \left(x \right) &= 2 F_{27}\! \left(x \right)+F_{192}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{200}\! \left(x , y_{0}\right) &= F_{201}\! \left(x , y_{0}\right)+F_{97}\! \left(x , y_{0}\right)\\
F_{201}\! \left(x , y_{0}\right) &= F_{202}\! \left(x , y_{0}\right)+F_{205}\! \left(x , y_{0}\right)\\
F_{202}\! \left(x , y_{0}\right) &= F_{203}\! \left(x , y_{0}\right)\\
F_{203}\! \left(x , y_{0}\right) &= F_{204}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{204}\! \left(x , y_{0}\right) &= F_{202}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{205}\! \left(x , y_{0}\right) &= 3 F_{27}\! \left(x \right)+F_{206}\! \left(x , y_{0}\right)+F_{208}\! \left(x , y_{0}\right)\\
F_{206}\! \left(x , y_{0}\right) &= F_{207}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{207}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{205}\! \left(x , y_{0}\right)\\
F_{208}\! \left(x , y_{0}\right) &= F_{209}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{209}\! \left(x , y_{0}\right) &= F_{210}\! \left(x , y_{0}\right)+F_{213}\! \left(x , y_{0}\right)\\
F_{210}\! \left(x , y_{0}\right) &= F_{211}\! \left(x , y_{0}\right)\\
F_{211}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{212}\! \left(x , y_{0}\right)\\
F_{212}\! \left(x , y_{0}\right) &= F_{210}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{213}\! \left(x , y_{0}\right) &= 3 F_{27}\! \left(x \right)+F_{208}\! \left(x , y_{0}\right)+F_{214}\! \left(x , y_{0}\right)\\
F_{214}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{215}\! \left(x , y_{0}\right)\\
F_{215}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{213}\! \left(x , y_{0}\right)\\
F_{216}\! \left(x , y_{0}\right) &= F_{217}\! \left(x , 1, y_{0}\right)\\
F_{217}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{1}\right)\\
F_{218}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{219}\! \left(x , y_{0}\right)\\
F_{219}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{220}\! \left(x , y_{0}\right)+F_{222}\! \left(x , y_{0}\right)+F_{226}\! \left(x , y_{0}\right)+F_{227}\! \left(x , y_{0}\right)\\
F_{220}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{221}\! \left(x , y_{0}\right)\\
F_{221}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{219}\! \left(x , y_{0}\right)+F_{219}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{222}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{223}\! \left(x , y_{0}\right)\\
F_{223}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{142}\! \left(x , y_{0}\right)+F_{222}\! \left(x , y_{0}\right)+F_{224}\! \left(x , y_{0}\right)\\
F_{224}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{225}\! \left(x , y_{0}\right)\\
F_{225}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{223}\! \left(x , y_{0}\right)+F_{223}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{226}\! \left(x , y_{0}\right) &= F_{183}\! \left(x , y_{0}\right) F_{21}\! \left(x \right)\\
F_{227}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{228}\! \left(x , y_{0}\right)\\
F_{228}\! \left(x , y_{0}\right) &= F_{148}\! \left(x , 1, y_{0}\right)\\
F_{229}\! \left(x \right) &= F_{21}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{231}\! \left(x \right)+F_{232}\! \left(x \right)+F_{369}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{21}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{21}\! \left(x \right) F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x , 1\right)\\
F_{234}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{231}\! \left(x \right)+F_{235}\! \left(x , y_{0}\right)+F_{363}\! \left(x , y_{0}\right)+F_{366}\! \left(x , y_{0}\right)\\
F_{235}\! \left(x , y_{0}\right) &= F_{236}\! \left(x , y_{0}, 1\right)\\
F_{236}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{237}\! \left(x , y_{0}, y_{1}\right)\\
F_{237}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{238}\! \left(x , y_{0}\right)+F_{284}\! \left(x , y_{0}, y_{1}\right)+F_{286}\! \left(x , y_{0}, y_{1}\right)+F_{353}\! \left(x , y_{0}, y_{1}\right)\\
F_{238}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{239}\! \left(x , y_{0}\right)\\
F_{239}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{238}\! \left(x , y_{0}\right)+F_{240}\! \left(x , y_{0}\right)+F_{259}\! \left(x , y_{0}\right)\\
F_{240}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{241}\! \left(x , y_{0}\right)\\
F_{241}\! \left(x , y_{0}\right) &= F_{242}\! \left(x , y_{0}\right)+F_{74}\! \left(x \right)\\
F_{242}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right)+F_{243}\! \left(x , y_{0}\right)\\
F_{243}\! \left(x , y_{0}\right) &= F_{244}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{244}\! \left(x , y_{0}\right) &= F_{245}\! \left(x , y_{0}\right)+F_{247}\! \left(x , y_{0}\right)+F_{249}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)\\
F_{245}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{246}\! \left(x , y_{0}\right)\\
F_{246}\! \left(x , y_{0}\right) &= F_{244}\! \left(x , y_{0}\right)+F_{76}\! \left(x \right)\\
F_{247}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{248}\! \left(x , y_{0}\right)\\
F_{248}\! \left(x , y_{0}\right) &= F_{244}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{249}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{250}\! \left(x , y_{0}\right)\\
F_{250}\! \left(x , y_{0}\right) &= F_{251}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{251}\! \left(x , y_{0}\right) &= F_{249}\! \left(x , y_{0}\right)+F_{252}\! \left(x , y_{0}\right)+F_{257}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)\\
F_{252}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{253}\! \left(x , y_{0}\right)\\
F_{253}\! \left(x , y_{0}\right) &= F_{194}\! \left(x \right)+F_{254}\! \left(x , y_{0}\right)\\
F_{254}\! \left(x , y_{0}\right) &= 2 F_{27}\! \left(x \right)+F_{252}\! \left(x , y_{0}\right)+F_{255}\! \left(x , y_{0}\right)\\
F_{255}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{256}\! \left(x , y_{0}\right)\\
F_{256}\! \left(x , y_{0}\right) &= F_{254}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{257}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{258}\! \left(x , y_{0}\right)\\
F_{258}\! \left(x , y_{0}\right) &= F_{251}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{259}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{260}\! \left(x , y_{0}\right)\\
F_{260}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{261}\! \left(x , y_{0}\right)+F_{262}\! \left(x , y_{0}\right)+F_{263}\! \left(x , y_{0}\right)+F_{264}\! \left(x , y_{0}\right)\\
F_{261}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{260}\! \left(x , y_{0}\right)\\
F_{262}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{260}\! \left(x , y_{0}\right)\\
F_{263}\! \left(x , y_{0}\right) &= F_{147}\! \left(x , y_{0}, 1\right)\\
F_{264}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{265}\! \left(x , y_{0}\right)\\
F_{265}\! \left(x , y_{0}\right) &= F_{266}\! \left(x \right)+F_{268}\! \left(x , y_{0}\right)\\
F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{268}\! \left(x , y_{0}\right) &= F_{154}\! \left(x , y_{0}\right)+F_{269}\! \left(x , y_{0}\right)\\
F_{269}\! \left(x , y_{0}\right) &= F_{155}\! \left(x , y_{0}\right)+F_{270}\! \left(x , y_{0}\right)\\
F_{270}\! \left(x , y_{0}\right) &= F_{254}\! \left(x , y_{0}\right)+F_{271}\! \left(x , y_{0}\right)\\
F_{271}\! \left(x , y_{0}\right) &= 2 F_{27}\! \left(x \right)+F_{272}\! \left(x , y_{0}\right)+F_{274}\! \left(x , y_{0}\right)+F_{276}\! \left(x , y_{0}\right)\\
F_{272}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{273}\! \left(x , y_{0}\right)\\
F_{273}\! \left(x , y_{0}\right) &= F_{197}\! \left(x \right)+F_{271}\! \left(x , y_{0}\right)\\
F_{274}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{275}\! \left(x , y_{0}\right)\\
F_{275}\! \left(x , y_{0}\right) &= F_{156}\! \left(x , y_{0}\right)+F_{271}\! \left(x , y_{0}\right)\\
F_{276}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{277}\! \left(x , y_{0}\right)\\
F_{277}\! \left(x , y_{0}\right) &= F_{278}\! \left(x , y_{0}\right)+F_{281}\! \left(x , y_{0}\right)\\
F_{278}\! \left(x , y_{0}\right) &= F_{279}\! \left(x , y_{0}\right)\\
F_{279}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{280}\! \left(x , y_{0}\right)\\
F_{280}\! \left(x , y_{0}\right) &= F_{278}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)\\
F_{281}\! \left(x , y_{0}\right) &= 3 F_{27}\! \left(x \right)+F_{276}\! \left(x , y_{0}\right)+F_{282}\! \left(x , y_{0}\right)\\
F_{282}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{283}\! \left(x , y_{0}\right)\\
F_{283}\! \left(x , y_{0}\right) &= F_{281}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)\\
F_{284}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{285}\! \left(x , y_{0}, y_{1}\right)\\
F_{285}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{239}\! \left(x , y_{0}\right)-y_{1} F_{239}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}\\
F_{286}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{287}\! \left(x , y_{0}, y_{1}\right)\\
F_{287}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{288}\! \left(x , y_{0}\right)-y_{1} F_{288}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}\\
F_{288}\! \left(x , y_{0}\right) &= F_{289}\! \left(x , y_{0}, 1\right)\\
F_{289}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{290}\! \left(x , y_{0}, y_{1}\right)+F_{291}\! \left(x , y_{0}, y_{1}\right)+F_{293}\! \left(x , y_{0}, y_{1}\right)+F_{312}\! \left(x , y_{0}, y_{1}\right)\\
F_{290}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{289}\! \left(x , y_{0}, y_{1}\right)\\
F_{291}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{292}\! \left(x , y_{0}, y_{1}\right)\\
F_{292}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{289}\! \left(x , y_{0}, y_{1}\right)+F_{289}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{293}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{294}\! \left(x , y_{0}, y_{1}\right)\\
F_{294}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{295}\! \left(x , y_{0}, y_{1}\right)+F_{295}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{295}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{296}\! \left(x , y_{0}, y_{1}\right)+F_{297}\! \left(x , y_{0}, y_{1}\right)+F_{298}\! \left(x , y_{0}, y_{1}\right)\\
F_{296}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{295}\! \left(x , y_{0}, y_{1}\right)\\
F_{297}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{295}\! \left(x , y_{0}, y_{1}\right)\\
F_{298}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{299}\! \left(x , y_{0}, y_{1}\right)\\
F_{299}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{300}\! \left(x , y_{0}, y_{1}\right)+F_{300}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{300}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{301}\! \left(x , y_{0}, y_{1}\right)+F_{302}\! \left(x , y_{0}, y_{1}\right)+F_{311}\! \left(x , y_{0}, y_{1}\right)\\
F_{301}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{300}\! \left(x , y_{0}, y_{1}\right)\\
F_{302}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{303}\! \left(x , y_{0}, y_{1}\right)\\
F_{303}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{1}\right)+F_{304}\! \left(x , y_{0}, y_{1}\right)\\
F_{304}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}\right)+F_{305}\! \left(x , y_{0}, y_{1}\right)\\
F_{305}\! \left(x , y_{0}, y_{1}\right) &= F_{306}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)\\
F_{306}\! \left(x , y_{0}, y_{1}\right) &= F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \right)+F_{307}\! \left(x , y_{0}, y_{1}\right)+F_{309}\! \left(x , y_{0}, y_{1}\right)\\
F_{307}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{308}\! \left(x , y_{0}, y_{1}\right)\\
F_{308}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{1}\right)+F_{306}\! \left(x , y_{0}, y_{1}\right)\\
F_{309}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{310}\! \left(x , y_{0}, y_{1}\right)\\
F_{310}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}\right)+F_{306}\! \left(x , y_{0}, y_{1}\right)\\
F_{311}\! \left(x , y_{0}, y_{1}\right) &= F_{149}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x \right)\\
F_{312}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{313}\! \left(x , y_{0}, y_{1}\right)\\
F_{313}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{314}\! \left(x , y_{0}, y_{1}\right)+F_{314}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{314}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{315}\! \left(x , y_{0}, y_{1}\right)+F_{317}\! \left(x , y_{0}, y_{1}\right)+F_{319}\! \left(x , y_{0}, y_{1}\right)+F_{351}\! \left(x , y_{0}, y_{1}\right)\\
F_{315}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{316}\! \left(x , y_{0}, y_{1}\right)\\
F_{316}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{300}\! \left(x , y_{0}, y_{1}\right)+F_{300}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{317}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{318}\! \left(x , y_{0}, y_{1}\right)\\
F_{318}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{314}\! \left(x , y_{0}, y_{1}\right)+F_{314}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{319}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{320}\! \left(x , y_{0}, y_{1}\right)\\
F_{320}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{319}\! \left(x , y_{0}, y_{1}\right)+F_{321}\! \left(x , y_{0}, y_{1}\right)+F_{344}\! \left(x , y_{0}, y_{1}\right)+F_{346}\! \left(x , y_{0}, y_{1}\right)\\
F_{321}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{322}\! \left(x , y_{0}, y_{1}\right)\\
F_{322}\! \left(x , y_{0}, y_{1}\right) &= F_{323}\! \left(x , y_{0}, y_{1}\right)+F_{95}\! \left(x , y_{1}\right)\\
F_{323}\! \left(x , y_{0}, y_{1}\right) &= F_{304}\! \left(x , y_{0}, y_{1}\right)+F_{324}\! \left(x , y_{0}, y_{1}\right)\\
F_{324}\! \left(x , y_{0}, y_{1}\right) &= F_{155}\! \left(x , y_{0}\right)+F_{325}\! \left(x , y_{0}, y_{1}\right)\\
F_{325}\! \left(x , y_{0}, y_{1}\right) &= F_{326}\! \left(x , y_{0}, y_{1}\right)+F_{331}\! \left(x , y_{0}, y_{1}\right)\\
F_{326}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{27}\! \left(x \right)+F_{327}\! \left(x , y_{0}, y_{1}\right)+F_{329}\! \left(x , y_{0}, y_{1}\right)\\
F_{327}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{328}\! \left(x , y_{0}, y_{1}\right)\\
F_{328}\! \left(x , y_{0}, y_{1}\right) &= F_{326}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{1}\right)\\
F_{329}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{330}\! \left(x , y_{0}, y_{1}\right)\\
F_{330}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}\right)+F_{326}\! \left(x , y_{0}, y_{1}\right)\\
F_{331}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{27}\! \left(x \right)+F_{332}\! \left(x , y_{0}, y_{1}\right)+F_{334}\! \left(x , y_{0}, y_{1}\right)+F_{336}\! \left(x , y_{0}, y_{1}\right)\\
F_{332}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{333}\! \left(x , y_{0}, y_{1}\right)\\
F_{333}\! \left(x , y_{0}, y_{1}\right) &= F_{101}\! \left(x , y_{1}\right)+F_{331}\! \left(x , y_{0}, y_{1}\right)\\
F_{334}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{335}\! \left(x , y_{0}, y_{1}\right)\\
F_{335}\! \left(x , y_{0}, y_{1}\right) &= F_{156}\! \left(x , y_{0}\right)+F_{331}\! \left(x , y_{0}, y_{1}\right)\\
F_{336}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{337}\! \left(x , y_{0}, y_{1}\right)\\
F_{337}\! \left(x , y_{0}, y_{1}\right) &= F_{338}\! \left(x , y_{0}, y_{1}\right)+F_{341}\! \left(x , y_{0}, y_{1}\right)\\
F_{338}\! \left(x , y_{0}, y_{1}\right) &= F_{339}\! \left(x , y_{0}, y_{1}\right)\\
F_{339}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{340}\! \left(x , y_{0}, y_{1}\right)\\
F_{340}\! \left(x , y_{0}, y_{1}\right) &= F_{338}\! \left(x , y_{0}, y_{1}\right)+F_{82}\! \left(x , y_{0}\right)\\
F_{341}\! \left(x , y_{0}, y_{1}\right) &= 3 F_{27}\! \left(x \right)+F_{336}\! \left(x , y_{0}, y_{1}\right)+F_{342}\! \left(x , y_{0}, y_{1}\right)\\
F_{342}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{343}\! \left(x , y_{0}, y_{1}\right)\\
F_{343}\! \left(x , y_{0}, y_{1}\right) &= F_{341}\! \left(x , y_{0}, y_{1}\right)+F_{85}\! \left(x , y_{0}\right)\\
F_{344}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{345}\! \left(x , y_{0}, y_{1}\right)\\
F_{345}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{320}\! \left(x , y_{0}, y_{1}\right)+F_{320}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{346}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{347}\! \left(x , y_{0}, y_{1}\right)\\
F_{347}\! \left(x , y_{0}, y_{1}\right) &= F_{348}\! \left(x , y_{0}, y_{1}\right)+F_{95}\! \left(x , y_{1}\right)\\
F_{348}\! \left(x , y_{0}, y_{1}\right) &= F_{349}\! \left(x , y_{0}, y_{1}\right)+F_{350}\! \left(x , y_{0}, y_{1}\right)\\
F_{349}\! \left(x , y_{0}, y_{1}\right) &= F_{162}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{0}\right)\\
F_{350}\! \left(x , y_{0}, y_{1}\right) &= F_{337}\! \left(x , y_{0}, y_{1}\right)+F_{81}\! \left(x , y_{0}\right)\\
F_{351}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{352}\! \left(x , y_{0}, y_{1}\right)\\
F_{352}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{149}\! \left(x , y_{0}, y_{1}\right)+F_{149}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{353}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x \right) F_{354}\! \left(x , y_{0}, y_{1}\right)\\
F_{354}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{355}\! \left(x , y_{0}\right)-y_{1} F_{355}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}\\
F_{355}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{356}\! \left(x , y_{0}\right)+F_{357}\! \left(x , y_{0}\right)+F_{359}\! \left(x , y_{0}\right)+F_{361}\! \left(x , y_{0}\right)\\
F_{356}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{355}\! \left(x , y_{0}\right)\\
F_{357}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{358}\! \left(x , y_{0}\right)\\
F_{358}\! \left(x , y_{0}\right) &= F_{354}\! \left(x , y_{0}, 1\right)\\
F_{359}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{360}\! \left(x , y_{0}\right)\\
F_{360}\! \left(x , y_{0}\right) &= F_{352}\! \left(x , y_{0}, 1\right)\\
F_{361}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{362}\! \left(x , y_{0}\right)\\
F_{362}\! \left(x , y_{0}\right) &= F_{320}\! \left(x , y_{0}, 1\right)\\
F_{363}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{364}\! \left(x , y_{0}\right)\\
F_{364}\! \left(x , y_{0}\right) &= F_{365}\! \left(x , y_{0}, 1\right)\\
F_{365}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{237}\! \left(x , y_{0}, y_{1}\right)+F_{237}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{366}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{367}\! \left(x , y_{0}\right)\\
F_{367}\! \left(x , y_{0}\right) &= F_{368}\! \left(x , y_{0}, 1\right)\\
F_{368}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{314}\! \left(x , y_{0}, y_{1}\right)+F_{314}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{369}\! \left(x \right) &= F_{370}\! \left(x , 1\right)\\
F_{370}\! \left(x , y_{0}\right) &= F_{21}\! \left(x \right) F_{371}\! \left(x , y_{0}\right)\\
F_{371}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{372}\! \left(x , y_{0}\right)+F_{374}\! \left(x , y_{0}\right)+F_{375}\! \left(x , y_{0}\right)+F_{376}\! \left(x , y_{0}\right)\\
F_{372}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{373}\! \left(x , y_{0}\right)\\
F_{373}\! \left(x , y_{0}\right) &= F_{299}\! \left(x , y_{0}, 1\right)\\
F_{374}\! \left(x , y_{0}\right) &= F_{317}\! \left(x , y_{0}, 1\right)\\
F_{375}\! \left(x , y_{0}\right) &= F_{319}\! \left(x , y_{0}, 1\right)\\
F_{376}\! \left(x , y_{0}\right) &= F_{351}\! \left(x , y_{0}, 1\right)\\
\end{align*}\)
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion Req Corrob Expand Verified" and has 309 rules.
Found on January 27, 2022.Finding the specification took 10847 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_{5}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{8}\! \left(x , y\right)+F_{84}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{17}\! \left(x , y\right)\\
F_{14}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{14}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= y x\\
F_{21}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x \right)+F_{31}\! \left(x , y\right)\\
F_{25}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{27}\! \left(x \right) &= 0\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{25}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{32}\! \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_{34}\! \left(x , y\right) &= F_{15}\! \left(x \right)+F_{32}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{25}\! \left(x \right)+F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{27}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{42}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{40}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{15}\! \left(x \right)+F_{40}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= 2 F_{27}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{47}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x \right)+F_{63}\! \left(x , y\right)\\
F_{50}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{5}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{5}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{5}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{59}\! \left(x \right) &= 2 F_{27}\! \left(x \right)+F_{54}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{5}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{5}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= 2 F_{27}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{26}\! \left(x \right)+F_{64}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= 3 F_{27}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{63}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}\\
F_{75}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{76}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{75}\! \left(x , y\right)+F_{77}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)+F_{68}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{82}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= -\frac{-y F_{76}\! \left(x , y\right)+F_{76}\! \left(x , 1\right)}{-1+y}\\
F_{83}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}\\
F_{90}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{92}\! \left(x \right) &= F_{5}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x , 1\right)\\
F_{94}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{306}\! \left(x , y\right)+F_{308}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{96}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{97}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{99}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= -\frac{-y F_{100}\! \left(x , y\right)+F_{100}\! \left(x , 1\right)}{-1+y}\\
F_{100}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{128}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{26}\! \left(x \right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{27}\! \left(x \right)\\
F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{108}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{40}\! \left(x , y\right)\\
F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{114}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{113}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= 2 F_{27}\! \left(x \right)+F_{109}\! \left(x , y\right)+F_{115}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{116}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{40}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{105}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{118}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{119}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{120}\! \left(x , y\right)\\
F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{122}\! \left(x , y\right) &= -\frac{-y F_{123}\! \left(x , y\right)+F_{123}\! \left(x , 1\right)}{-1+y}\\
F_{124}\! \left(x , y\right) &= -\frac{-y F_{123}\! \left(x , y\right)+F_{123}\! \left(x , 1\right)}{-1+y}\\
F_{125}\! \left(x , y\right) &= F_{124}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{125}\! \left(x , y\right) &= F_{126}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{126}\! \left(x , y\right)+F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{100}\! \left(x , 1\right)\\
F_{128}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{129}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{96}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{131}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)+F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)\\
F_{132}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{133}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)\\
F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{305}\! \left(x , y\right)\\
F_{138}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{299}\! \left(x , y\right)\\
F_{139}\! \left(x , y\right) &= F_{138}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{140}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)+F_{238}\! \left(x , y\right)\\
F_{140}\! \left(x , y\right) &= F_{141}\! \left(x , y\right)+F_{236}\! \left(x , y\right)\\
F_{141}\! \left(x , y\right) &= F_{142}\! \left(x \right)+F_{143}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{235}\! \left(x , y\right)\\
F_{142}\! \left(x \right) &= F_{14} \left(x \right)^{2}\\
F_{143}\! \left(x , y\right) &= F_{141}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{145}\! \left(x , y\right) &= F_{142}\! \left(x \right)+F_{144}\! \left(x , y\right)+F_{227}\! \left(x , y\right)+F_{228}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)+F_{225}\! \left(x \right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{217}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{148}\! \left(x , y\right)+F_{180}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)+F_{177}\! \left(x \right)\\
F_{149}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{150}\! \left(x \right)+F_{152}\! \left(x , y\right)+F_{174}\! \left(x , y\right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{153}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{154}\! \left(x , y\right)+F_{155}\! \left(x , y\right)+F_{172}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\
F_{154}\! \left(x , y\right) &= F_{153}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{156}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\
F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)+F_{164}\! \left(x , y\right)\\
F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right)+F_{160}\! \left(x , y\right)\\
F_{159}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{15}\! \left(x \right)\\
F_{160}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)+F_{56}\! \left(x \right)\\
F_{161}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{163}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{26}\! \left(x \right)\\
F_{166}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)+F_{59}\! \left(x \right)\\
F_{167}\! \left(x , y\right) &= 3 F_{27}\! \left(x \right)+F_{168}\! \left(x , y\right)+F_{170}\! \left(x , y\right)\\
F_{168}\! \left(x , y\right) &= F_{169}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{169}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{170}\! \left(x , y\right) &= F_{171}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{171}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)+F_{167}\! \left(x , y\right)\\
F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{173}\! \left(x , y\right) &= -\frac{-y F_{153}\! \left(x , y\right)+F_{153}\! \left(x , 1\right)}{-1+y}\\
F_{174}\! \left(x , y\right) &= F_{175}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{175}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{176}\! \left(x , y\right)\\
F_{176}\! \left(x , y\right) &= F_{159}\! \left(x , y\right)+F_{165}\! \left(x , y\right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x , 1\right)\\
F_{179}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{180}\! \left(x , y\right) &= F_{181}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{181}\! \left(x , y\right) &= F_{182}\! \left(x , y\right)+F_{211}\! \left(x \right)\\
F_{182}\! \left(x , y\right) &= F_{183}\! \left(x , y\right)+F_{194}\! \left(x , y\right)\\
F_{183}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{184}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{193}\! \left(x , y\right)\\
F_{184}\! \left(x , y\right) &= F_{185}\! \left(x , y\right)\\
F_{185}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{186}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{186}\! \left(x , y\right) &= -\frac{-y F_{187}\! \left(x , y\right)+F_{187}\! \left(x , 1\right)}{-1+y}\\
F_{187}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{188}\! \left(x , y\right)+F_{190}\! \left(x , y\right)\\
F_{188}\! \left(x , y\right) &= F_{189}\! \left(x , y\right)\\
F_{189}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{187}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{190}\! \left(x , y\right) &= F_{187}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{191}\! \left(x , y\right) &= F_{192}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{192}\! \left(x , y\right) &= -\frac{-y F_{183}\! \left(x , y\right)+F_{183}\! \left(x , 1\right)}{-1+y}\\
F_{193}\! \left(x , y\right) &= F_{183}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{194}\! \left(x , y\right) &= F_{195}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{195}\! \left(x , y\right) &= F_{183}\! \left(x , y\right)+F_{196}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{209}\! \left(x , y\right)\\
F_{196}\! \left(x , y\right) &= F_{195}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{197}\! \left(x , y\right) &= F_{198}\! \left(x , y\right)\\
F_{198}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{199}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{199}\! \left(x , y\right) &= -\frac{-y F_{200}\! \left(x , y\right)+F_{200}\! \left(x , 1\right)}{-1+y}\\
F_{200}\! \left(x , y\right) &= F_{187}\! \left(x , y\right)+F_{201}\! \left(x , y\right)+F_{202}\! \left(x , y\right)\\
F_{201}\! \left(x , y\right) &= F_{200}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{202}\! \left(x , y\right) &= F_{203}\! \left(x , y\right)\\
F_{203}\! \left(x , y\right) &= F_{187}\! \left(x , y\right) F_{204}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{205}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{151}\! \left(x \right) F_{204}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{209}\! \left(x , y\right) &= F_{210}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{210}\! \left(x , y\right) &= -\frac{-y F_{195}\! \left(x , y\right)+F_{195}\! \left(x , 1\right)}{-1+y}\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x , 1\right)\\
F_{214}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{215}\! \left(x , y\right)\\
F_{215}\! \left(x , y\right) &= F_{216}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{216}\! \left(x , y\right) &= -\frac{-y F_{214}\! \left(x , y\right)+F_{214}\! \left(x , 1\right)}{-1+y}\\
F_{217}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{218}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{218}\! \left(x , y\right) &= F_{219}\! \left(x , y\right)+F_{220}\! \left(x \right)\\
F_{219}\! \left(x , y\right) &= F_{187}\! \left(x , y\right)+F_{201}\! \left(x , y\right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{224}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{123}\! \left(x , 1\right)\\
F_{224}\! \left(x \right) &= F_{213}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{14}\! \left(x \right) F_{222}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{227}\! \left(x , y\right) &= F_{145}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{228}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{229}\! \left(x , y\right)\\
F_{229}\! \left(x , y\right) &= F_{142}\! \left(x \right)+F_{228}\! \left(x , y\right)+F_{230}\! \left(x , y\right)\\
F_{230}\! \left(x , y\right) &= F_{231}\! \left(x , y\right)\\
F_{231}\! \left(x , y\right) &= F_{232}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{232}\! \left(x , y\right) &= F_{233}\! \left(x , y\right)+F_{234}\! \left(x , y\right)\\
F_{233}\! \left(x , y\right) &= -\frac{-y F_{229}\! \left(x , y\right)+F_{229}\! \left(x , 1\right)}{-1+y}\\
F_{234}\! \left(x , y\right) &= F_{14} \left(x \right)^{2} F_{187}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{235}\! \left(x , y\right) &= F_{141}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{236}\! \left(x , y\right) &= F_{237}\! \left(x , y\right)\\
F_{237}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{214}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{140}\! \left(x , y\right) &= F_{238}\! \left(x , y\right)+F_{239}\! \left(x , y\right)\\
F_{239}\! \left(x , y\right) &= F_{240}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{240}\! \left(x , y\right) &= F_{241}\! \left(x , y\right)+F_{252}\! \left(x , y\right)\\
F_{241}\! \left(x , y\right) &= F_{242}\! \left(x , y\right)+F_{250}\! \left(x , y\right)\\
F_{242}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{243}\! \left(x , y\right)+F_{244}\! \left(x , y\right)+F_{247}\! \left(x , y\right)+F_{249}\! \left(x , y\right)\\
F_{243}\! \left(x , y\right) &= F_{242}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{244}\! \left(x , y\right) &= F_{245}\! \left(x , y\right)\\
F_{245}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{246}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{246}\! \left(x , y\right) &= -\frac{-y F_{219}\! \left(x , y\right)+F_{219}\! \left(x , 1\right)}{-1+y}\\
F_{247}\! \left(x , y\right) &= F_{248}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{248}\! \left(x , y\right) &= -\frac{-y F_{182}\! \left(x , y\right)+F_{182}\! \left(x , 1\right)}{-1+y}\\
F_{249}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{242}\! \left(x , y\right)\\
F_{250}\! \left(x , y\right) &= F_{251}\! \left(x , y\right)\\
F_{251}\! \left(x , y\right) &= F_{216}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{252}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{253}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{253}\! \left(x , y\right) &= F_{254}\! \left(x \right)+F_{265}\! \left(x , y\right)+F_{275}\! \left(x , y\right)+F_{277}\! \left(x , y\right)+F_{281}\! \left(x , y\right)\\
F_{254}\! \left(x \right) &= F_{14}\! \left(x \right) F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{258}\! \left(x \right)+F_{259}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{257}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{261}\! \left(x , 1\right)\\
F_{261}\! \left(x , y\right) &= -\frac{-y F_{262}\! \left(x , y\right)+F_{262}\! \left(x , 1\right)}{-1+y}\\
F_{262}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{263}\! \left(x , y\right)+F_{264}\! \left(x , y\right)\\
F_{263}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{262}\! \left(x , y\right)\\
F_{264}\! \left(x , y\right) &= F_{261}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{265}\! \left(x , y\right) &= F_{266}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{266}\! \left(x , y\right) &= -\frac{-y F_{267}\! \left(x , y\right)+F_{267}\! \left(x , 1\right)}{-1+y}\\
F_{267}\! \left(x , y\right) &= F_{268}\! \left(x , y\right)+F_{274}\! \left(x , y\right)\\
F_{268}\! \left(x , y\right) &= -\frac{-y F_{269}\! \left(x , y\right)+F_{269}\! \left(x , 1\right)}{-1+y}\\
F_{270}\! \left(x , y\right) &= F_{269}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{271}\! \left(x , y\right) &= F_{255}\! \left(x \right)+F_{270}\! \left(x , y\right)+F_{273}\! \left(x , y\right)\\
F_{271}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{272}\! \left(x , y\right)\\
F_{272}\! \left(x , y\right) &= F_{179}\! \left(x , y\right)\\
F_{273}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{271}\! \left(x , y\right)\\
F_{274}\! \left(x , y\right) &= F_{266}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{275}\! \left(x , y\right) &= F_{276}\! \left(x , y\right)\\
F_{276}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{253}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{277}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{278}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{278}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{279}\! \left(x , y\right)\\
F_{279}\! \left(x , y\right) &= F_{280}\! \left(x , y\right)\\
F_{280}\! \left(x , y\right) &= F_{122}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{281}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{282}\! \left(x , y\right)\\
F_{282}\! \left(x , y\right) &= F_{283}\! \left(x , y\right)+F_{291}\! \left(x , y\right)\\
F_{283}\! \left(x , y\right) &= F_{284}\! \left(x , y\right)+F_{289}\! \left(x , y\right)\\
F_{284}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{285}\! \left(x , y\right)+F_{286}\! \left(x , y\right)+F_{288}\! \left(x , y\right)\\
F_{285}\! \left(x , y\right) &= F_{284}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{286}\! \left(x , y\right) &= F_{287}\! \left(x , y\right)\\
F_{287}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{219}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{288}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{284}\! \left(x , y\right)\\
F_{289}\! \left(x , y\right) &= F_{290}\! \left(x , y\right)\\
F_{290}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{14}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{291}\! \left(x , y\right) &= F_{292}\! \left(x , y\right)\\
F_{292}\! \left(x , y\right) &= F_{103}\! \left(x , y\right) F_{293}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{293}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{294}\! \left(x \right)+F_{295}\! \left(x , y\right)+F_{297}\! \left(x , y\right)+F_{298}\! \left(x , y\right)\\
F_{294}\! \left(x \right) &= F_{206}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{295}\! \left(x , y\right) &= F_{296}\! \left(x , y\right)\\
F_{296}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{293}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{297}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{175}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{298}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{293}\! \left(x , y\right)\\
F_{299}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{300}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{301}\! \left(x , y\right) &= F_{300}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{302}\! \left(x , y\right) &= F_{278}\! \left(x , y\right)+F_{301}\! \left(x , y\right)\\
F_{302}\! \left(x , y\right) &= F_{284}\! \left(x , y\right)+F_{303}\! \left(x , y\right)\\
F_{303}\! \left(x , y\right) &= F_{304}\! \left(x , y\right)\\
F_{304}\! \left(x , y\right) &= F_{214}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{305}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{300}\! \left(x , y\right)\\
F_{306}\! \left(x , y\right) &= F_{307}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{307}\! \left(x , y\right) &= -\frac{-y F_{94}\! \left(x , y\right)+F_{94}\! \left(x , 1\right)}{-1+y}\\
F_{308}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{94}\! \left(x , y\right)\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion Req Corrob" and has 194 rules.
Found on April 24, 2021.Finding the specification took 43 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_{5}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{119}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{101}\! \left(x , y_{0}\right)+F_{117}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}, 1\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{100}\! \left(x , y_{1}, y_{0}\right)+F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{74}\! \left(x , y_{0}, y_{1}\right)+F_{76}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{1}, y_{0}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{1}, y_{0}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}\right) &= F_{24}\! \left(x \right)+F_{27}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{27}\! \left(x , y_{0}\right) &= F_{28}\! \left(x \right)+F_{29}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)\\
F_{28}\! \left(x \right) &= 0\\
F_{29}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{24}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{37}\! \left(x , y_{1}, y_{0}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{1}, y_{0}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{28}\! \left(x \right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{1}, y_{0}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{40}\! \left(x , y_{1}, y_{0}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{46}\! \left(x , y_{1}\right)+F_{64}\! \left(x , y_{0}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}\right) &= F_{47}\! \left(x \right)+F_{52}\! \left(x , y_{0}\right)\\
F_{47}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{5}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{52}\! \left(x , y_{0}\right) &= F_{28}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)\\
F_{53}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{54}\! \left(x , y_{0}\right)\\
F_{54}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)\\
F_{55}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{56}\! \left(x , y_{0}\right)\\
F_{56}\! \left(x , y_{0}\right) &= F_{57}\! \left(x , y_{0}\right)+F_{60}\! \left(x , y_{0}\right)\\
F_{57}\! \left(x , y_{0}\right) &= F_{58}\! \left(x , y_{0}\right)\\
F_{58}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{59}\! \left(x , y_{0}\right)\\
F_{59}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)+F_{57}\! \left(x , y_{0}\right)\\
F_{60}\! \left(x , y_{0}\right) &= 2 F_{28}\! \left(x \right)+F_{55}\! \left(x , y_{0}\right)+F_{61}\! \left(x , y_{0}\right)\\
F_{61}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{62}\! \left(x , y_{0}\right)\\
F_{62}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)+F_{60}\! \left(x , y_{0}\right)\\
F_{63}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{65}\! \left(x , y_{0}\right)+F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{65}\! \left(x , y_{0}\right) &= 2 F_{28}\! \left(x \right)+F_{66}\! \left(x , y_{0}\right)+F_{68}\! \left(x , y_{0}\right)\\
F_{66}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{67}\! \left(x , y_{0}\right)\\
F_{67}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)\\
F_{68}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)\\
F_{69}\! \left(x , y_{0}\right) &= F_{47}\! \left(x \right)+F_{65}\! \left(x , y_{0}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= 3 F_{28}\! \left(x \right)+F_{71}\! \left(x , y_{0}, y_{1}\right)+F_{73}\! \left(x , y_{1}, y_{0}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{5}\! \left(x \right) F_{72}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{73}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{64}\! \left(x , y_{1}, y_{0}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= F_{5}\! \left(x \right) F_{75}\! \left(x , y_{0}, y_{1}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{10}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{76}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right) F_{77}\! \left(x , y_{0}\right)\\
F_{77}\! \left(x , y_{0}\right) &= F_{78}\! \left(x , 1, y_{0}\right)\\
F_{78}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{79}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)+F_{99}\! \left(x , y_{1}, y_{0}\right)\\
F_{79}\! \left(x , y_{0}, y_{1}\right) &= F_{80}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{80}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}\right) F_{81}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{81}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{1}, y_{2}\right)+F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{83}\! \left(x , y_{0}, y_{2}\right)+F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{83}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{84}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x \right)+F_{85}\! \left(x , y_{0}, y_{1}\right)+F_{87}\! \left(x , y_{1}, y_{0}\right)\\
F_{85}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{86}\! \left(x , y_{0}, y_{1}\right)\\
F_{86}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{87}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{1}, y_{0}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{84}\! \left(x , y_{0}, y_{1}\right)+F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= 2 F_{28}\! \left(x \right)+F_{90}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{92}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{90}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}\right) F_{91}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{91}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{20}\! \left(x , y_{1}, y_{2}\right)+F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{92}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}\right) F_{88}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
F_{93}\! \left(x , y_{0}, y_{1}\right) &= F_{94}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{94}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}\right) F_{95}\! \left(x , y_{1}, y_{0}, y_{2}\right)\\
F_{95}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{96}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{96}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\
F_{96}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{97}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{80}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{94}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{98}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}\right) F_{97}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
F_{99}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{1}, y_{0}\right)\\
F_{100}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{101}\! \left(x , y_{0}\right) &= F_{102}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{102}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{101}\! \left(x , y_{0}\right)+F_{103}\! \left(x , y_{0}\right)+F_{115}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}\right) &= F_{104}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{104}\! \left(x , y_{0}\right) &= F_{105}\! \left(x , y_{0}\right)+F_{109}\! \left(x , y_{0}\right)\\
F_{105}\! \left(x , y_{0}\right) &= F_{106}\! \left(x , y_{0}\right)+F_{26}\! \left(x \right)\\
F_{106}\! \left(x , y_{0}\right) &= F_{107}\! \left(x , y_{0}\right)+F_{16}\! \left(x , y_{0}\right)\\
F_{107}\! \left(x , y_{0}\right) &= F_{108}\! \left(x , y_{0}\right)\\
F_{108}\! \left(x , y_{0}\right) &= F_{106}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{109}\! \left(x , y_{0}\right) &= F_{110}\! \left(x , y_{0}\right)+F_{51}\! \left(x \right)\\
F_{110}\! \left(x , y_{0}\right) &= F_{111}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)\\
F_{111}\! \left(x , y_{0}\right) &= 2 F_{28}\! \left(x \right)+F_{112}\! \left(x , y_{0}\right)+F_{114}\! \left(x , y_{0}\right)\\
F_{112}\! \left(x , y_{0}\right) &= F_{113}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{113}\! \left(x , y_{0}\right) &= F_{107}\! \left(x , y_{0}\right)+F_{111}\! \left(x , y_{0}\right)\\
F_{114}\! \left(x , y_{0}\right) &= F_{110}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{115}\! \left(x , y_{0}\right) &= F_{116}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{116}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{102}\! \left(x , y_{0}\right)+F_{102}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{117}\! \left(x , y_{0}\right) &= F_{118}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{118}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{7}\! \left(x , y_{0}\right)+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x , 1\right)\\
F_{121}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{122}\! \left(x , y_{0}\right)+F_{191}\! \left(x , y_{0}\right)+F_{193}\! \left(x , y_{0}\right)\\
F_{122}\! \left(x , y_{0}\right) &= F_{123}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{123}\! \left(x , y_{0}\right) &= F_{124}\! \left(x , 1, y_{0}\right)\\
F_{124}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{125}\! \left(x , y_{0}, y_{1}\right)+F_{127}\! \left(x , y_{0}, y_{1}\right)+F_{180}\! \left(x , y_{0}, y_{1}\right)+F_{182}\! \left(x , y_{0}, y_{1}\right)\\
F_{125}\! \left(x , y_{0}, y_{1}\right) &= F_{126}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{126}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{10}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{127}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{128}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{127}\! \left(x , y_{0}, y_{1}\right)+F_{129}\! \left(x , y_{0}, y_{1}\right)+F_{145}\! \left(x , y_{0}, y_{1}\right)+F_{147}\! \left(x , y_{0}, y_{1}\right)\\
F_{129}\! \left(x , y_{0}, y_{1}\right) &= F_{130}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{130}\! \left(x , y_{0}, y_{1}\right) &= F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{137}\! \left(x , y_{0}, y_{1}\right)\\
F_{131}\! \left(x , y_{0}, y_{1}\right) &= F_{132}\! \left(x , y_{1}\right)+F_{133}\! \left(x , y_{0}, y_{1}\right)\\
F_{132}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)\\
F_{133}\! \left(x , y_{0}, y_{1}\right) &= F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)\\
F_{134}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}\right)+F_{135}\! \left(x , y_{0}, y_{1}\right)\\
F_{135}\! \left(x , y_{0}, y_{1}\right) &= F_{136}\! \left(x , y_{1}, y_{0}\right)\\
F_{136}\! \left(x , y_{0}, y_{1}\right) &= F_{134}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{137}\! \left(x , y_{0}, y_{1}\right) &= F_{138}\! \left(x , y_{1}\right)+F_{139}\! \left(x , y_{0}, y_{1}\right)\\
F_{138}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)\\
F_{139}\! \left(x , y_{0}, y_{1}\right) &= F_{140}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{140}\! \left(x , y_{0}, y_{1}\right) &= F_{111}\! \left(x , y_{0}\right)+F_{141}\! \left(x , y_{0}, y_{1}\right)\\
F_{141}\! \left(x , y_{0}, y_{1}\right) &= 3 F_{28}\! \left(x \right)+F_{142}\! \left(x , y_{0}, y_{1}\right)+F_{144}\! \left(x , y_{1}, y_{0}\right)\\
F_{142}\! \left(x , y_{0}, y_{1}\right) &= F_{143}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{143}\! \left(x , y_{0}, y_{1}\right) &= F_{135}\! \left(x , y_{0}, y_{1}\right)+F_{141}\! \left(x , y_{0}, y_{1}\right)\\
F_{144}\! \left(x , y_{0}, y_{1}\right) &= F_{140}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{145}\! \left(x , y_{0}, y_{1}\right) &= F_{146}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{146}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{128}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{147}\! \left(x , y_{0}, y_{1}\right) &= F_{148}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{1}\right)\\
F_{148}\! \left(x , y_{0}, y_{1}\right) &= F_{149}\! \left(x , y_{0}, y_{1}\right)+F_{157}\! \left(x , y_{0}, y_{1}\right)\\
F_{149}\! \left(x , y_{0}, y_{1}\right) &= F_{150}\! \left(x , y_{1}\right)+F_{151}\! \left(x , y_{0}, y_{1}\right)\\
F_{150}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)\\
F_{151}\! \left(x , y_{0}, y_{1}\right) &= F_{152}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{0}, y_{1}\right)\\
F_{152}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}\right)+F_{153}\! \left(x , y_{0}, y_{1}\right)\\
F_{153}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{28}\! \left(x \right)+F_{154}\! \left(x , y_{0}, y_{1}\right)+F_{156}\! \left(x , y_{1}, y_{0}\right)\\
F_{154}\! \left(x , y_{0}, y_{1}\right) &= F_{155}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{155}\! \left(x , y_{0}, y_{1}\right) &= F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{156}\! \left(x , y_{0}, y_{1}\right) &= F_{152}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{157}\! \left(x , y_{0}, y_{1}\right) &= F_{158}\! \left(x , y_{1}\right)+F_{159}\! \left(x , y_{0}, y_{1}\right)\\
F_{158}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)\\
F_{159}\! \left(x , y_{0}, y_{1}\right) &= F_{160}\! \left(x , y_{0}, y_{1}\right)+F_{170}\! \left(x , y_{0}, y_{1}\right)\\
F_{160}\! \left(x , y_{0}, y_{1}\right) &= F_{161}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}\right)\\
F_{161}\! \left(x , y_{0}, y_{1}\right) &= F_{162}\! \left(x , y_{0}, y_{1}\right)+F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{169}\! \left(x , y_{1}, y_{0}\right)+F_{28}\! \left(x \right)\\
F_{162}\! \left(x , y_{0}, y_{1}\right) &= F_{163}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{163}\! \left(x , y_{0}, y_{1}\right) &= F_{161}\! \left(x , y_{0}, y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{164}\! \left(x , y_{0}, y_{1}\right) &= F_{165}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{165}\! \left(x , y_{0}, y_{1}\right) &= F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{1}\right)\\
F_{166}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{28}\! \left(x \right)+F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{167}\! \left(x , y_{0}, y_{1}\right)\\
F_{167}\! \left(x , y_{0}, y_{1}\right) &= F_{168}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{168}\! \left(x , y_{0}, y_{1}\right) &= F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{169}\! \left(x , y_{0}, y_{1}\right) &= F_{160}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{170}\! \left(x , y_{0}, y_{1}\right) &= F_{111}\! \left(x , y_{0}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)\\
F_{171}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{28}\! \left(x \right)+F_{172}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \left(x , y_{1}, y_{0}\right)\\
F_{172}\! \left(x , y_{0}, y_{1}\right) &= F_{173}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{173}\! \left(x , y_{0}, y_{1}\right) &= F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)\\
F_{174}\! \left(x , y_{0}, y_{1}\right) &= F_{175}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{175}\! \left(x , y_{0}, y_{1}\right) &= F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{176}\! \left(x , y_{0}, y_{1}\right)\\
F_{176}\! \left(x , y_{0}, y_{1}\right) &= 3 F_{28}\! \left(x \right)+F_{174}\! \left(x , y_{0}, y_{1}\right)+F_{177}\! \left(x , y_{0}, y_{1}\right)\\
F_{177}\! \left(x , y_{0}, y_{1}\right) &= F_{178}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{178}\! \left(x , y_{0}, y_{1}\right) &= F_{153}\! \left(x , y_{0}, y_{1}\right)+F_{176}\! \left(x , y_{0}, y_{1}\right)\\
F_{179}\! \left(x , y_{0}, y_{1}\right) &= F_{170}\! \left(x , y_{1}, y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{180}\! \left(x , y_{0}, y_{1}\right) &= F_{181}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{181}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{124}\! \left(x , y_{0}, y_{1}\right)+F_{124}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{182}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{1}\right) F_{183}\! \left(x , y_{0}, y_{1}\right)\\
F_{183}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{184}\! \left(x , y_{0}, y_{1}\right)+F_{184}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{184}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{185}\! \left(x , y_{0}, y_{1}\right)+F_{186}\! \left(x , y_{0}, y_{1}\right)+F_{190}\! \left(x , y_{0}, y_{1}\right)\\
F_{185}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{186}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}\right) F_{187}\! \left(x , y_{0}, y_{1}\right)\\
F_{187}\! \left(x , y_{0}, y_{1}\right) &= F_{188}\! \left(x , y_{0}, y_{1}\right)+F_{189}\! \left(x , y_{0}, y_{1}\right)\\
F_{188}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{1}\right)+F_{83}\! \left(x , y_{0}, y_{1}\right)\\
F_{189}\! \left(x , y_{0}, y_{1}\right) &= F_{160}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{1}\right)\\
F_{190}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{1}\right) F_{184}\! \left(x , y_{0}, y_{1}\right)\\
F_{191}\! \left(x , y_{0}\right) &= F_{192}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{192}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{121}\! \left(x , y_{0}\right)+F_{121}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{193}\! \left(x , y_{0}\right) &= F_{121}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
\end{align*}\)