PermPal Database

Av(1324, 2341)

Generating Function

\frac{(- 4 x^{4} + 17 x^{3} - 26 x^{2} + 13 x - 2) \sqrt{1 - 4 x} + 4 x^{4} + 7 x^{3} - 6 x^{2} + x}{8 (- \frac{1}{4} + x) {(x^{2} - 3 x + 1)}^{2}}

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Counting Sequence

1, 1, 2, 6, 22, 87, 352, 1428, 5768, 23156, 92416, 367007, 1451780, 5725959, 22535868, ...

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Implicit Equation for the Generating Function

(- 1 + 4 x) {(x^{2} - 3 x + 1)}^{4} F {(x)}^{2} - x (- 1 + 4 x) (x^{2} + 2 x - 1) {(x^{2} - 3 x + 1)}^{2} F (x) + 4 x^{8} - 33 x^{7} + 128 x^{6} - 246 x^{5} + 279 x^{4} - 184 x^{3} + 68 x^{2} - 13 x + 1 = 0

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Recurrence

a (0) = 1

a (1) = 1

a (2) = 2

a (3) = 6

a (4) = 22

a (5) = 87

a (6) = 352

a (7) = 1428

a (8) = 5768

a (n + 9) = \frac{4 (1 + 2 n) a (n)}{n + 9} - \frac{3 (37 + 28 n) a (n + 1)}{n + 9} + \frac{(1651 + 729 n) a (n + 2)}{2 n + 18} - \frac{18 (154 + 47 n) a (n + 3)}{n + 9} + \frac{2 (2432 + 567 n) a (n + 4)}{n + 9} - \frac{4 (1176 + 223 n) a (n + 5)}{n + 9} + \frac{32 (81 + 13 n) a (n + 6)}{n + 9} - \frac{(810 + 113 n) a (n + 7)}{n + 9} + \frac{3 (89 + 11 n) a (n + 8)}{2 (n + 9)}, n \geq 9

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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 Col Placements Tracked Fusion Req Corrob" and has 141 rules.

Found on April 26, 2021.

Finding the specification took 1795 seconds.

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\begin{aligned} F_{0} (x) & = F_{1} (x) + F_{2} (x) \\ F_{1} (x) & = 1 \\ F_{2} (x) & = F_{3} (x) \\ F_{3} (x) & = F_{4} (x) F_{6} (x) \\ F_{4} (x) & = F_{1} (x) + F_{5} (x) + F_{85} (x) \\ F_{5} (x) & = F_{6} (x) F_{7} (x) \\ F_{6} (x) & = x \\ F_{7} (x) & = F_{1} (x) + F_{69} (x) + F_{70} (x) + F_{8} (x) \\ F_{8} (x) & = F_{9} (x, 1) \\ F_{9} (x, y) & = F_{10} (x, y) F_{6} (x) \\ F_{10} (x, y) & = F_{11} (x, y) + F_{38} (x, y) \\ F_{11} (x, y) & = F_{1} (x) + F_{12} (x, y) + F_{17} (x) + F_{37} (x, y) \\ F_{12} (x, y) & = F_{13} (x, y) F_{6} (x) \\ F_{13} (x, y) & = F_{1} (x) + F_{14} (x, y) + F_{15} (x, y) + F_{9} (x, y) \\ F_{14} (x, y) & = F_{13} (x, y) F_{6} (x) \\ F_{15} (x, y) & = F_{13} (x, y) F_{16} (x, y) \\ F_{16} (x, y) & = y x \\ F_{17} (x) & = F_{18} (x) F_{6} (x) \\ F_{18} (x) & = F_{1} (x) + F_{19} (x) \\ F_{19} (x) & = F_{20} (x) \\ F_{20} (x) & = F_{21} (x) F_{6} (x) \\ F_{21} (x) & = F_{1} (x) + F_{22} (x) + F_{36} (x) \\ F_{22} (x) & = F_{23} (x) \\ F_{23} (x) & = F_{18} (x) F_{24} (x) F_{6} (x) \\ F_{24} (x) & = F_{25} (x) + F_{26} (x) \\ F_{25} (x) & = F_{1} (x) + F_{6} (x) \\ F_{26} (x) & = F_{27} (x) + F_{29} (x) \\ F_{27} (x) & = F_{28} (x) \\ F_{28} (x) & = F_{24} (x) F_{6} (x) \\ F_{29} (x) & = F_{30} (x) + F_{31} (x) + F_{35} (x) \\ F_{30} (x) & = 0 \\ F_{31} (x) & = F_{32} (x) F_{6} (x) \\ F_{32} (x) & = F_{33} (x) + F_{34} (x) \\ F_{33} (x) & = F_{6} (x) \\ F_{34} (x) & = F_{29} (x) \\ F_{35} (x) & = F_{27} (x) F_{6} (x) \\ F_{36} (x) & = F_{21} (x) F_{6} (x) \\ F_{37} (x, y) & = F_{11} (x, y) F_{16} (x, y) \\ F_{38} (x, y) & = F_{39} (x) + F_{41} (x, y) \\ F_{39} (x) & = F_{40} (x) \\ F_{40} (x) & = F_{18} (x) F_{26} (x) \\ F_{41} (x, y) & = 3 F_{30} (x) + F_{42} (x, y) + F_{68} (x, y) \\ F_{42} (x, y) & = F_{43} (x, y) F_{6} (x) \\ F_{43} (x, y) & = F_{44} (x, y) + F_{67} (x, y) \\ F_{44} (x, y) & = F_{45} (x, y) + F_{54} (x, y) \\ F_{45} (x, y) & = F_{30} (x) + F_{46} (x, y) + F_{50} (x, y) + F_{51} (x, y) \\ F_{46} (x, y) & = F_{47} (x, y) F_{6} (x) \\ F_{47} (x, y) & = F_{15} (x, y) + F_{30} (x) + F_{48} (x, y) + F_{49} (x, y) \\ F_{48} (x, y) & = F_{44} (x, y) F_{6} (x) \\ F_{49} (x, y) & = F_{47} (x, y) F_{6} (x) \\ F_{50} (x, y) & = F_{44} (x, y) F_{6} (x) \\ F_{51} (x, y) & = F_{16} (x, y) F_{52} (x, y) \\ F_{52} (x, y) & = F_{1} (x) + F_{12} (x, y) + F_{51} (x, y) + F_{53} (x, y) \\ F_{53} (x, y) & = F_{10} (x, y) F_{6} (x) \\ F_{54} (x, y) & = F_{55} (x, y) \\ F_{55} (x, y) & = F_{18} (x) F_{56} (x, y) \\ F_{56} (x, y) & = F_{57} (x, y) + F_{60} (x, y) \\ F_{57} (x, y) & = F_{58} (x, y) \\ F_{58} (x, y) & = F_{16} (x, y) F_{59} (x, y) \\ F_{59} (x, y) & = F_{57} (x, y) + F_{6} (x) \\ F_{60} (x, y) & = 2 F_{30} (x) + F_{61} (x, y) + F_{65} (x, y) \\ F_{61} (x, y) & = F_{6} (x) F_{62} (x, y) \\ F_{62} (x, y) & = F_{63} (x, y) + F_{64} (x, y) \\ F_{63} (x, y) & = F_{57} (x, y) \\ F_{64} (x, y) & = F_{60} (x, y) \\ F_{65} (x, y) & = F_{16} (x, y) F_{66} (x, y) \\ F_{66} (x, y) & = F_{29} (x) + F_{60} (x, y) \\ F_{67} (x, y) & = F_{55} (x, y) \\ F_{68} (x, y) & = F_{16} (x, y) F_{38} (x, y) \\ F_{69} (x) & = F_{6} (x) F_{7} (x) \\ F_{70} (x) & = F_{6} (x) F_{71} (x) \\ F_{71} (x) & = F_{7} (x) + F_{72} (x) \\ F_{72} (x) & = F_{73} (x) \\ F_{73} (x) & = F_{6} (x) F_{74} (x) F_{77} (x) \\ F_{74} (x) & = F_{7} (x) + F_{75} (x) \\ F_{75} (x) & = F_{19} (x) F_{76} (x) \\ F_{76} (x) & = F_{77} (x) + F_{80} (x) \\ F_{77} (x) & = F_{1} (x) + F_{78} (x) \\ F_{78} (x) & = F_{79} (x) \\ F_{79} (x) & = F_{6} (x) F_{77} (x) \\ F_{80} (x) & = F_{78} (x) + F_{81} (x) \\ F_{81} (x) & = F_{30} (x) + F_{82} (x) + F_{84} (x) \\ F_{82} (x) & = F_{6} (x) F_{83} (x) \\ F_{83} (x) & = F_{78} (x) + F_{81} (x) \\ F_{84} (x) & = F_{6} (x) F_{80} (x) \\ F_{85} (x) & = F_{6} (x) F_{86} (x) \\ F_{86} (x) & = F_{87} (x, 1) \\ F_{87} (x, y) & = F_{1} (x) + F_{132} (x, y) + F_{140} (x, y) + F_{88} (x, y) \\ F_{88} (x, y) & = F_{6} (x) F_{89} (x, y) \\ F_{89} (x, y) & = F_{1} (x) + F_{130} (x, y) + F_{90} (x, y) + F_{93} (x, y) + F_{94} (x, y) \\ F_{90} (x, y) & = F_{6} (x) F_{91} (x, y) \\ F_{91} (x, y) & = F_{10} (x, y) + F_{92} (x, y) \\ F_{92} (x, y) & = \frac{F_{44} (x, y) - F_{44} (x, 1)}{- 1 + y} \\ F_{93} (x, y) & = F_{6} (x) F_{89} (x, y) \\ F_{94} (x, y) & = F_{6} (x) F_{95} (x, y) \\ F_{95} (x, y) & = F_{89} (x, y) + F_{96} (x, y) \\ F_{96} (x, y) & = 2 F_{30} (x) + F_{122} (x, y) + F_{124} (x, y) + F_{93} (x, y) + F_{97} (x, y) \\ F_{97} (x, y) & = F_{98} (x, y) \\ F_{98} (x, y) & = F_{18} (x) F_{6} (x) F_{99} (x, y) \\ F_{99} (x, y) & = F_{100} (x, y) + F_{107} (x, y) \\ F_{100} (x, y) & = F_{101} (x, y) + F_{59} (x, y) \\ F_{101} (x, y) & = F_{102} (x) + F_{105} (x, y) \\ F_{102} (x) & = F_{103} (x) \\ F_{103} (x) & = F_{104} (x) F_{6} (x) \\ F_{104} (x) & = F_{102} (x) + F_{6} (x) \\ F_{105} (x, y) & = F_{106} (x, y) \\ F_{106} (x, y) & = F_{101} (x, y) F_{16} (x, y) \\ F_{107} (x, y) & = F_{108} (x, y) + F_{66} (x, y) \\ F_{108} (x, y) & = F_{109} (x) + F_{116} (x, y) \\ F_{109} (x) & = 2 F_{30} (x) + F_{110} (x) + F_{114} (x) \\ F_{110} (x) & = F_{111} (x) F_{6} (x) \\ F_{111} (x) & = F_{112} (x) + F_{113} (x) \\ F_{112} (x) & = F_{102} (x) \\ F_{113} (x) & = F_{109} (x) \\ F_{114} (x) & = F_{115} (x) F_{6} (x) \\ F_{115} (x) & = F_{109} (x) + F_{29} (x) \\ F_{116} (x, y) & = 3 F_{30} (x) + F_{117} (x, y) + F_{121} (x, y) \\ F_{117} (x, y) & = F_{118} (x, y) F_{6} (x) \\ F_{118} (x, y) & = F_{119} (x, y) + F_{120} (x, y) \\ F_{119} (x, y) & = F_{105} (x, y) \\ F_{120} (x, y) & = F_{116} (x, y) \\ F_{121} (x, y) & = F_{108} (x, y) F_{16} (x, y) \\ F_{122} (x, y) & = F_{123} (x, y) \\ F_{123} (x, y) & = F_{6} (x) F_{96} (x, y) \\ F_{124} (x, y) & = F_{125} (x, y) \\ F_{125} (x, y) & = F_{126} (x, y) F_{16} (x, y) \\ F_{126} (x, y) & = 2 F_{30} (x) + F_{125} (x, y) + F_{127} (x, y) + F_{14} (x, y) \\ F_{127} (x, y) & = F_{128} (x, y) \\ F_{128} (x, y) & = F_{129} (x, y) F_{18} (x) F_{6} (x) \\ F_{129} (x, y) & = F_{59} (x, y) + F_{66} (x, y) \\ F_{130} (x, y) & = F_{131} (x, y) F_{16} (x, y) \\ F_{131} (x, y) & = F_{126} (x, y) + F_{13} (x, y) \\ F_{132} (x, y) & = F_{133} (x, y) F_{6} (x) \\ F_{133} (x, y) & = F_{1} (x) + F_{134} (x, y) + F_{136} (x, y) + F_{138} (x) + F_{139} (x, y) \\ F_{134} (x, y) & = F_{135} (x, y) F_{6} (x) \\ F_{135} (x, y) & = \frac{y F_{89} (x, y) - F_{89} (x, 1)}{- 1 + y} \\ F_{136} (x, y) & = F_{137} (x, y) F_{6} (x) \\ F_{137} (x, y) & = \frac{y F_{133} (x, y) - F_{133} (x, 1)}{- 1 + y} \\ F_{138} (x) & = F_{6} (x) F_{86} (x) \\ F_{139} (x, y) & = F_{133} (x, y) F_{16} (x, y) \\ F_{140} (x, y) & = F_{16} (x, y) F_{87} (x, y) \end{aligned}

This specification was found using the strategy pack "Point And Row Placements Tracked Fusion" and has 263 rules.

Found on April 26, 2021.

Finding the specification took 1123 seconds.

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\begin{aligned} F_{0} (x) & = F_{1} (x) + F_{2} (x) \\ F_{1} (x) & = 1 \\ F_{2} (x) & = F_{12} (x) F_{3} (x) \\ F_{3} (x) & = F_{13} (x) + F_{4} (x) \\ F_{4} (x) & = F_{1} (x) + F_{5} (x) \\ F_{5} (x) & = F_{12} (x) F_{6} (x) \\ F_{6} (x) & = F_{7} (x, 1) \\ F_{7} (x, y) & = F_{1} (x) + F_{10} (x, y) + F_{8} (x, y) \\ F_{8} (x, y) & = F_{7} (x, y) F_{9} (x, y) \\ F_{9} (x, y) & = y x \\ F_{10} (x, y) & = F_{11} (x, y) F_{12} (x) \\ F_{11} (x, y) & = - \frac{- y F_{7} (x, y) + F_{7} (x, 1)}{- 1 + y} \\ F_{12} (x) & = x \\ F_{13} (x) & = F_{14} (x) + F_{15} (x) + F_{170} (x) \\ F_{14} (x) & = 0 \\ F_{15} (x) & = F_{12} (x) F_{16} (x) \\ F_{16} (x) & = F_{14} (x) + F_{168} (x) + F_{169} (x) + F_{17} (x) \\ F_{17} (x) & = F_{18} (x, 1) \\ F_{18} (x, y) & = F_{19} (x, y) F_{9} (x, y) \\ F_{19} (x, y) & = F_{14} (x) + F_{18} (x, y) + F_{20} (x, y) + F_{22} (x, y) \\ F_{20} (x, y) & = F_{12} (x) F_{21} (x, y) \\ F_{21} (x, y) & = - \frac{- y F_{19} (x, y) + F_{19} (x, 1)}{- 1 + y} \\ F_{22} (x, y) & = F_{12} (x) F_{23} (x, y) \\ F_{23} (x, y) & = F_{108} (x, y) + F_{24} (x, y) \\ F_{24} (x, y) & = F_{1} (x) + F_{25} (x, y) + F_{26} (x, y) + F_{27} (x, y) \\ F_{25} (x, y) & = F_{24} (x, y) F_{9} (x, y) \\ F_{26} (x, y) & = F_{12} (x) F_{24} (x, y) \\ F_{27} (x, y) & = F_{12} (x) F_{28} (x, y) \\ F_{28} (x, y) & = F_{29} (x, y) + F_{52} (x, y) \\ F_{29} (x, y) & = F_{30} (x) + F_{43} (x, y) \\ F_{30} (x) & = F_{31} (x) \\ F_{31} (x) & = F_{32} (x) F_{33} (x) \\ F_{32} (x) & = F_{1} (x) + F_{12} (x) \\ F_{33} (x) & = F_{1} (x) + F_{34} (x) \\ F_{34} (x) & = F_{35} (x) \\ F_{35} (x) & = F_{12} (x) F_{36} (x) \\ F_{36} (x) & = F_{33} (x) + F_{37} (x) \\ F_{37} (x) & = F_{34} (x) + F_{38} (x) \\ F_{38} (x) & = F_{39} (x) \\ F_{39} (x) & = F_{12} (x) F_{40} (x) \\ F_{40} (x) & = F_{41} (x) + F_{42} (x) \\ F_{41} (x) & = F_{34} (x) \\ F_{42} (x) & = F_{38} (x) \\ F_{43} (x, y) & = 2 F_{14} (x) + F_{44} (x, y) + F_{45} (x, y) \\ F_{44} (x, y) & = F_{29} (x, y) F_{9} (x, y) \\ F_{45} (x, y) & = F_{12} (x) F_{46} (x, y) \\ F_{46} (x, y) & = F_{14} (x) + F_{25} (x, y) + F_{47} (x, y) + F_{48} (x, y) \\ F_{47} (x, y) & = F_{12} (x) F_{46} (x, y) \\ F_{48} (x, y) & = F_{12} (x) F_{49} (x, y) \\ F_{49} (x, y) & = F_{43} (x, y) + F_{50} (x, y) \\ F_{50} (x, y) & = 3 F_{14} (x) + F_{107} (x, y) + F_{51} (x, y) \\ F_{51} (x, y) & = F_{52} (x, y) F_{9} (x, y) \\ F_{52} (x, y) & = 2 F_{14} (x) + F_{51} (x, y) + F_{53} (x) + F_{64} (x, y) \\ F_{53} (x) & = F_{54} (x) \\ F_{54} (x) & = F_{12} (x) F_{33} (x) F_{55} (x) \\ F_{55} (x) & = F_{56} (x) \\ F_{56} (x) & = F_{12} (x) F_{57} (x) \\ F_{57} (x) & = F_{58} (x) + F_{61} (x) \\ F_{58} (x) & = F_{1} (x) + F_{59} (x) \\ F_{59} (x) & = F_{60} (x) \\ F_{60} (x) & = F_{12} (x) F_{58} (x) \\ F_{61} (x) & = F_{55} (x) + F_{62} (x) \\ F_{62} (x) & = F_{63} (x) \\ F_{63} (x) & = F_{12} (x) F_{61} (x) \\ F_{64} (x, y) & = F_{12} (x) F_{65} (x, y) \\ F_{65} (x, y) & = F_{66} (x) + F_{83} (x, y) \\ F_{66} (x) & = F_{67} (x) \\ F_{67} (x) & = F_{33} (x) F_{68} (x) \\ F_{68} (x) & = F_{69} (x) + F_{82} (x) \\ F_{69} (x) & = F_{70} (x) + F_{71} (x) \\ F_{70} (x) & = F_{1} (x) + F_{55} (x) \\ F_{71} (x) & = F_{12} (x) + F_{72} (x) \\ F_{72} (x) & = F_{14} (x) + F_{73} (x) + F_{74} (x) \\ F_{73} (x) & = F_{12} (x) F_{59} (x) \\ F_{74} (x) & = F_{12} (x) F_{75} (x) \\ F_{75} (x) & = F_{76} (x) + F_{79} (x) \\ F_{76} (x) & = F_{12} (x) + F_{77} (x) \\ F_{77} (x) & = F_{78} (x) \\ F_{78} (x) & = F_{12} (x) F_{76} (x) \\ F_{79} (x) & = F_{72} (x) + F_{80} (x) \\ F_{80} (x) & = F_{81} (x) \\ F_{81} (x) & = F_{12} (x) F_{79} (x) \\ F_{82} (x) & = F_{71} (x) \\ F_{83} (x, y) & = F_{49} (x, y) + F_{84} (x, y) \\ F_{84} (x, y) & = F_{85} (x, y) \\ F_{85} (x, y) & = F_{33} (x) F_{86} (x, y) \\ F_{86} (x, y) & = F_{87} (x, y) + F_{92} (x, y) \\ F_{87} (x, y) & = F_{88} (x, y) \\ F_{88} (x, y) & = F_{12} (x) F_{89} (x, y) \\ F_{89} (x, y) & = F_{90} (x, y) \\ F_{90} (x, y) & = F_{9} (x, y) F_{91} (x, y) \\ F_{91} (x, y) & = F_{1} (x) + F_{89} (x, y) \\ F_{92} (x, y) & = 2 F_{14} (x) + F_{93} (x, y) + F_{99} (x, y) \\ F_{93} (x, y) & = F_{12} (x) F_{94} (x, y) \\ F_{94} (x, y) & = F_{14} (x) + F_{95} (x, y) + F_{97} (x, y) \\ F_{95} (x, y) & = F_{9} (x, y) F_{96} (x, y) \\ F_{96} (x, y) & = F_{59} (x) + F_{94} (x, y) \\ F_{97} (x, y) & = F_{12} (x) F_{98} (x, y) \\ F_{98} (x, y) & = F_{89} (x, y) + F_{94} (x, y) \\ F_{99} (x, y) & = F_{100} (x, y) F_{12} (x) \\ F_{100} (x, y) & = F_{101} (x, y) + F_{104} (x, y) \\ F_{101} (x, y) & = F_{102} (x, y) + F_{87} (x, y) \\ F_{102} (x, y) & = F_{103} (x, y) \\ F_{103} (x, y) & = F_{101} (x, y) F_{12} (x) \\ F_{104} (x, y) & = F_{105} (x, y) + F_{92} (x, y) \\ F_{105} (x, y) & = F_{106} (x, y) \\ F_{106} (x, y) & = F_{104} (x, y) F_{12} (x) \\ F_{107} (x, y) & = F_{12} (x) F_{83} (x, y) \\ F_{108} (x, y) & = F_{109} (x, y) + F_{114} (x, y) + F_{14} (x) + F_{165} (x, y) + F_{166} (x, y) \\ F_{109} (x, y) & = F_{110} (x, y) F_{9} (x, y) \\ F_{110} (x, y) & = 2 F_{14} (x) + F_{109} (x, y) + F_{111} (x, y) + F_{26} (x, y) \\ F_{111} (x, y) & = F_{112} (x, y) \\ F_{112} (x, y) & = F_{113} (x, y) F_{12} (x) F_{33} (x) \\ F_{113} (x, y) & = F_{71} (x) + F_{86} (x, y) \\ F_{114} (x, y) & = F_{115} (x, y) F_{12} (x) \\ F_{115} (x, y) & = F_{116} (x, y) + F_{23} (x, y) \\ F_{116} (x, y) & = 2 F_{14} (x) + F_{117} (x, y) + F_{118} (x, y) + F_{120} (x, y) + F_{121} (x, y) \\ F_{117} (x, y) & = F_{109} (x, y) \\ F_{118} (x, y) & = F_{119} (x, y) \\ F_{119} (x, y) & = F_{116} (x, y) F_{12} (x) \\ F_{120} (x, y) & = F_{12} (x) F_{23} (x, y) \\ F_{121} (x, y) & = F_{122} (x, y) \\ F_{122} (x, y) & = F_{12} (x) F_{123} (x, y) F_{33} (x) \\ F_{123} (x, y) & = F_{124} (x) + F_{143} (x, y) \\ F_{124} (x) & = F_{125} (x) + F_{71} (x) \\ F_{125} (x) & = F_{126} (x) + F_{128} (x) \\ F_{126} (x) & = F_{127} (x) \\ F_{127} (x) & = F_{12} (x) F_{59} (x) \\ F_{128} (x) & = 2 F_{14} (x) + F_{129} (x) + F_{135} (x) \\ F_{129} (x) & = F_{12} (x) F_{130} (x) \\ F_{130} (x) & = F_{131} (x) + F_{133} (x) + F_{14} (x) \\ F_{131} (x) & = F_{12} (x) F_{132} (x) \\ F_{132} (x) & = F_{130} (x) + F_{59} (x) \\ F_{133} (x) & = F_{12} (x) F_{134} (x) \\ F_{134} (x) & = F_{130} (x) + F_{59} (x) \\ F_{135} (x) & = F_{12} (x) F_{136} (x) \\ F_{136} (x) & = F_{137} (x) + F_{140} (x) \\ F_{137} (x) & = F_{126} (x) + F_{138} (x) \\ F_{138} (x) & = F_{139} (x) \\ F_{139} (x) & = F_{12} (x) F_{137} (x) \\ F_{140} (x) & = F_{128} (x) + F_{141} (x) \\ F_{141} (x) & = F_{142} (x) \\ F_{142} (x) & = F_{12} (x) F_{140} (x) \\ F_{143} (x, y) & = F_{144} (x, y) + F_{86} (x, y) \\ F_{144} (x, y) & = F_{145} (x, y) + F_{150} (x, y) \\ F_{145} (x, y) & = F_{146} (x, y) \\ F_{146} (x, y) & = F_{12} (x) F_{147} (x, y) \\ F_{147} (x, y) & = F_{148} (x, y) \\ F_{148} (x, y) & = F_{12} (x) F_{149} (x, y) \\ F_{149} (x, y) & = F_{147} (x, y) + F_{89} (x, y) \\ F_{150} (x, y) & = 3 F_{14} (x) + F_{151} (x, y) + F_{157} (x, y) \\ F_{151} (x, y) & = F_{12} (x) F_{152} (x, y) \\ F_{152} (x, y) & = 2 F_{14} (x) + F_{153} (x, y) + F_{155} (x, y) \\ F_{153} (x, y) & = F_{12} (x) F_{154} (x, y) \\ F_{154} (x, y) & = F_{152} (x, y) + F_{94} (x, y) \\ F_{155} (x, y) & = F_{12} (x) F_{156} (x, y) \\ F_{156} (x, y) & = F_{147} (x, y) + F_{152} (x, y) \\ F_{157} (x, y) & = F_{12} (x) F_{158} (x, y) \\ F_{158} (x, y) & = F_{159} (x, y) + F_{162} (x, y) \\ F_{159} (x, y) & = F_{145} (x, y) + F_{160} (x, y) \\ F_{160} (x, y) & = F_{161} (x, y) \\ F_{161} (x, y) & = F_{12} (x) F_{159} (x, y) \\ F_{162} (x, y) & = F_{150} (x, y) + F_{163} (x, y) \\ F_{163} (x, y) & = F_{164} (x, y) \\ F_{164} (x, y) & = F_{12} (x) F_{162} (x, y) \\ F_{165} (x, y) & = F_{108} (x, y) F_{12} (x) \\ F_{166} (x, y) & = F_{12} (x) F_{167} (x, y) \\ F_{167} (x, y) & = - \frac{F_{49} (x, 1) - F_{49} (x, y)}{- 1 + y} \\ F_{168} (x) & = F_{20} (x, 1) \\ F_{169} (x) & = F_{22} (x, 1) \\ F_{170} (x) & = F_{12} (x) F_{171} (x) \\ F_{171} (x) & = F_{1} (x) + F_{172} (x) + F_{206} (x) + F_{208} (x) \\ F_{172} (x) & = F_{12} (x) F_{173} (x) \\ F_{173} (x) & = F_{171} (x) + F_{174} (x) \\ F_{174} (x) & = F_{175} (x) \\ F_{175} (x) & = F_{176} (x, 1) \\ F_{176} (x, y) & = F_{177} (x) F_{33} (x) F_{89} (x, y) \\ F_{177} (x) & = F_{178} (x) + F_{181} (x) \\ F_{178} (x) & = F_{1} (x) + F_{179} (x) \\ F_{179} (x) & = F_{180} (x) \\ F_{180} (x) & = F_{12} (x) F_{178} (x) \\ F_{181} (x) & = F_{182} (x) + F_{192} (x) \\ F_{182} (x) & = F_{183} (x) \\ F_{183} (x) & = F_{12} (x) F_{184} (x) \\ F_{184} (x) & = F_{185} (x) + F_{32} (x) \\ F_{185} (x) & = F_{182} (x) + F_{186} (x) \\ F_{186} (x) & = F_{14} (x) + F_{187} (x) + F_{191} (x) \\ F_{187} (x) & = F_{12} (x) F_{188} (x) \\ F_{188} (x) & = F_{189} (x) + F_{190} (x) \\ F_{189} (x) & = F_{12} (x) \\ F_{190} (x) & = F_{186} (x) \\ F_{191} (x) & = F_{12} (x) F_{182} (x) \\ F_{192} (x) & = F_{14} (x) + F_{193} (x) + F_{205} (x) \\ F_{193} (x) & = F_{12} (x) F_{194} (x) \\ F_{194} (x) & = F_{195} (x) + F_{198} (x) \\ F_{195} (x) & = F_{179} (x) + F_{196} (x) \\ F_{196} (x) & = F_{197} (x) \\ F_{197} (x) & = F_{12} (x) F_{179} (x) \\ F_{198} (x) & = F_{192} (x) + F_{199} (x) \\ F_{199} (x) & = 2 F_{14} (x) + F_{200} (x) + F_{204} (x) \\ F_{200} (x) & = F_{12} (x) F_{201} (x) \\ F_{201} (x) & = F_{202} (x) + F_{203} (x) \\ F_{202} (x) & = F_{196} (x) \\ F_{203} (x) & = F_{199} (x) \\ F_{204} (x) & = F_{12} (x) F_{192} (x) \\ F_{205} (x) & = F_{12} (x) F_{181} (x) \\ F_{206} (x) & = F_{207} (x) \\ F_{207} (x) & = F_{12} (x) F_{177} (x) F_{33} (x) \\ F_{208} (x) & = F_{12} (x) F_{209} (x) \\ F_{209} (x) & = F_{210} (x, 1) \\ F_{210} (x, y) & = F_{1} (x) + F_{206} (x) + F_{211} (x, y) + F_{214} (x, y) + F_{261} (x, y) \\ F_{211} (x, y) & = F_{12} (x) F_{212} (x, y) \\ F_{212} (x, y) & = F_{210} (x, y) + F_{213} (x, y) \\ F_{213} (x, y) & = F_{175} (x) \\ F_{214} (x, y) & = F_{215} (x, y) \\ F_{215} (x, y) & = F_{216} (x, y) F_{33} (x) F_{9} (x, y) \\ F_{216} (x, y) & = F_{217} (x, y) + F_{225} (x, y) \\ F_{217} (x, y) & = F_{218} (x, y) + F_{221} (x, y) \\ F_{218} (x, y) & = F_{1} (x) + F_{219} (x, y) \\ F_{219} (x, y) & = F_{220} (x, y) \\ F_{220} (x, y) & = F_{218} (x, y) F_{9} (x, y) \\ F_{221} (x, y) & = F_{179} (x) + F_{222} (x, y) \\ F_{222} (x, y) & = F_{223} (x, y) \\ F_{223} (x, y) & = F_{12} (x) F_{224} (x, y) \\ F_{224} (x, y) & = F_{219} (x, y) + F_{222} (x, y) \\ F_{225} (x, y) & = F_{226} (x, y) + F_{245} (x, y) \\ F_{226} (x, y) & = F_{182} (x) + F_{227} (x, y) \\ F_{227} (x, y) & = F_{14} (x) + F_{228} (x, y) + F_{240} (x, y) \\ F_{228} (x, y) & = F_{12} (x) F_{229} (x, y) \\ F_{229} (x, y) & = F_{230} (x, y) + F_{233} (x, y) \\ F_{230} (x, y) & = F_{219} (x, y) + F_{231} (x, y) \\ F_{231} (x, y) & = F_{232} (x, y) \\ F_{232} (x, y) & = F_{12} (x) F_{219} (x, y) \\ F_{233} (x, y) & = F_{227} (x, y) + F_{234} (x, y) \\ F_{234} (x, y) & = 2 F_{14} (x) + F_{235} (x, y) + F_{239} (x, y) \\ F_{235} (x, y) & = F_{12} (x) F_{236} (x, y) \\ F_{236} (x, y) & = F_{237} (x, y) + F_{238} (x, y) \\ F_{237} (x, y) & = F_{231} (x, y) \\ F_{238} (x, y) & = F_{234} (x, y) \\ F_{239} (x, y) & = F_{12} (x) F_{227} (x, y) \\ F_{240} (x, y) & = F_{241} (x, y) F_{9} (x, y) \\ F_{241} (x, y) & = F_{242} (x, y) + F_{59} (x) \\ F_{242} (x, y) & = F_{14} (x) + F_{240} (x, y) + F_{243} (x, y) \\ F_{243} (x, y) & = F_{12} (x) F_{244} (x, y) \\ F_{244} (x, y) & = F_{219} (x, y) + F_{242} (x, y) \\ F_{245} (x, y) & = F_{192} (x) + F_{246} (x, y) \\ F_{246} (x, y) & = 2 F_{14} (x) + F_{247} (x, y) + F_{259} (x, y) \\ F_{247} (x, y) & = F_{12} (x) F_{248} (x, y) \\ F_{248} (x, y) & = F_{249} (x, y) + F_{252} (x, y) \\ F_{249} (x, y) & = F_{222} (x, y) + F_{250} (x, y) \\ F_{250} (x, y) & = F_{251} (x, y) \\ F_{251} (x, y) & = F_{12} (x) F_{222} (x, y) \\ F_{252} (x, y) & = F_{246} (x, y) + F_{253} (x, y) \\ F_{253} (x, y) & = 3 F_{14} (x) + F_{254} (x, y) + F_{258} (x, y) \\ F_{254} (x, y) & = F_{12} (x) F_{255} (x, y) \\ F_{255} (x, y) & = F_{256} (x, y) + F_{257} (x, y) \\ F_{256} (x, y) & = F_{250} (x, y) \\ F_{257} (x, y) & = F_{253} (x, y) \\ F_{258} (x, y) & = F_{12} (x) F_{246} (x, y) \\ F_{259} (x, y) & = F_{12} (x) F_{260} (x, y) \\ F_{260} (x, y) & = F_{227} (x, y) + F_{246} (x, y) \\ F_{261} (x, y) & = F_{12} (x) F_{262} (x, y) \\ F_{262} (x, y) & = - \frac{- y F_{210} (x, y) + F_{210} (x, 1)}{- 1 + y} \end{aligned}

This specification was found using the strategy pack "Insertion Row Placements Tracked Fusion" and has 427 rules.

Found on April 26, 2021.

Finding the specification took 111 seconds.

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\begin{aligned} F_{0} (x) & = F_{1} (x) + F_{2} (x) \\ F_{1} (x) & = 1 \\ F_{2} (x) & = F_{3} (x) \\ F_{3} (x) & = F_{4} (x) F_{8} (x) \\ F_{4} (x) & = F_{16} (x) + F_{5} (x) \\ F_{5} (x) & = F_{1} (x) + F_{6} (x) \\ F_{6} (x) & = F_{7} (x) \\ F_{7} (x) & = F_{8} (x) F_{9} (x) \\ F_{8} (x) & = x \\ F_{9} (x) & = F_{10} (x) + F_{5} (x) \\ F_{10} (x) & = F_{11} (x) + F_{6} (x) \\ F_{11} (x) & = F_{12} (x) \\ F_{12} (x) & = F_{13} (x) F_{8} (x) \\ F_{13} (x) & = F_{14} (x) + F_{15} (x) \\ F_{14} (x) & = F_{6} (x) \\ F_{15} (x) & = F_{11} (x) \\ F_{16} (x) & = F_{17} (x) + F_{25} (x) \\ F_{17} (x) & = F_{18} (x) \\ F_{18} (x) & = F_{19} (x) F_{8} (x) \\ F_{19} (x) & = F_{20} (x, 1) \\ F_{20} (x, y) & = F_{1} (x) + F_{21} (x, y) + F_{23} (x, y) \\ F_{21} (x, y) & = F_{20} (x, y) F_{22} (x, y) \\ F_{22} (x, y) & = y x \\ F_{23} (x, y) & = F_{24} (x, y) F_{8} (x) \\ F_{24} (x, y) & = - \frac{- y F_{20} (x, y) + F_{20} (x, 1)}{- 1 + y} \\ F_{25} (x) & = F_{26} (x) + F_{27} (x) + F_{313} (x) \\ F_{26} (x) & = 0 \\ F_{27} (x) & = F_{28} (x) F_{8} (x) \\ F_{28} (x) & = F_{29} (x) + F_{30} (x) \\ F_{29} (x) & = F_{25} (x) + F_{6} (x) \\ F_{30} (x) & = F_{31} (x, 1) \\ F_{31} (x, y) & = F_{32} (x, y) + F_{94} (x, y) \\ F_{32} (x, y) & = F_{26} (x) + F_{33} (x, y) + F_{35} (x, y) \\ F_{33} (x, y) & = F_{22} (x, y) F_{34} (x, y) \\ F_{34} (x, y) & = F_{32} (x, y) + F_{6} (x) \\ F_{35} (x, y) & = F_{36} (x, y) F_{8} (x) \\ F_{36} (x, y) & = F_{37} (x, y) + F_{41} (x, y) \\ F_{37} (x, y) & = F_{32} (x, y) + F_{38} (x, y) \\ F_{38} (x, y) & = F_{39} (x, y) \\ F_{39} (x, y) & = F_{22} (x, y) F_{40} (x, y) \\ F_{40} (x, y) & = F_{1} (x) + F_{38} (x, y) \\ F_{41} (x, y) & = F_{42} (x, y) + F_{50} (x, y) \\ F_{42} (x, y) & = F_{26} (x) + F_{43} (x, y) + F_{48} (x, y) \\ F_{43} (x, y) & = F_{22} (x, y) F_{44} (x, y) \\ F_{44} (x, y) & = F_{42} (x, y) + F_{45} (x) \\ F_{45} (x) & = F_{46} (x) \\ F_{46} (x) & = F_{47} (x) F_{8} (x) \\ F_{47} (x) & = F_{1} (x) + F_{45} (x) \\ F_{48} (x, y) & = F_{49} (x, y) F_{8} (x) \\ F_{49} (x, y) & = F_{38} (x, y) + F_{42} (x, y) \\ F_{50} (x, y) & = F_{26} (x) + F_{51} (x, y) + F_{72} (x, y) + F_{74} (x, y) \\ F_{51} (x, y) & = F_{22} (x, y) F_{52} (x, y) \\ F_{52} (x, y) & = F_{50} (x, y) + F_{53} (x) \\ F_{53} (x) & = F_{26} (x) + F_{54} (x) + F_{56} (x) \\ F_{54} (x) & = F_{55} (x) F_{8} (x) \\ F_{55} (x) & = F_{53} (x) + F_{6} (x) \\ F_{56} (x) & = F_{57} (x) \\ F_{57} (x) & = F_{5} (x) F_{58} (x) F_{8} (x) \\ F_{58} (x) & = F_{59} (x) + F_{8} (x) \\ F_{59} (x) & = F_{26} (x) + F_{60} (x) + F_{64} (x) \\ F_{60} (x) & = F_{61} (x) F_{8} (x) \\ F_{61} (x) & = F_{62} (x) \\ F_{62} (x) & = F_{63} (x) F_{8} (x) \\ F_{63} (x) & = F_{1} (x) + F_{61} (x) \\ F_{64} (x) & = F_{65} (x) F_{8} (x) \\ F_{65} (x) & = F_{66} (x) + F_{69} (x) \\ F_{66} (x) & = F_{67} (x) + F_{8} (x) \\ F_{67} (x) & = F_{68} (x) \\ F_{68} (x) & = F_{66} (x) F_{8} (x) \\ F_{69} (x) & = F_{59} (x) + F_{70} (x) \\ F_{70} (x) & = F_{71} (x) \\ F_{71} (x) & = F_{69} (x) F_{8} (x) \\ F_{72} (x, y) & = F_{73} (x, y) F_{8} (x) \\ F_{73} (x, y) & = F_{32} (x, y) + F_{50} (x, y) \\ F_{74} (x, y) & = F_{75} (x, y) \\ F_{75} (x, y) & = F_{5} (x) F_{76} (x, y) F_{8} (x) \\ F_{76} (x, y) & = F_{77} (x, y) + F_{79} (x, y) \\ F_{77} (x, y) & = F_{78} (x, y) \\ F_{78} (x, y) & = F_{38} (x, y) F_{8} (x) \\ F_{79} (x, y) & = 2 F_{26} (x) + F_{80} (x, y) + F_{86} (x, y) \\ F_{80} (x, y) & = F_{8} (x) F_{81} (x, y) \\ F_{81} (x, y) & = F_{26} (x) + F_{82} (x, y) + F_{84} (x, y) \\ F_{82} (x, y) & = F_{22} (x, y) F_{83} (x, y) \\ F_{83} (x, y) & = F_{61} (x) + F_{81} (x, y) \\ F_{84} (x, y) & = F_{8} (x) F_{85} (x, y) \\ F_{85} (x, y) & = F_{38} (x, y) + F_{81} (x, y) \\ F_{86} (x, y) & = F_{8} (x) F_{87} (x, y) \\ F_{87} (x, y) & = F_{88} (x, y) + F_{91} (x, y) \\ F_{88} (x, y) & = F_{77} (x, y) + F_{89} (x, y) \\ F_{89} (x, y) & = F_{90} (x, y) \\ F_{90} (x, y) & = F_{8} (x) F_{88} (x, y) \\ F_{91} (x, y) & = F_{79} (x, y) + F_{92} (x, y) \\ F_{92} (x, y) & = F_{93} (x, y) \\ F_{93} (x, y) & = F_{8} (x) F_{91} (x, y) \\ F_{94} (x, y) & = F_{26} (x) + F_{95} (x, y) + F_{97} (x, y) + F_{99} (x, y) \\ F_{95} (x, y) & = F_{22} (x, y) F_{96} (x, y) \\ F_{96} (x, y) & = F_{25} (x) + F_{94} (x, y) \\ F_{97} (x, y) & = - \frac{y (F_{98} (x, 1) - F_{98} (x, y))}{- 1 + y} \\ F_{98} (x, y) & = F_{31} (x, y) F_{8} (x) \\ F_{99} (x, y) & = F_{100} (x, y) F_{8} (x) \\ F_{100} (x, y) & = F_{101} (x, y) + F_{236} (x, y) \\ F_{101} (x, y) & = F_{102} (x, y) + F_{117} (x, y) \\ F_{102} (x, y) & = F_{103} (x, y) + F_{106} (x, y) + F_{26} (x) \\ F_{103} (x, y) & = F_{104} (x, y) F_{22} (x, y) \\ F_{104} (x, y) & = F_{105} (x, y) + F_{8} (x) \\ F_{105} (x, y) & = F_{103} (x, y) + F_{26} (x) + F_{78} (x, y) \\ F_{106} (x, y) & = F_{107} (x, y) F_{8} (x) \\ F_{107} (x, y) & = F_{108} (x, y) + F_{109} (x, y) \\ F_{108} (x, y) & = F_{105} (x, y) + F_{38} (x, y) \\ F_{109} (x, y) & = F_{102} (x, y) + F_{110} (x, y) \\ F_{110} (x, y) & = F_{111} (x, y) + F_{112} (x, y) + F_{116} (x, y) + F_{26} (x) \\ F_{111} (x, y) & = 0 \\ F_{112} (x, y) & = F_{113} (x, y) F_{8} (x) \\ F_{113} (x, y) & = F_{114} (x, y) + F_{115} (x, y) \\ F_{114} (x, y) & = F_{105} (x, y) \\ F_{115} (x, y) & = F_{110} (x, y) \\ F_{116} (x, y) & = F_{102} (x, y) F_{8} (x) \\ F_{117} (x, y) & = F_{118} (x, y) + F_{124} (x, y) + F_{157} (x, y) + F_{26} (x) \\ F_{118} (x, y) & = F_{119} (x, y) F_{22} (x, y) \\ F_{119} (x, y) & = F_{120} (x) + F_{122} (x, y) \\ F_{120} (x) & = F_{121} (x) + F_{26} (x) + F_{56} (x) \\ F_{121} (x) & = F_{6} (x) F_{8} (x) \\ F_{122} (x, y) & = F_{118} (x, y) + F_{123} (x, y) + F_{26} (x) + F_{74} (x, y) \\ F_{123} (x, y) & = F_{32} (x, y) F_{8} (x) \\ F_{124} (x, y) & = F_{125} (x, y) F_{8} (x) \\ F_{125} (x, y) & = F_{126} (x, y) + F_{127} (x, y) \\ F_{126} (x, y) & = F_{122} (x, y) + F_{32} (x, y) \\ F_{127} (x, y) & = F_{117} (x, y) + F_{128} (x, y) \\ F_{128} (x, y) & = F_{129} (x, y) + F_{130} (x, y) + F_{133} (x, y) + F_{134} (x, y) + F_{26} (x) \\ F_{129} (x, y) & = 0 \\ F_{130} (x, y) & = F_{131} (x, y) \\ F_{131} (x, y) & = F_{132} (x, y) F_{8} (x) \\ F_{132} (x, y) & = F_{122} (x, y) + F_{128} (x, y) \\ F_{133} (x, y) & = F_{117} (x, y) F_{8} (x) \\ F_{134} (x, y) & = F_{135} (x, y) \\ F_{135} (x, y) & = F_{136} (x, y) F_{5} (x) F_{8} (x) \\ F_{136} (x, y) & = F_{137} (x, y) + F_{142} (x, y) \\ F_{137} (x, y) & = F_{138} (x, y) \\ F_{138} (x, y) & = F_{139} (x, y) F_{8} (x) \\ F_{139} (x, y) & = F_{140} (x, y) \\ F_{140} (x, y) & = F_{141} (x, y) F_{8} (x) \\ F_{141} (x, y) & = F_{139} (x, y) + F_{38} (x, y) \\ F_{142} (x, y) & = 3 F_{26} (x) + F_{143} (x, y) + F_{149} (x, y) \\ F_{143} (x, y) & = F_{144} (x, y) F_{8} (x) \\ F_{144} (x, y) & = 2 F_{26} (x) + F_{145} (x, y) + F_{147} (x, y) \\ F_{145} (x, y) & = F_{146} (x, y) F_{8} (x) \\ F_{146} (x, y) & = F_{144} (x, y) + F_{81} (x, y) \\ F_{147} (x, y) & = F_{148} (x, y) F_{8} (x) \\ F_{148} (x, y) & = F_{139} (x, y) + F_{144} (x, y) \\ F_{149} (x, y) & = F_{150} (x, y) F_{8} (x) \\ F_{150} (x, y) & = F_{151} (x, y) + F_{154} (x, y) \\ F_{151} (x, y) & = F_{137} (x, y) + F_{152} (x, y) \\ F_{152} (x, y) & = F_{153} (x, y) \\ F_{153} (x, y) & = F_{151} (x, y) F_{8} (x) \\ F_{154} (x, y) & = F_{142} (x, y) + F_{155} (x, y) \\ F_{155} (x, y) & = F_{156} (x, y) \\ F_{156} (x, y) & = F_{154} (x, y) F_{8} (x) \\ F_{157} (x, y) & = F_{158} (x, y) F_{8} (x) \\ F_{158} (x, y) & = F_{159} (x, y) + F_{195} (x, y) \\ F_{159} (x, y) & = - \frac{F_{160} (x, 1) y - F_{160} (x, y)}{- 1 + y} \\ F_{160} (x, y) & = F_{161} (x, y) + F_{163} (x, y) \\ F_{161} (x, y) & = F_{162} (x, y) \\ F_{162} (x, y) & = F_{22} (x, y) F_{38} (x, y) \\ F_{163} (x, y) & = F_{164} (x, y) + F_{165} (x, y) + F_{26} (x) \\ F_{164} (x, y) & = F_{22} (x, y) F_{32} (x, y) \\ F_{165} (x, y) & = F_{166} (x, y) F_{8} (x) \\ F_{166} (x, y) & = F_{160} (x, y) + F_{167} (x, y) \\ F_{167} (x, y) & = F_{168} (x, y) + F_{172} (x, y) \\ F_{168} (x, y) & = F_{169} (x, y) + F_{170} (x, y) + F_{26} (x) \\ F_{169} (x, y) & = F_{22} (x, y) F_{42} (x, y) \\ F_{170} (x, y) & = F_{171} (x, y) F_{8} (x) \\ F_{171} (x, y) & = F_{161} (x, y) + F_{168} (x, y) \\ F_{172} (x, y) & = F_{173} (x, y) + F_{174} (x, y) + F_{176} (x, y) + F_{26} (x) \\ F_{173} (x, y) & = F_{22} (x, y) F_{50} (x, y) \\ F_{174} (x, y) & = F_{175} (x, y) F_{8} (x) \\ F_{175} (x, y) & = F_{163} (x, y) + F_{172} (x, y) \\ F_{176} (x, y) & = F_{177} (x, y) \\ F_{177} (x, y) & = F_{178} (x, y) F_{5} (x) F_{8} (x) \\ F_{178} (x, y) & = F_{179} (x, y) + F_{181} (x, y) \\ F_{179} (x, y) & = F_{180} (x, y) \\ F_{180} (x, y) & = F_{161} (x, y) F_{8} (x) \\ F_{181} (x, y) & = 2 F_{26} (x) + F_{182} (x, y) + F_{187} (x, y) \\ F_{182} (x, y) & = F_{183} (x, y) F_{8} (x) \\ F_{183} (x, y) & = F_{184} (x, y) + F_{185} (x, y) + F_{26} (x) \\ F_{184} (x, y) & = F_{22} (x, y) F_{81} (x, y) \\ F_{185} (x, y) & = F_{186} (x, y) F_{8} (x) \\ F_{186} (x, y) & = F_{161} (x, y) + F_{183} (x, y) \\ F_{187} (x, y) & = F_{188} (x, y) F_{8} (x) \\ F_{188} (x, y) & = F_{189} (x, y) + F_{192} (x, y) \\ F_{189} (x, y) & = F_{179} (x, y) + F_{190} (x, y) \\ F_{190} (x, y) & = F_{191} (x, y) \\ F_{191} (x, y) & = F_{189} (x, y) F_{8} (x) \\ F_{192} (x, y) & = F_{181} (x, y) + F_{193} (x, y) \\ F_{193} (x, y) & = F_{194} (x, y) \\ F_{194} (x, y) & = F_{192} (x, y) F_{8} (x) \\ F_{195} (x, y) & = F_{196} (x, y) + F_{215} (x, y) \\ F_{196} (x, y) & = 2 F_{26} (x) + F_{145} (x, y) + F_{197} (x, y) \\ F_{197} (x, y) & = F_{198} (x, y) F_{8} (x) \\ F_{198} (x, y) & = F_{148} (x, y) + F_{199} (x, y) \\ F_{199} (x, y) & = F_{196} (x, y) + F_{200} (x, y) \\ F_{200} (x, y) & = 3 F_{26} (x) + F_{201} (x, y) + F_{214} (x, y) \\ F_{201} (x, y) & = F_{202} (x, y) F_{8} (x) \\ F_{202} (x, y) & = F_{203} (x, y) + F_{211} (x, y) \\ F_{203} (x, y) & = 2 F_{26} (x) + F_{204} (x, y) + F_{209} (x, y) \\ F_{204} (x, y) & = F_{205} (x, y) F_{22} (x, y) \\ F_{205} (x, y) & = F_{203} (x, y) + F_{206} (x) \\ F_{206} (x) & = F_{207} (x) \\ F_{207} (x) & = F_{208} (x) F_{8} (x) \\ F_{208} (x) & = F_{206} (x) + F_{61} (x) \\ F_{209} (x, y) & = F_{210} (x, y) F_{8} (x) \\ F_{210} (x, y) & = F_{203} (x, y) + F_{81} (x, y) \\ F_{211} (x, y) & = 3 F_{26} (x) + F_{201} (x, y) + F_{212} (x, y) \\ F_{212} (x, y) & = F_{213} (x, y) F_{8} (x) \\ F_{213} (x, y) & = F_{144} (x, y) + F_{211} (x, y) \\ F_{214} (x, y) & = F_{199} (x, y) F_{8} (x) \\ F_{215} (x, y) & = - \frac{F_{216} (x, 1) y - F_{216} (x, y)}{- 1 + y} \\ F_{216} (x, y) & = 2 F_{26} (x) + F_{217} (x, y) + F_{231} (x, y) \\ F_{217} (x, y) & = F_{218} (x, y) F_{22} (x, y) \\ F_{218} (x, y) & = 2 F_{26} (x) + F_{219} (x, y) + F_{226} (x, y) \\ F_{219} (x, y) & = F_{22} (x, y) F_{220} (x, y) \\ F_{220} (x, y) & = F_{218} (x, y) + F_{221} (x) \\ F_{221} (x) & = F_{222} (x) \\ F_{222} (x) & = F_{223} (x) F_{6} (x) \\ F_{223} (x) & = F_{224} (x) \\ F_{224} (x) & = F_{225} (x) F_{63} (x) F_{8} (x) \\ F_{225} (x) & = F_{1} (x) + F_{223} (x) \\ F_{226} (x, y) & = F_{227} (x, y) F_{8} (x) \\ F_{227} (x, y) & = F_{228} (x, y) + F_{229} (x, y) \\ F_{228} (x, y) & = F_{218} (x, y) + F_{32} (x, y) \\ F_{229} (x, y) & = F_{230} (x, y) \\ F_{230} (x, y) & = F_{6} (x) F_{76} (x, y) \\ F_{231} (x, y) & = F_{232} (x, y) F_{8} (x) \\ F_{232} (x, y) & = F_{233} (x, y) + F_{234} (x, y) \\ F_{233} (x, y) & = F_{163} (x, y) + F_{216} (x, y) \\ F_{234} (x, y) & = F_{235} (x, y) \\ F_{235} (x, y) & = F_{178} (x, y) F_{6} (x) \\ F_{236} (x, y) & = F_{237} (x, y) + F_{257} (x, y) \\ F_{237} (x, y) & = F_{238} (x, y) + F_{244} (x, y) + F_{255} (x, y) + F_{26} (x) \\ F_{238} (x, y) & = F_{22} (x, y) F_{239} (x, y) \\ F_{239} (x, y) & = F_{240} (x) + F_{242} (x, y) \\ F_{240} (x) & = F_{241} (x) \\ F_{241} (x) & = F_{45} (x) F_{8} (x) \\ F_{242} (x, y) & = 2 F_{26} (x) + F_{238} (x, y) + F_{243} (x, y) \\ F_{243} (x, y) & = F_{42} (x, y) F_{8} (x) \\ F_{244} (x, y) & = F_{245} (x, y) F_{8} (x) \\ F_{245} (x, y) & = F_{246} (x, y) + F_{247} (x, y) \\ F_{246} (x, y) & = F_{242} (x, y) + F_{42} (x, y) \\ F_{247} (x, y) & = F_{237} (x, y) + F_{248} (x, y) \\ F_{248} (x, y) & = 2 F_{26} (x) + F_{249} (x, y) + F_{250} (x, y) + F_{254} (x, y) \\ F_{249} (x, y) & = 0 \\ F_{250} (x, y) & = F_{251} (x, y) F_{8} (x) \\ F_{251} (x, y) & = F_{252} (x, y) + F_{253} (x, y) \\ F_{252} (x, y) & = F_{242} (x, y) \\ F_{253} (x, y) & = F_{248} (x, y) \\ F_{254} (x, y) & = F_{237} (x, y) F_{8} (x) \\ F_{255} (x, y) & = F_{256} (x, y) F_{8} (x) \\ F_{256} (x, y) & = F_{102} (x, y) + F_{237} (x, y) \\ F_{257} (x, y) & = F_{134} (x, y) + F_{258} (x, y) + F_{26} (x) + F_{300} (x, y) + F_{311} (x, y) \\ F_{258} (x, y) & = F_{22} (x, y) F_{259} (x, y) \\ F_{259} (x, y) & = F_{260} (x) + F_{297} (x, y) \\ F_{260} (x) & = F_{261} (x) \\ F_{261} (x) & = F_{262} (x, 1) \\ F_{262} (x, y) & = F_{263} (x, y) \\ F_{263} (x, y) & = 2 F_{26} (x) + F_{264} (x, y) + F_{269} (x, y) \\ F_{264} (x, y) & = F_{265} (x, y) \\ F_{265} (x, y) & = F_{22} (x, y) F_{266} (x, y) F_{6} (x) F_{8} (x) \\ F_{266} (x, y) & = F_{1} (x) + F_{267} (x, y) \\ F_{267} (x, y) & = F_{268} (x, y) \\ F_{268} (x, y) & = F_{22} (x, y) F_{266} (x, y) \\ F_{269} (x, y) & = F_{270} (x, y) F_{8} (x) \\ F_{270} (x, y) & = F_{271} (x, y) + F_{274} (x, y) \\ F_{271} (x, y) & = F_{263} (x, y) + F_{272} (x, y) \\ F_{272} (x, y) & = F_{273} (x, y) \\ F_{273} (x, y) & = F_{267} (x, y) F_{8} (x) \\ F_{274} (x, y) & = - \frac{F_{275} (x, 1) y - F_{275} (x, y)}{- 1 + y} \\ F_{275} (x, y) & = F_{276} (x, y) + F_{280} (x, y) \\ F_{276} (x, y) & = F_{277} (x, y) \\ F_{277} (x, y) & = F_{278} (x, y) F_{8} (x) \\ F_{278} (x, y) & = F_{279} (x, y) \\ F_{279} (x, y) & = F_{22} (x, y) F_{267} (x, y) \\ F_{280} (x, y) & = F_{281} (x, y) \\ F_{281} (x, y) & = F_{282} (x, y) F_{8} (x) \\ F_{282} (x, y) & = F_{26} (x) + F_{283} (x, y) + F_{285} (x, y) \\ F_{283} (x, y) & = F_{284} (x, y) \\ F_{284} (x, y) & = F_{22} (x, y) F_{267} (x, y) F_{6} (x) \\ F_{285} (x, y) & = F_{286} (x, y) F_{8} (x) \\ F_{286} (x, y) & = F_{287} (x, y) + F_{288} (x, y) \\ F_{287} (x, y) & = F_{278} (x, y) + F_{282} (x, y) \\ F_{288} (x, y) & = F_{289} (x, y) + F_{294} (x, y) \\ F_{289} (x, y) & = F_{290} (x, y) \\ F_{290} (x, y) & = F_{22} (x, y) F_{291} (x, y) \\ F_{291} (x, y) & = F_{292} (x, y) \\ F_{292} (x, y) & = F_{22} (x, y) F_{293} (x, y) \\ F_{293} (x, y) & = F_{291} (x, y) + F_{45} (x) \\ F_{294} (x, y) & = F_{295} (x, y) \\ F_{295} (x, y) & = F_{22} (x, y) F_{296} (x, y) \\ F_{296} (x, y) & = - \frac{F_{282} (x, 1) y - F_{282} (x, y)}{- 1 + y} \\ F_{297} (x, y) & = 2 F_{26} (x) + F_{258} (x, y) + F_{298} (x, y) + F_{299} (x, y) \\ F_{298} (x, y) & = F_{50} (x, y) F_{8} (x) \\ F_{299} (x, y) & = 0 \\ F_{300} (x, y) & = F_{301} (x, y) F_{8} (x) \\ F_{301} (x, y) & = F_{302} (x, y) + F_{303} (x, y) \\ F_{302} (x, y) & = F_{297} (x, y) + F_{50} (x, y) \\ F_{303} (x, y) & = F_{257} (x, y) + F_{304} (x, y) \\ F_{304} (x, y) & = 2 F_{26} (x) + F_{305} (x, y) + F_{306} (x, y) + F_{309} (x, y) + F_{310} (x, y) \\ F_{305} (x, y) & = 0 \\ F_{306} (x, y) & = F_{307} (x, y) \\ F_{307} (x, y) & = F_{308} (x, y) F_{8} (x) \\ F_{308} (x, y) & = F_{297} (x, y) + F_{304} (x, y) \\ F_{309} (x, y) & = F_{257} (x, y) F_{8} (x) \\ F_{310} (x, y) & = 0 \\ F_{311} (x, y) & = F_{312} (x, y) F_{8} (x) \\ F_{312} (x, y) & = F_{117} (x, y) + F_{257} (x, y) \\ F_{313} (x) & = F_{314} (x) F_{8} (x) \\ F_{314} (x) & = F_{315} (x) + F_{379} (x) \\ F_{315} (x) & = F_{316} (x) + F_{327} (x) \\ F_{316} (x) & = F_{317} (x) \\ F_{317} (x) & = F_{318} (x) F_{8} (x) \\ F_{318} (x) & = F_{319} (x) + F_{320} (x) \\ F_{319} (x) & = F_{1} (x) + F_{8} (x) \\ F_{320} (x) & = F_{316} (x) + F_{321} (x) \\ F_{321} (x) & = F_{26} (x) + F_{322} (x) + F_{326} (x) \\ F_{322} (x) & = F_{323} (x) F_{8} (x) \\ F_{323} (x) & = F_{324} (x) + F_{325} (x) \\ F_{324} (x) & = F_{8} (x) \\ F_{325} (x) & = F_{321} (x) \\ F_{326} (x) & = F_{316} (x) F_{8} (x) \\ F_{327} (x) & = F_{26} (x) + F_{328} (x) + F_{334} (x) \\ F_{328} (x) & = F_{329} (x) F_{8} (x) \\ F_{329} (x) & = F_{330} (x) + F_{331} (x) \\ F_{330} (x) & = F_{327} (x) + F_{6} (x) \\ F_{331} (x) & = F_{332} (x) \\ F_{332} (x) & = F_{333} (x) F_{6} (x) F_{61} (x) \\ F_{333} (x) & = F_{1} (x) + F_{316} (x) \\ F_{334} (x) & = F_{335} (x) F_{8} (x) \\ F_{335} (x) & = F_{315} (x) + F_{336} (x) \\ F_{336} (x) & = F_{337} (x, 1) \\ F_{337} (x, y) & = F_{338} (x, y) + F_{354} (x, y) \\ F_{338} (x, y) & = F_{26} (x) + F_{339} (x, y) + F_{349} (x, y) \\ F_{339} (x, y) & = F_{340} (x, y) F_{8} (x) \\ F_{340} (x, y) & = F_{341} (x, y) + F_{342} (x, y) \\ F_{341} (x, y) & = F_{267} (x, y) + F_{272} (x, y) \\ F_{342} (x, y) & = F_{338} (x, y) + F_{343} (x, y) \\ F_{343} (x, y) & = 2 F_{26} (x) + F_{344} (x, y) + F_{348} (x, y) \\ F_{344} (x, y) & = F_{345} (x, y) F_{8} (x) \\ F_{345} (x, y) & = F_{346} (x, y) + F_{347} (x, y) \\ F_{346} (x, y) & = F_{272} (x, y) \\ F_{347} (x, y) & = F_{343} (x, y) \\ F_{348} (x, y) & = F_{338} (x, y) F_{8} (x) \\ F_{349} (x, y) & = F_{22} (x, y) F_{350} (x, y) \\ F_{350} (x, y) & = F_{351} (x, y) + F_{61} (x) \\ F_{351} (x, y) & = F_{26} (x) + F_{349} (x, y) + F_{352} (x, y) \\ F_{352} (x, y) & = F_{353} (x, y) F_{8} (x) \\ F_{353} (x, y) & = F_{267} (x, y) + F_{351} (x, y) \\ F_{354} (x, y) & = F_{26} (x) + F_{355} (x, y) + F_{374} (x, y) + F_{377} (x, y) \\ F_{355} (x, y) & = F_{356} (x, y) \\ F_{356} (x, y) & = F_{357} (x, y) F_{8} (x) \\ F_{357} (x, y) & = F_{354} (x, y) + F_{358} (x, y) \\ F_{358} (x, y) & = F_{26} (x) + F_{359} (x, y) + F_{361} (x, y) \\ F_{359} (x, y) & = F_{22} (x, y) F_{360} (x, y) \\ F_{360} (x, y) & = F_{358} (x, y) + F_{6} (x) \\ F_{361} (x, y) & = F_{362} (x, y) \\ F_{362} (x, y) & = F_{363} (x, y) F_{5} (x) F_{8} (x) \\ F_{363} (x, y) & = F_{22} (x, y) + F_{364} (x, y) \\ F_{364} (x, y) & = F_{26} (x) + F_{365} (x, y) + F_{366} (x, y) \\ F_{365} (x, y) & = F_{22} (x, y) F_{61} (x) \\ F_{366} (x, y) & = F_{367} (x, y) F_{8} (x) \\ F_{367} (x, y) & = F_{368} (x, y) + F_{371} (x, y) \\ F_{368} (x, y) & = F_{22} (x, y) + F_{369} (x, y) \\ F_{369} (x, y) & = F_{370} (x, y) \\ F_{370} (x, y) & = F_{368} (x, y) F_{8} (x) \\ F_{371} (x, y) & = F_{364} (x, y) + F_{372} (x, y) \\ F_{372} (x, y) & = F_{373} (x, y) \\ F_{373} (x, y) & = F_{371} (x, y) F_{8} (x) \\ F_{374} (x, y) & = F_{375} (x, y) \\ F_{375} (x, y) & = F_{22} (x, y) F_{376} (x, y) F_{6} (x) \\ F_{376} (x, y) & = F_{316} (x) + F_{338} (x, y) \\ F_{377} (x, y) & = F_{378} (x, y) F_{8} (x) \\ F_{378} (x, y) & = - \frac{y (F_{337} (x, 1) - F_{337} (x, y))}{- 1 + y} \\ F_{379} (x) & = F_{380} (x) + F_{393} (x) \\ F_{380} (x) & = F_{26} (x) + F_{381} (x) + F_{391} (x) \\ F_{381} (x) & = F_{382} (x) F_{8} (x) \\ F_{382} (x) & = F_{383} (x) + F_{384} (x) \\ F_{383} (x) & = F_{240} (x) + F_{45} (x) \\ F_{384} (x) & = F_{380} (x) + F_{385} (x) \\ F_{385} (x) & = 2 F_{26} (x) + F_{386} (x) + F_{390} (x) \\ F_{386} (x) & = F_{387} (x) F_{8} (x) \\ F_{387} (x) & = F_{388} (x) + F_{389} (x) \\ F_{388} (x) & = F_{240} (x) \\ F_{389} (x) & = F_{385} (x) \\ F_{390} (x) & = F_{380} (x) F_{8} (x) \\ F_{391} (x) & = F_{392} (x) F_{8} (x) \\ F_{392} (x) & = F_{316} (x) + F_{380} (x) \\ F_{393} (x) & = F_{26} (x) + F_{394} (x) + F_{404} (x) + F_{406} (x) \\ F_{394} (x) & = F_{395} (x) F_{8} (x) \\ F_{395} (x) & = F_{396} (x) + F_{397} (x) \\ F_{396} (x) & = F_{260} (x) + F_{53} (x) \\ F_{397} (x) & = F_{393} (x) + F_{398} (x) \\ F_{398} (x) & = 2 F_{26} (x) + F_{399} (x) + F_{402} (x) + F_{403} (x) \\ F_{399} (x) & = F_{400} (x) \\ F_{400} (x) & = F_{401} (x) F_{8} (x) \\ F_{401} (x) & = F_{260} (x) + F_{398} (x) \\ F_{402} (x) & = F_{393} (x) F_{8} (x) \\ F_{403} (x) & = 0 \\ F_{404} (x) & = F_{405} (x) F_{8} (x) \\ F_{405} (x) & = F_{327} (x) + F_{393} (x) \\ F_{406} (x) & = F_{407} (x) \\ F_{407} (x) & = F_{408} (x, 1) \\ F_{408} (x, y) & = F_{409} (x, y) F_{5} (x) F_{8} (x) \\ F_{409} (x, y) & = F_{410} (x, y) + F_{412} (x, y) \\ F_{410} (x, y) & = F_{411} (x, y) \\ F_{411} (x, y) & = F_{22} (x, y) F_{61} (x) \\ F_{412} (x, y) & = 2 F_{26} (x) + F_{413} (x, y) + F_{419} (x, y) \\ F_{413} (x, y) & = F_{22} (x, y) F_{414} (x) \\ F_{414} (x) & = F_{26} (x) + F_{415} (x) + F_{417} (x) \\ F_{415} (x) & = F_{416} (x) F_{8} (x) \\ F_{416} (x) & = F_{414} (x) + F_{61} (x) \\ F_{417} (x) & = F_{418} (x) F_{8} (x) \\ F_{418} (x) & = F_{414} (x) + F_{61} (x) \\ F_{419} (x, y) & = F_{420} (x, y) F_{8} (x) \\ F_{420} (x, y) & = F_{421} (x, y) + F_{424} (x, y) \\ F_{421} (x, y) & = F_{410} (x, y) + F_{422} (x, y) \\ F_{422} (x, y) & = F_{423} (x, y) \\ F_{423} (x, y) & = F_{421} (x, y) F_{8} (x) \\ F_{424} (x, y) & = F_{412} (x, y) + F_{425} (x, y) \\ F_{425} (x, y) & = F_{426} (x, y) \\ F_{426} (x, y) & = F_{424} (x, y) F_{8} (x) \end{aligned}

This specification was found using the strategy pack "Insertion Row And Col Placements Tracked Fusion Req Corrob" and has 370 rules.

Found on April 26, 2021.

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\begin{aligned} F_{0} (x) & = F_{1} (x) + F_{2} (x) \\ F_{1} (x) & = 1 \\ F_{2} (x) & = F_{3} (x) \\ F_{3} (x) & = F_{13} (x) F_{4} (x) \\ F_{4} (x) & = F_{14} (x) + F_{5} (x) \\ F_{5} (x) & = F_{1} (x) + F_{6} (x) \\ F_{6} (x) & = F_{13} (x) F_{7} (x) \\ F_{7} (x) & = F_{8} (x, 1) \\ F_{8} (x, y) & = F_{1} (x) + F_{11} (x, y) + F_{9} (x, y) \\ F_{9} (x, y) & = F_{10} (x, y) F_{8} (x, y) \\ F_{10} (x, y) & = y x \\ F_{11} (x, y) & = F_{12} (x, y) F_{13} (x) \\ F_{12} (x, y) & = - \frac{- y F_{8} (x, y) + F_{8} (x, 1)}{- 1 + y} \\ F_{13} (x) & = x \\ F_{14} (x) & = F_{15} (x) + F_{48} (x) \\ F_{15} (x) & = F_{16} (x) \\ F_{16} (x) & = F_{13} (x) F_{17} (x) \\ F_{17} (x) & = F_{18} (x) + F_{21} (x) \\ F_{18} (x) & = F_{1} (x) + F_{19} (x) \\ F_{19} (x) & = F_{20} (x) \\ F_{20} (x) & = F_{13} (x) F_{18} (x) \\ F_{21} (x) & = F_{22} (x) + F_{34} (x) \\ F_{22} (x) & = F_{23} (x) \\ F_{23} (x) & = F_{13} (x) F_{24} (x) \\ F_{24} (x) & = F_{25} (x) + F_{26} (x) \\ F_{25} (x) & = F_{1} (x) + F_{13} (x) \\ F_{26} (x) & = F_{22} (x) + F_{27} (x) \\ F_{27} (x) & = F_{28} (x) + F_{29} (x) + F_{33} (x) \\ F_{28} (x) & = 0 \\ F_{29} (x) & = F_{13} (x) F_{30} (x) \\ F_{30} (x) & = F_{31} (x) + F_{32} (x) \\ F_{31} (x) & = F_{13} (x) \\ F_{32} (x) & = F_{27} (x) \\ F_{33} (x) & = F_{13} (x) F_{22} (x) \\ F_{34} (x) & = F_{28} (x) + F_{35} (x) + F_{47} (x) \\ F_{35} (x) & = F_{13} (x) F_{36} (x) \\ F_{36} (x) & = F_{37} (x) + F_{40} (x) \\ F_{37} (x) & = F_{19} (x) + F_{38} (x) \\ F_{38} (x) & = F_{39} (x) \\ F_{39} (x) & = F_{13} (x) F_{19} (x) \\ F_{40} (x) & = F_{34} (x) + F_{41} (x) \\ F_{41} (x) & = 2 F_{28} (x) + F_{42} (x) + F_{46} (x) \\ F_{42} (x) & = F_{13} (x) F_{43} (x) \\ F_{43} (x) & = F_{44} (x) + F_{45} (x) \\ F_{44} (x) & = F_{38} (x) \\ F_{45} (x) & = F_{41} (x) \\ F_{46} (x) & = F_{13} (x) F_{34} (x) \\ F_{47} (x) & = F_{13} (x) F_{21} (x) \\ F_{48} (x) & = F_{246} (x) + F_{28} (x) + F_{49} (x) \\ F_{49} (x) & = F_{13} (x) F_{50} (x) \\ F_{50} (x) & = F_{51} (x) + F_{71} (x) \\ F_{51} (x) & = F_{52} (x) + F_{61} (x) \\ F_{52} (x) & = F_{53} (x) \\ F_{53} (x) & = F_{13} (x) F_{54} (x) \\ F_{54} (x) & = F_{55} (x) + F_{58} (x) \\ F_{55} (x) & = F_{1} (x) + F_{56} (x) \\ F_{56} (x) & = F_{57} (x) \\ F_{57} (x) & = F_{13} (x) F_{55} (x) \\ F_{58} (x) & = F_{52} (x) + F_{59} (x) \\ F_{59} (x) & = F_{60} (x) \\ F_{60} (x) & = F_{13} (x) F_{58} (x) \\ F_{61} (x) & = F_{28} (x) + F_{62} (x) + F_{63} (x) \\ F_{62} (x) & = F_{13} (x) F_{51} (x) \\ F_{63} (x) & = F_{13} (x) F_{64} (x) \\ F_{64} (x) & = F_{65} (x) + F_{68} (x) \\ F_{65} (x) & = F_{19} (x) + F_{66} (x) \\ F_{66} (x) & = F_{67} (x) \\ F_{67} (x) & = F_{13} (x) F_{65} (x) \\ F_{68} (x) & = F_{61} (x) + F_{69} (x) \\ F_{69} (x) & = F_{70} (x) \\ F_{70} (x) & = F_{13} (x) F_{68} (x) \\ F_{71} (x) & = F_{227} (x) + F_{72} (x) \\ F_{72} (x) & = F_{73} (x) \\ F_{73} (x) & = F_{13} (x) F_{74} (x) \\ F_{74} (x) & = F_{75} (x) + F_{76} (x) \\ F_{75} (x) & = F_{55} {(x)}^{2} F_{15} (x) \\ F_{76} (x) & = F_{153} (x) + F_{77} (x) \\ F_{77} (x) & = F_{78} (x) + F_{79} (x) \\ F_{78} (x) & = F_{15} (x) F_{55} (x) \\ F_{79} (x) & = F_{151} (x) + F_{80} (x) \\ F_{80} (x) & = F_{115} (x) + F_{28} (x) + F_{81} (x) \\ F_{81} (x) & = F_{13} (x) F_{82} (x) \\ F_{82} (x) & = F_{83} (x) + F_{86} (x) \\ F_{83} (x) & = F_{19} (x) + F_{84} (x) \\ F_{84} (x) & = F_{85} (x) \\ F_{85} (x) & = F_{13} (x) F_{83} (x) \\ F_{86} (x) & = F_{101} (x) + F_{87} (x) \\ F_{87} (x) & = F_{28} (x) + F_{88} (x) + F_{96} (x) \\ F_{88} (x) & = F_{13} (x) F_{89} (x) \\ F_{89} (x) & = F_{37} (x) + F_{90} (x) \\ F_{90} (x) & = F_{87} (x) + F_{91} (x) \\ F_{91} (x) & = 2 F_{28} (x) + F_{92} (x) + F_{95} (x) \\ F_{92} (x) & = F_{13} (x) F_{93} (x) \\ F_{93} (x) & = F_{44} (x) + F_{94} (x) \\ F_{94} (x) & = F_{91} (x) \\ F_{95} (x) & = F_{13} (x) F_{87} (x) \\ F_{96} (x) & = F_{13} (x) F_{97} (x) \\ F_{97} (x) & = F_{56} (x) + F_{98} (x) \\ F_{98} (x) & = F_{28} (x) + F_{96} (x) + F_{99} (x) \\ F_{99} (x) & = F_{100} (x) F_{13} (x) \\ F_{100} (x) & = F_{19} (x) + F_{98} (x) \\ F_{101} (x) & = 2 F_{28} (x) + F_{102} (x) + F_{114} (x) \\ F_{102} (x) & = F_{103} (x) F_{13} (x) \\ F_{103} (x) & = F_{104} (x) + F_{107} (x) \\ F_{104} (x) & = F_{105} (x) + F_{84} (x) \\ F_{105} (x) & = F_{106} (x) \\ F_{106} (x) & = F_{13} (x) F_{84} (x) \\ F_{107} (x) & = F_{101} (x) + F_{108} (x) \\ F_{108} (x) & = 3 F_{28} (x) + F_{109} (x) + F_{113} (x) \\ F_{109} (x) & = F_{110} (x) F_{13} (x) \\ F_{110} (x) & = F_{111} (x) + F_{112} (x) \\ F_{111} (x) & = F_{105} (x) \\ F_{112} (x) & = F_{108} (x) \\ F_{113} (x) & = F_{101} (x) F_{13} (x) \\ F_{114} (x) & = F_{13} (x) F_{86} (x) \\ F_{115} (x) & = F_{116} (x) F_{13} (x) \\ F_{116} (x) & = F_{117} (x) + F_{97} (x) \\ F_{117} (x) & = F_{118} (x) + F_{134} (x) \\ F_{118} (x) & = F_{119} (x) + F_{123} (x) + F_{28} (x) \\ F_{119} (x) & = F_{120} (x) F_{13} (x) \\ F_{120} (x) & = F_{121} (x) + F_{13} (x) \\ F_{121} (x) & = F_{119} (x) + F_{122} (x) + F_{28} (x) \\ F_{122} (x) & = F_{13} (x) F_{56} (x) \\ F_{123} (x) & = F_{124} (x) F_{13} (x) \\ F_{124} (x) & = F_{125} (x) + F_{126} (x) \\ F_{125} (x) & = F_{121} (x) + F_{56} (x) \\ F_{126} (x) & = F_{118} (x) + F_{127} (x) \\ F_{127} (x) & = F_{128} (x) + F_{129} (x) + F_{133} (x) + F_{28} (x) \\ F_{128} (x) & = 0 \\ F_{129} (x) & = F_{13} (x) F_{130} (x) \\ F_{130} (x) & = F_{131} (x) + F_{132} (x) \\ F_{131} (x) & = F_{121} (x) \\ F_{132} (x) & = F_{127} (x) \\ F_{133} (x) & = F_{118} (x) F_{13} (x) \\ F_{134} (x) & = F_{135} (x) + F_{139} (x) + F_{150} (x) + F_{28} (x) \\ F_{135} (x) & = F_{13} (x) F_{136} (x) \\ F_{136} (x) & = F_{137} (x) + F_{38} (x) \\ F_{137} (x) & = 2 F_{28} (x) + F_{135} (x) + F_{138} (x) \\ F_{138} (x) & = F_{13} (x) F_{98} (x) \\ F_{139} (x) & = F_{13} (x) F_{140} (x) \\ F_{140} (x) & = F_{141} (x) + F_{142} (x) \\ F_{141} (x) & = F_{137} (x) + F_{98} (x) \\ F_{142} (x) & = F_{134} (x) + F_{143} (x) \\ F_{143} (x) & = 2 F_{28} (x) + F_{144} (x) + F_{145} (x) + F_{149} (x) \\ F_{144} (x) & = 0 \\ F_{145} (x) & = F_{13} (x) F_{146} (x) \\ F_{146} (x) & = F_{147} (x) + F_{148} (x) \\ F_{147} (x) & = F_{137} (x) \\ F_{148} (x) & = F_{143} (x) \\ F_{149} (x) & = F_{13} (x) F_{134} (x) \\ F_{150} (x) & = F_{117} (x) F_{13} (x) \\ F_{151} (x) & = F_{152} (x) \\ F_{152} (x) & = F_{56} {(x)}^{2} F_{15} (x) \\ F_{153} (x) & = F_{154} (x) + F_{155} (x) \\ F_{154} (x) & = F_{55} (x) F_{72} (x) \\ F_{155} (x) & = F_{156} (x, 1) \\ F_{156} (x, y) & = F_{157} (x, y) + F_{225} (x, y) \\ F_{157} (x, y) & = F_{158} (x, y) + F_{170} (x, y) + F_{28} (x) \\ F_{158} (x, y) & = F_{159} (x, y) \\ F_{159} (x, y) & = F_{13} (x) F_{160} (x, y) \\ F_{160} (x, y) & = F_{161} (x, y) + F_{166} (x, y) \\ F_{161} (x, y) & = F_{157} (x, y) + F_{162} (x, y) \\ F_{162} (x, y) & = F_{15} (x) F_{163} (x, y) \\ F_{163} (x, y) & = F_{164} (x, y) \\ F_{164} (x, y) & = F_{10} (x, y) F_{165} (x, y) \\ F_{165} (x, y) & = F_{1} (x) + F_{163} (x, y) \\ F_{166} (x, y) & = F_{163} (x, y) F_{167} (x, y) \\ F_{167} (x, y) & = F_{168} (x, y) + F_{169} (x, y) \\ F_{168} (x, y) & = F_{15} (x) F_{165} (x, y) \\ F_{169} (x, y) & = F_{157} (x, y) + F_{80} (x) \\ F_{170} (x, y) & = F_{171} (x, y) \\ F_{171} (x, y) & = F_{13} (x) F_{172} (x, y) \\ F_{172} (x, y) & = F_{173} (x, y) + F_{222} (x, y) \\ F_{173} (x, y) & = F_{174} (x, y) + F_{216} (x, y) \\ F_{174} (x, y) & = F_{175} (x, y) + F_{214} (x, y) + F_{28} (x) \\ F_{175} (x, y) & = F_{13} (x) F_{176} (x, y) \\ F_{176} (x, y) & = F_{177} (x, y) + F_{182} (x, y) \\ F_{177} (x, y) & = F_{163} (x, y) + F_{178} (x, y) \\ F_{178} (x, y) & = F_{179} (x, y) + F_{180} (x, y) + F_{28} (x) \\ F_{179} (x, y) & = F_{13} (x) F_{177} (x, y) \\ F_{180} (x, y) & = F_{10} (x, y) F_{181} (x, y) \\ F_{181} (x, y) & = F_{178} (x, y) + F_{19} (x) \\ F_{182} (x, y) & = F_{174} (x, y) + F_{183} (x, y) \\ F_{183} (x, y) & = F_{184} (x, y) + F_{204} (x, y) + F_{205} (x, y) + F_{28} (x) \\ F_{184} (x, y) & = F_{185} (x, y) \\ F_{185} (x, y) & = F_{13} (x) F_{186} (x, y) F_{203} (x) \\ F_{186} (x, y) & = F_{187} (x, y) + F_{190} (x, y) \\ F_{187} (x, y) & = F_{188} (x, y) \\ F_{188} (x, y) & = F_{10} (x, y) F_{189} (x, y) \\ F_{189} (x, y) & = F_{13} (x) + F_{187} (x, y) \\ F_{190} (x, y) & = 2 F_{28} (x) + F_{191} (x, y) + F_{195} (x, y) \\ F_{191} (x, y) & = F_{13} (x) F_{192} (x, y) \\ F_{192} (x, y) & = F_{193} (x, y) + F_{194} (x, y) \\ F_{193} (x, y) & = F_{187} (x, y) \\ F_{194} (x, y) & = F_{190} (x, y) \\ F_{195} (x, y) & = F_{10} (x, y) F_{196} (x, y) \\ F_{196} (x, y) & = F_{190} (x, y) + F_{197} (x) \\ F_{197} (x) & = F_{198} (x) + F_{202} (x) + F_{28} (x) \\ F_{198} (x) & = F_{13} (x) F_{199} (x) \\ F_{199} (x) & = F_{200} (x) + F_{201} (x) \\ F_{200} (x) & = F_{13} (x) \\ F_{201} (x) & = F_{197} (x) \\ F_{202} (x) & = F_{13} (x) F_{22} (x) \\ F_{203} (x) & = F_{1} (x) + F_{15} (x) \\ F_{204} (x, y) & = F_{13} (x) F_{182} (x, y) \\ F_{205} (x, y) & = F_{10} (x, y) F_{206} (x, y) \\ F_{206} (x, y) & = F_{183} (x, y) + F_{207} (x) \\ F_{207} (x) & = F_{208} (x) \\ F_{208} (x) & = F_{13} (x) F_{18} (x) F_{209} (x) \\ F_{209} (x) & = F_{15} (x) + F_{210} (x) \\ F_{210} (x) & = F_{211} (x) + F_{212} (x) \\ F_{211} (x) & = F_{203} (x) F_{56} (x) \\ F_{212} (x) & = F_{213} (x) \\ F_{213} (x) & = F_{13} (x) F_{210} (x) F_{55} (x) \\ F_{214} (x, y) & = F_{10} (x, y) F_{215} (x, y) \\ F_{215} (x, y) & = F_{15} (x) + F_{174} (x, y) \\ F_{216} (x, y) & = F_{15} (x) F_{217} (x, y) \\ F_{217} (x, y) & = F_{218} (x, y) + F_{220} (x, y) + F_{28} (x) \\ F_{218} (x, y) & = F_{13} (x) F_{219} (x, y) \\ F_{219} (x, y) & = F_{163} (x, y) + F_{217} (x, y) \\ F_{220} (x, y) & = F_{10} (x, y) F_{221} (x, y) \\ F_{221} (x, y) & = F_{217} (x, y) + F_{56} (x) \\ F_{222} (x, y) & = F_{157} (x, y) + F_{223} (x, y) \\ F_{223} (x, y) & = F_{224} (x, y) \\ F_{224} (x, y) & = F_{15} (x) F_{217} (x, y) F_{56} (x) \\ F_{225} (x, y) & = F_{226} (x, y) \\ F_{226} (x, y) & = F_{15} (x) F_{217} (x, y) F_{56} (x) \\ F_{227} (x) & = F_{228} (x) \\ F_{228} (x) & = F_{13} (x) F_{229} (x) \\ F_{229} (x) & = F_{230} (x) + F_{236} (x) \\ F_{230} (x) & = F_{15} (x) F_{231} (x) \\ F_{231} (x) & = F_{232} (x) + F_{51} (x) \\ F_{232} (x) & = F_{233} (x) F_{56} (x) \\ F_{233} (x) & = F_{234} (x) + F_{235} (x) \\ F_{234} (x) & = F_{1} (x) + F_{52} (x) \\ F_{235} (x) & = F_{19} (x) + F_{61} (x) \\ F_{236} (x) & = F_{237} (x) + F_{238} (x) \\ F_{237} (x) & = F_{210} (x) F_{51} (x) \\ F_{238} (x) & = F_{233} (x) F_{239} (x) \\ F_{239} (x) & = F_{240} (x) + F_{72} (x) \\ F_{240} (x) & = F_{15} (x) F_{241} (x) \\ F_{241} (x) & = F_{242} (x) + F_{244} (x) + F_{28} (x) \\ F_{242} (x) & = F_{13} (x) F_{243} (x) \\ F_{243} (x) & = F_{241} (x) + F_{56} (x) \\ F_{244} (x) & = F_{13} (x) F_{245} (x) \\ F_{245} (x) & = F_{241} (x) + F_{56} (x) \\ F_{246} (x) & = F_{13} (x) F_{247} (x) \\ F_{247} (x) & = F_{248} (x, 1) \\ F_{248} (x, y) & = F_{215} (x, y) + F_{249} (x, y) \\ F_{249} (x, y) & = F_{250} (x, y) + F_{48} (x) \\ F_{250} (x, y) & = F_{251} (x, y) + F_{28} (x) + F_{366} (x, y) + F_{369} (x, y) \\ F_{251} (x, y) & = F_{13} (x) F_{252} (x, y) \\ F_{252} (x, y) & = F_{253} (x, y) + F_{290} (x, y) \\ F_{253} (x, y) & = F_{254} (x, y) + F_{270} (x, y) \\ F_{254} (x, y) & = F_{255} (x, y) + F_{268} (x, y) + F_{28} (x) \\ F_{255} (x, y) & = F_{13} (x) F_{256} (x, y) \\ F_{256} (x, y) & = F_{257} (x, y) + F_{261} (x, y) \\ F_{257} (x, y) & = F_{163} (x, y) + F_{258} (x, y) \\ F_{258} (x, y) & = F_{259} (x, y) \\ F_{259} (x, y) & = F_{10} (x, y) F_{260} (x, y) \\ F_{260} (x, y) & = F_{258} (x, y) + F_{56} (x) \\ F_{261} (x, y) & = F_{262} (x, y) + F_{265} (x, y) \\ F_{262} (x, y) & = F_{263} (x, y) \\ F_{263} (x, y) & = F_{10} (x, y) F_{264} (x, y) \\ F_{264} (x, y) & = F_{262} (x, y) + F_{52} (x) \\ F_{265} (x, y) & = F_{266} (x, y) \\ F_{266} (x, y) & = F_{10} (x, y) F_{267} (x, y) \\ F_{267} (x, y) & = F_{265} (x, y) + F_{59} (x) \\ F_{268} (x, y) & = F_{10} (x, y) F_{269} (x, y) \\ F_{269} (x, y) & = F_{254} (x, y) + F_{52} (x) \\ F_{270} (x, y) & = F_{271} (x, y) + F_{272} (x, y) + F_{28} (x) + F_{288} (x, y) \\ F_{271} (x, y) & = F_{13} (x) F_{253} (x, y) \\ F_{272} (x, y) & = F_{13} (x) F_{273} (x, y) \\ F_{273} (x, y) & = F_{274} (x, y) + F_{281} (x, y) \\ F_{274} (x, y) & = F_{275} (x, y) + F_{278} (x, y) \\ F_{275} (x, y) & = F_{276} (x, y) \\ F_{276} (x, y) & = F_{10} (x, y) F_{277} (x, y) \\ F_{277} (x, y) & = F_{19} (x) + F_{275} (x, y) \\ F_{278} (x, y) & = F_{279} (x, y) \\ F_{279} (x, y) & = F_{10} (x, y) F_{280} (x, y) \\ F_{280} (x, y) & = F_{278} (x, y) + F_{66} (x) \\ F_{281} (x, y) & = F_{282} (x, y) + F_{285} (x, y) \\ F_{282} (x, y) & = F_{283} (x, y) \\ F_{283} (x, y) & = F_{10} (x, y) F_{284} (x, y) \\ F_{284} (x, y) & = F_{282} (x, y) + F_{61} (x) \\ F_{285} (x, y) & = F_{286} (x, y) \\ F_{286} (x, y) & = F_{10} (x, y) F_{287} (x, y) \\ F_{287} (x, y) & = F_{285} (x, y) + F_{69} (x) \\ F_{288} (x, y) & = F_{10} (x, y) F_{289} (x, y) \\ F_{289} (x, y) & = F_{270} (x, y) + F_{61} (x) \\ F_{290} (x, y) & = F_{291} (x, y) + F_{345} (x, y) \\ F_{291} (x, y) & = F_{292} (x, y) \\ F_{292} (x, y) & = F_{13} (x) F_{293} (x, y) \\ F_{293} (x, y) & = F_{294} (x, y) + F_{299} (x, y) \\ F_{294} (x, y) & = F_{295} (x, y) \\ F_{295} (x, y) & = F_{15} (x) F_{296} (x, y) F_{55} (x) \\ F_{296} (x, y) & = F_{297} (x, y) + F_{298} (x, y) \\ F_{297} (x, y) & = F_{163} (x, y) F_{55} (x) \\ F_{298} (x, y) & = F_{163} (x, y) F_{165} (x, y) \\ F_{299} (x, y) & = F_{300} (x, y) + F_{308} (x, y) \\ F_{300} (x, y) & = F_{301} (x, y) + F_{303} (x, y) \\ F_{301} (x, y) & = F_{302} (x, y) \\ F_{302} (x, y) & = F_{163} (x, y) F_{210} (x) F_{55} (x) \\ F_{303} (x, y) & = F_{304} (x, y) + F_{305} (x, y) \\ F_{304} (x, y) & = F_{165} (x, y) F_{174} (x, y) F_{55} (x) \\ F_{305} (x, y) & = F_{156} (x, y) + F_{306} (x, y) \\ F_{306} (x, y) & = F_{307} (x, y) \\ F_{307} (x, y) & = F_{15} (x) F_{163} (x, y) F_{217} (x, y) F_{55} (x) \\ F_{308} (x, y) & = F_{309} (x, y) + F_{310} (x, y) \\ F_{309} (x, y) & = F_{291} (x, y) F_{55} (x) \\ F_{310} (x, y) & = - \frac{F_{311} (x, 1) y - F_{311} (x, y)}{- 1 + y} \\ F_{311} (x, y) & = F_{312} (x, y) + F_{343} (x, y) \\ F_{312} (x, y) & = F_{28} (x) + F_{313} (x, y) + F_{327} (x, y) \\ F_{313} (x, y) & = F_{314} (x, y) \\ F_{314} (x, y) & = F_{13} (x) F_{315} (x, y) \\ F_{315} (x, y) & = F_{316} (x, y) + F_{320} (x, y) \\ F_{316} (x, y) & = F_{312} (x, y) + F_{317} (x, y) \\ F_{317} (x, y) & = F_{15} (x) F_{318} (x, y) \\ F_{318} (x, y) & = F_{319} (x, y) \\ F_{319} (x, y) & = F_{10} (x, y) F_{163} (x, y) \\ F_{320} (x, y) & = F_{321} (x, y) + F_{324} (x, y) \\ F_{321} (x, y) & = F_{15} (x) F_{322} (x, y) \\ F_{322} (x, y) & = F_{318} (x, y) + F_{323} (x, y) \\ F_{323} (x, y) & = F_{163} {(x, y)}^{2} \\ F_{324} (x, y) & = F_{325} (x, y) + F_{326} (x, y) \\ F_{325} (x, y) & = F_{318} (x, y) F_{80} (x) \\ F_{326} (x, y) & = F_{157} (x, y) F_{163} (x, y) \\ F_{327} (x, y) & = F_{328} (x, y) \\ F_{328} (x, y) & = F_{13} (x) F_{329} (x, y) \\ F_{329} (x, y) & = F_{330} (x, y) + F_{340} (x, y) \\ F_{330} (x, y) & = F_{331} (x, y) + F_{335} (x, y) \\ F_{331} (x, y) & = F_{332} (x, y) \\ F_{332} (x, y) & = F_{10} (x, y) F_{333} (x, y) \\ F_{333} (x, y) & = F_{162} (x, y) + F_{334} (x, y) \\ F_{334} (x, y) & = F_{157} (x, y) + F_{174} (x, y) \\ F_{335} (x, y) & = F_{15} (x) F_{336} (x, y) \\ F_{336} (x, y) & = F_{28} (x) + F_{337} (x, y) + F_{339} (x, y) \\ F_{337} (x, y) & = F_{13} (x) F_{338} (x, y) \\ F_{338} (x, y) & = F_{318} (x, y) + F_{336} (x, y) \\ F_{339} (x, y) & = F_{10} (x, y) F_{217} (x, y) \\ F_{340} (x, y) & = F_{312} (x, y) + F_{341} (x, y) \\ F_{341} (x, y) & = F_{342} (x, y) \\ F_{342} (x, y) & = F_{15} (x) F_{336} (x, y) F_{56} (x) \\ F_{343} (x, y) & = F_{344} (x, y) \\ F_{344} (x, y) & = F_{15} (x) F_{336} (x, y) F_{56} (x) \\ F_{345} (x, y) & = F_{346} (x, y) \\ F_{346} (x, y) & = F_{13} (x) F_{347} (x, y) \\ F_{347} (x, y) & = F_{348} (x, y) + F_{354} (x, y) \\ F_{348} (x, y) & = F_{349} (x, y) \\ F_{349} (x, y) & = F_{15} (x) F_{350} (x, y) \\ F_{350} (x, y) & = F_{253} (x, y) + F_{351} (x, y) \\ F_{351} (x, y) & = F_{163} (x, y) F_{352} (x, y) \\ F_{352} (x, y) & = F_{232} (x) + F_{353} (x, y) \\ F_{353} (x, y) & = F_{269} (x, y) + F_{289} (x, y) \\ F_{354} (x, y) & = F_{355} (x, y) + F_{358} (x, y) \\ F_{355} (x, y) & = F_{356} (x, y) + F_{357} (x, y) \\ F_{356} (x, y) & = F_{210} (x) F_{253} (x, y) \\ F_{357} (x, y) & = F_{173} (x, y) F_{353} (x, y) \\ F_{358} (x, y) & = F_{233} (x) F_{359} (x, y) \\ F_{359} (x, y) & = F_{291} (x, y) + F_{360} (x, y) \\ F_{360} (x, y) & = F_{15} (x) F_{361} (x, y) \\ F_{361} (x, y) & = 2 F_{28} (x) + F_{362} (x, y) + F_{364} (x, y) \\ F_{362} (x, y) & = F_{13} (x) F_{363} (x, y) \\ F_{363} (x, y) & = F_{258} (x, y) + F_{361} (x, y) \\ F_{364} (x, y) & = F_{10} (x, y) F_{365} (x, y) \\ F_{365} (x, y) & = F_{241} (x) + F_{361} (x, y) \\ F_{366} (x, y) & = - \frac{y (F_{367} (x, 1) - F_{367} (x, y))}{- 1 + y} \\ F_{367} (x, y) & = F_{13} (x) F_{368} (x, y) \\ F_{368} (x, y) & = F_{174} (x, y) + F_{250} (x, y) \\ F_{369} (x, y) & = F_{10} (x, y) F_{249} (x, y) \end{aligned}

This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Req Corrob" and has 164 rules.

Found on April 26, 2021.

Finding the specification took 1868 seconds.

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\begin{aligned} F_{0} (x) & = F_{1} (x) + F_{2} (x) \\ F_{1} (x) & = 1 \\ F_{2} (x) & = F_{11} (x) F_{3} (x) \\ F_{3} (x) & = F_{1} (x) + F_{152} (x) + F_{4} (x) \\ F_{4} (x) & = F_{11} (x) F_{5} (x) \\ F_{5} (x) & = F_{6} (x, 1) \\ F_{6} (x, y) & = F_{1} (x) + F_{12} (x, y) + F_{7} (x, y) + F_{9} (x, y) \\ F_{7} (x, y) & = F_{6} (x, y) F_{8} (x, y) \\ F_{8} (x, y) & = y x \\ F_{9} (x, y) & = F_{10} (x, y) F_{11} (x) \\ F_{10} (x, y) & = - \frac{- y F_{6} (x, y) + F_{6} (x, 1)}{- 1 + y} \\ F_{11} (x) & = x \\ F_{12} (x, y) & = F_{11} (x) F_{13} (x, y) \\ F_{13} (x, y) & = F_{14} (x, y) + F_{92} (x, y) \\ F_{14} (x, y) & = F_{1} (x) + F_{15} (x, y) + F_{16} (x, y) + F_{17} (x, y) \\ F_{15} (x, y) & = F_{14} (x, y) F_{8} (x, y) \\ F_{16} (x, y) & = F_{11} (x) F_{14} (x, y) \\ F_{17} (x, y) & = F_{11} (x) F_{18} (x, y) \\ F_{18} (x, y) & = F_{1} (x) + F_{19} (x, y) + F_{20} (x) + F_{42} (x, y) + F_{91} (x, y) \\ F_{19} (x, y) & = F_{18} (x, y) F_{8} (x, y) \\ F_{20} (x) & = F_{21} (x) \\ F_{21} (x) & = F_{11} (x) F_{22} (x) F_{32} (x) \\ F_{22} (x) & = F_{1} (x) + F_{23} (x) \\ F_{23} (x) & = F_{24} (x) \\ F_{24} (x) & = F_{11} (x) F_{25} (x) \\ F_{25} (x) & = F_{26} (x) + F_{29} (x) \\ F_{26} (x) & = F_{1} (x) + F_{27} (x) \\ F_{27} (x) & = F_{28} (x) \\ F_{28} (x) & = F_{11} (x) F_{26} (x) \\ F_{29} (x) & = F_{23} (x) + F_{30} (x) \\ F_{30} (x) & = F_{31} (x) \\ F_{31} (x) & = F_{11} (x) F_{29} (x) \\ F_{32} (x) & = F_{1} (x) + F_{33} (x) \\ F_{33} (x) & = F_{34} (x) \\ F_{34} (x) & = F_{11} (x) F_{35} (x) \\ F_{35} (x) & = F_{32} (x) + F_{36} (x) \\ F_{36} (x) & = F_{33} (x) + F_{37} (x) \\ F_{37} (x) & = F_{38} (x) \\ F_{38} (x) & = F_{11} (x) F_{39} (x) \\ F_{39} (x) & = F_{40} (x) + F_{41} (x) \\ F_{40} (x) & = F_{33} (x) \\ F_{41} (x) & = F_{37} (x) \\ F_{42} (x, y) & = F_{11} (x) F_{43} (x, y) \\ F_{43} (x, y) & = F_{44} (x) + F_{61} (x, y) \\ F_{44} (x) & = F_{45} (x) \\ F_{45} (x) & = F_{32} (x) F_{46} (x) \\ F_{46} (x) & = F_{47} (x) + F_{60} (x) \\ F_{47} (x) & = F_{22} (x) + F_{48} (x) \\ F_{48} (x) & = F_{11} (x) + F_{49} (x) \\ F_{49} (x) & = F_{50} (x) + F_{51} (x) + F_{52} (x) \\ F_{50} (x) & = 0 \\ F_{51} (x) & = F_{11} (x) F_{27} (x) \\ F_{52} (x) & = F_{11} (x) F_{53} (x) \\ F_{53} (x) & = F_{54} (x) + F_{57} (x) \\ F_{54} (x) & = F_{11} (x) + F_{55} (x) \\ F_{55} (x) & = F_{56} (x) \\ F_{56} (x) & = F_{11} (x) F_{54} (x) \\ F_{57} (x) & = F_{49} (x) + F_{58} (x) \\ F_{58} (x) & = F_{59} (x) \\ F_{59} (x) & = F_{11} (x) F_{57} (x) \\ F_{60} (x) & = F_{48} (x) \\ F_{61} (x, y) & = F_{62} (x, y) + F_{68} (x, y) \\ F_{62} (x, y) & = 2 F_{50} (x) + F_{19} (x, y) + F_{63} (x, y) + F_{64} (x, y) \\ F_{63} (x, y) & = F_{11} (x) F_{61} (x, y) \\ F_{64} (x, y) & = F_{11} (x) F_{65} (x, y) \\ F_{65} (x, y) & = F_{15} (x, y) + F_{50} (x) + F_{66} (x, y) + F_{67} (x, y) \\ F_{66} (x, y) & = F_{11} (x) F_{65} (x, y) \\ F_{67} (x, y) & = F_{11} (x) F_{62} (x, y) \\ F_{68} (x, y) & = F_{69} (x, y) \\ F_{69} (x, y) & = F_{32} (x) F_{70} (x, y) \\ F_{70} (x, y) & = F_{71} (x, y) + F_{76} (x, y) \\ F_{71} (x, y) & = F_{72} (x, y) \\ F_{72} (x, y) & = F_{11} (x) F_{73} (x, y) \\ F_{73} (x, y) & = F_{74} (x, y) \\ F_{74} (x, y) & = F_{75} (x, y) F_{8} (x, y) \\ F_{75} (x, y) & = F_{1} (x) + F_{73} (x, y) \\ F_{76} (x, y) & = 2 F_{50} (x) + F_{77} (x, y) + F_{83} (x, y) \\ F_{77} (x, y) & = F_{11} (x) F_{78} (x, y) \\ F_{78} (x, y) & = F_{50} (x) + F_{79} (x, y) + F_{81} (x, y) \\ F_{79} (x, y) & = F_{8} (x, y) F_{80} (x, y) \\ F_{80} (x, y) & = F_{27} (x) + F_{78} (x, y) \\ F_{81} (x, y) & = F_{11} (x) F_{82} (x, y) \\ F_{82} (x, y) & = F_{73} (x, y) + F_{78} (x, y) \\ F_{83} (x, y) & = F_{11} (x) F_{84} (x, y) \\ F_{84} (x, y) & = F_{85} (x, y) + F_{88} (x, y) \\ F_{85} (x, y) & = F_{71} (x, y) + F_{86} (x, y) \\ F_{86} (x, y) & = F_{87} (x, y) \\ F_{87} (x, y) & = F_{11} (x) F_{85} (x, y) \\ F_{88} (x, y) & = F_{76} (x, y) + F_{89} (x, y) \\ F_{89} (x, y) & = F_{90} (x, y) \\ F_{90} (x, y) & = F_{11} (x) F_{88} (x, y) \\ F_{91} (x, y) & = F_{11} (x) F_{14} (x, y) \\ F_{92} (x, y) & = F_{149} (x, y) + F_{150} (x, y) + F_{50} (x) + F_{93} (x, y) + F_{98} (x, y) \\ F_{93} (x, y) & = F_{8} (x, y) F_{94} (x, y) \\ F_{94} (x, y) & = 2 F_{50} (x) + F_{16} (x, y) + F_{93} (x, y) + F_{95} (x, y) \\ F_{95} (x, y) & = F_{96} (x, y) \\ F_{96} (x, y) & = F_{11} (x) F_{32} (x) F_{97} (x, y) \\ F_{97} (x, y) & = F_{48} (x) + F_{70} (x, y) \\ F_{98} (x, y) & = F_{11} (x) F_{99} (x, y) \\ F_{99} (x, y) & = F_{100} (x, y) + F_{13} (x, y) \\ F_{100} (x, y) & = 2 F_{50} (x) + F_{101} (x, y) + F_{102} (x, y) + F_{104} (x, y) + F_{105} (x, y) \\ F_{101} (x, y) & = F_{93} (x, y) \\ F_{102} (x, y) & = F_{103} (x, y) \\ F_{103} (x, y) & = F_{100} (x, y) F_{11} (x) \\ F_{104} (x, y) & = F_{11} (x) F_{13} (x, y) \\ F_{105} (x, y) & = F_{106} (x, y) \\ F_{106} (x, y) & = F_{107} (x, y) F_{11} (x) F_{32} (x) \\ F_{107} (x, y) & = F_{108} (x) + F_{127} (x, y) \\ F_{108} (x) & = F_{109} (x) + F_{48} (x) \\ F_{109} (x) & = F_{110} (x) + F_{112} (x) \\ F_{110} (x) & = F_{111} (x) \\ F_{111} (x) & = F_{11} (x) F_{27} (x) \\ F_{112} (x) & = 2 F_{50} (x) + F_{113} (x) + F_{119} (x) \\ F_{113} (x) & = F_{11} (x) F_{114} (x) \\ F_{114} (x) & = F_{115} (x) + F_{117} (x) + F_{50} (x) \\ F_{115} (x) & = F_{11} (x) F_{116} (x) \\ F_{116} (x) & = F_{114} (x) + F_{27} (x) \\ F_{117} (x) & = F_{11} (x) F_{118} (x) \\ F_{118} (x) & = F_{114} (x) + F_{27} (x) \\ F_{119} (x) & = F_{11} (x) F_{120} (x) \\ F_{120} (x) & = F_{121} (x) + F_{124} (x) \\ F_{121} (x) & = F_{110} (x) + F_{122} (x) \\ F_{122} (x) & = F_{123} (x) \\ F_{123} (x) & = F_{11} (x) F_{121} (x) \\ F_{124} (x) & = F_{112} (x) + F_{125} (x) \\ F_{125} (x) & = F_{126} (x) \\ F_{126} (x) & = F_{11} (x) F_{124} (x) \\ F_{127} (x, y) & = F_{128} (x, y) + F_{70} (x, y) \\ F_{128} (x, y) & = F_{129} (x, y) + F_{134} (x, y) \\ F_{129} (x, y) & = F_{130} (x, y) \\ F_{130} (x, y) & = F_{11} (x) F_{131} (x, y) \\ F_{131} (x, y) & = F_{132} (x, y) \\ F_{132} (x, y) & = F_{11} (x) F_{133} (x, y) \\ F_{133} (x, y) & = F_{131} (x, y) + F_{73} (x, y) \\ F_{134} (x, y) & = 3 F_{50} (x) + F_{135} (x, y) + F_{141} (x, y) \\ F_{135} (x, y) & = F_{11} (x) F_{136} (x, y) \\ F_{136} (x, y) & = 2 F_{50} (x) + F_{137} (x, y) + F_{139} (x, y) \\ F_{137} (x, y) & = F_{11} (x) F_{138} (x, y) \\ F_{138} (x, y) & = F_{136} (x, y) + F_{78} (x, y) \\ F_{139} (x, y) & = F_{11} (x) F_{140} (x, y) \\ F_{140} (x, y) & = F_{131} (x, y) + F_{136} (x, y) \\ F_{141} (x, y) & = F_{11} (x) F_{142} (x, y) \\ F_{142} (x, y) & = F_{143} (x, y) + F_{146} (x, y) \\ F_{143} (x, y) & = F_{129} (x, y) + F_{144} (x, y) \\ F_{144} (x, y) & = F_{145} (x, y) \\ F_{145} (x, y) & = F_{11} (x) F_{143} (x, y) \\ F_{146} (x, y) & = F_{134} (x, y) + F_{147} (x, y) \\ F_{147} (x, y) & = F_{148} (x, y) \\ F_{148} (x, y) & = F_{11} (x) F_{146} (x, y) \\ F_{149} (x, y) & = F_{11} (x) F_{92} (x, y) \\ F_{150} (x, y) & = F_{11} (x) F_{151} (x, y) \\ F_{151} (x, y) & = - \frac{- F_{62} (x, y) + F_{62} (x, 1)}{- 1 + y} \\ F_{152} (x) & = F_{11} (x) F_{153} (x) \\ F_{153} (x) & = F_{1} (x) + F_{154} (x) + F_{159} (x) + F_{162} (x) \\ F_{154} (x) & = F_{11} (x) F_{155} (x) \\ F_{155} (x) & = F_{153} (x) + F_{156} (x) \\ F_{156} (x) & = 2 F_{50} (x) + F_{157} (x) + F_{159} (x) + F_{160} (x) \\ F_{157} (x) & = F_{158} (x) \\ F_{158} (x) & = F_{11} (x) F_{156} (x) \\ F_{159} (x) & = F_{11} (x) F_{153} (x) \\ F_{160} (x) & = F_{161} (x) \\ F_{161} (x) & = F_{108} (x) F_{11} (x) F_{32} (x) \\ F_{162} (x) & = F_{11} (x) F_{163} (x) \\ F_{163} (x) & = F_{18} (x, 1) \end{aligned}

Av(1324, 2341)

This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Req Corrob" and has 141 rules.

Proof Tree

System of Equations

This specification was found using the strategy pack "Point And Row Placements Tracked Fusion" and has 263 rules.

Proof Tree

System of Equations

This specification was found using the strategy pack "Insertion Row Placements Tracked Fusion" and has 427 rules.

Proof Tree

System of Equations

This specification was found using the strategy pack "Insertion Row And Col Placements Tracked Fusion Req Corrob" and has 370 rules.

Proof Tree

System of Equations

This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Req Corrob" and has 164 rules.

Proof Tree

System of Equations