Av(1243, 1324, 1432)
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Counting Sequence
1, 1, 2, 6, 21, 79, 310, 1251, 5150, 21517, 90921, 387595, 1663936, 7183750, 31158310, ...
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This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Req Corrob" and has 24 rules.

Found on June 03, 2021.

Finding the specification took 703 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{15}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\ F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , 1, y\right)\\ F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , y z \right)\\ F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , z\right)+F_{18}\! \left(x , y , z\right)\\ F_{11}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x \right)\\ F_{14}\! \left(x , y\right) &= \frac{y F_{8}\! \left(x , y\right)-F_{8}\! \left(x , 1\right)}{-1+y}\\ F_{15}\! \left(x \right) &= x\\ F_{16}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= y x\\ F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\ F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\ F_{21}\! \left(x , y , z\right) &= F_{15}\! \left(x \right) F_{22}\! \left(x , y , z\right)\\ F_{22}\! \left(x , y , z\right) &= -\frac{y \left(F_{18}\! \left(x , 1, z\right)-F_{18}\! \left(x , y , z\right)\right)}{-1+y}\\ F_{23}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{18}\! \left(x , y , z\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Req Corrob" and has 31 rules.

Found on June 03, 2021.

Finding the specification took 797 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_{4}\! \left(x \right)\\ F_{3}\! \left(x \right) &= x\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\ F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , 1, y\right)\\ F_{8}\! \left(x , y , z\right) &= F_{9}\! \left(x , z , y\right)\\ F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y z , z\right)\\ F_{11}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , y z \right)\\ F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(x , y\right)+F_{30}\! \left(x , y , z\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\ F_{13}\! \left(x \right) &= 0\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{3}\! \left(x \right)\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , 1, y\right)\\ F_{17}\! \left(x , y , z\right) &= \frac{z \left(F_{18}\! \left(x , y , 1\right)-F_{18}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}\\ F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , y z \right)\\ F_{20}\! \left(x , y , z\right) &= F_{19}\! \left(x , y z , z\right)\\ F_{20}\! \left(x , y , z\right) &= F_{12}\! \left(x , z\right)+F_{21}\! \left(x , y , z\right)\\ F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y z , z\right)\\ F_{22}\! \left(x , y , z\right) &= F_{23}\! \left(x , z , y\right)\\ F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , z , y\right) F_{27}\! \left(x , y\right)\\ F_{24}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)\\ F_{25}\! \left(x , y , z\right) &= F_{26}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\ F_{26}\! \left(x , y , z\right) &= -\frac{y \left(F_{24}\! \left(x , 1, z\right)-F_{24}\! \left(x , y , z\right)\right)}{-1+y}\\ F_{27}\! \left(x , y\right) &= y x\\ F_{28}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{29}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)\\ F_{30}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , y z \right)\\ \end{align*}\)

This specification was found using the strategy pack "Insertion Row And Col Placements Tracked Fusion" and has 85 rules.

Found on June 03, 2021.

Finding the specification took 901 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8} \left(x \right)^{2} F_{9}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{9}\! \left(x \right) &= x\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{17}\! \left(x \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_{9}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x , 1\right)\\ F_{19}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{24}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= y x\\ F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{5}\! \left(x \right)\\ F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\ F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\ F_{32}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{6}\! \left(x \right)\\ F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right) F_{8}\! \left(x \right)\\ F_{34}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{6}\! \left(x \right)\\ F_{35}\! \left(x , y\right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\ F_{36}\! \left(x \right) &= 0\\ F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= -\frac{y \left(F_{39}\! \left(x , 1\right)-F_{39}\! \left(x , y\right)\right)}{-1+y}\\ F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{17}\! \left(x \right) F_{42}\! \left(x , y\right)\\ F_{42}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{36}\! \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_{9}\! \left(x \right)\\ F_{47}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y , 1\right)\\ F_{54}\! \left(x , y , z\right) &= F_{35}\! \left(x , y\right)+F_{55}\! \left(x , y , z\right)\\ F_{55}\! \left(x , y , z\right) &= F_{36}\! \left(x \right)+F_{56}\! \left(x , y , z\right)+F_{68}\! \left(x , y , z\right)\\ F_{56}\! \left(x , y , z\right) &= F_{57}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\ F_{57}\! \left(x , y , z\right) &= F_{58}\! \left(x , y , z\right)+F_{64}\! \left(x , y , z\right)\\ F_{58}\! \left(x , y , z\right) &= F_{42}\! \left(x , y\right) F_{59}\! \left(x , z\right)\\ F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\ F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)\\ F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{62}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= -\frac{y \left(F_{20}\! \left(x , 1\right)-F_{20}\! \left(x , y\right)\right)}{-1+y}\\ F_{64}\! \left(x , y , z\right) &= F_{65}\! \left(x , y , z\right)+F_{67}\! \left(x , y , z\right)\\ F_{65}\! \left(x , y , z\right) &= F_{66}\! \left(x , y , z\right)\\ F_{66}\! \left(x , y , z\right) &= F_{15}\! \left(x \right) F_{42}\! \left(x , z\right) F_{45}\! \left(x , y\right)\\ F_{67}\! \left(x , y , z\right) &= -\frac{z \left(F_{55}\! \left(x , y , 1\right)-F_{55}\! \left(x , y , z\right)\right)}{-1+z}\\ F_{68}\! \left(x , y , z\right) &= F_{26}\! \left(x , y\right) F_{69}\! \left(x , y , z\right)\\ F_{69}\! \left(x , y , z\right) &= F_{55}\! \left(x , y , z\right)+F_{70}\! \left(x , z\right)\\ F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{72}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{72}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)+F_{73}\! \left(x , y\right)\\ F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)\\ F_{74}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{42}\! \left(x , y\right) F_{50}\! \left(x \right)\\ F_{76}\! \left(x , y\right) &= -\frac{y \left(F_{70}\! \left(x , 1\right)-F_{70}\! \left(x , y\right)\right)}{-1+y}\\ F_{77}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\ F_{78}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{35}\! \left(x , y\right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{15}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x , 1\right)\\ F_{83}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{70}\! \left(x , y\right)\\ F_{84}\! \left(x \right) &= F_{43}\! \left(x , 1\right)\\ \end{align*}\)

This specification was found using the strategy pack "Insertion Row And Col Placements Tracked Fusion Req Corrob" and has 87 rules.

Found on June 03, 2021.

Finding the specification took 1352 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8} \left(x \right)^{2} F_{9}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{9}\! \left(x \right) &= x\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{17}\! \left(x \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_{9}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x , 1\right)\\ F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{26}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)\\ F_{27}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\ F_{28}\! \left(x , y\right) &= y x\\ F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{5}\! \left(x \right)\\ F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\ F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\ F_{32}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{33}\! \left(x , y\right)\\ F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{6}\! \left(x \right)\\ F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{8}\! \left(x \right)\\ F_{36}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)+F_{6}\! \left(x \right)\\ F_{37}\! \left(x , y\right) &= F_{38}\! \left(x \right)+F_{39}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\ F_{38}\! \left(x \right) &= 0\\ F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= -\frac{y \left(F_{41}\! \left(x , 1\right)-F_{41}\! \left(x , y\right)\right)}{-1+y}\\ F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{42}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{17}\! \left(x \right) F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{38}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{49}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{51}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y , 1\right)\\ F_{56}\! \left(x , y , z\right) &= F_{37}\! \left(x , y\right)+F_{57}\! \left(x , y , z\right)\\ F_{57}\! \left(x , y , z\right) &= F_{38}\! \left(x \right)+F_{58}\! \left(x , y , z\right)+F_{70}\! \left(x , y , z\right)\\ F_{58}\! \left(x , y , z\right) &= F_{59}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\ F_{59}\! \left(x , y , z\right) &= F_{60}\! \left(x , y , z\right)+F_{66}\! \left(x , y , z\right)\\ F_{60}\! \left(x , y , z\right) &= F_{44}\! \left(x , y\right) F_{61}\! \left(x , z\right)\\ F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)+F_{65}\! \left(x , y\right)\\ F_{62}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{64}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{65}\! \left(x , y\right) &= -\frac{y \left(F_{22}\! \left(x , 1\right)-F_{22}\! \left(x , y\right)\right)}{-1+y}\\ F_{66}\! \left(x , y , z\right) &= F_{67}\! \left(x , y , z\right)+F_{69}\! \left(x , y , z\right)\\ F_{67}\! \left(x , y , z\right) &= F_{68}\! \left(x , y , z\right)\\ F_{68}\! \left(x , y , z\right) &= F_{15}\! \left(x \right) F_{44}\! \left(x , z\right) F_{47}\! \left(x , y\right)\\ F_{69}\! \left(x , y , z\right) &= -\frac{z \left(F_{57}\! \left(x , y , 1\right)-F_{57}\! \left(x , y , z\right)\right)}{-1+z}\\ F_{70}\! \left(x , y , z\right) &= F_{28}\! \left(x , y\right) F_{71}\! \left(x , y , z\right)\\ F_{71}\! \left(x , y , z\right) &= F_{57}\! \left(x , y , z\right)+F_{72}\! \left(x , z\right)\\ F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)\\ F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{74}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\ F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\ F_{77}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{44}\! \left(x , y\right) F_{52}\! \left(x \right)\\ F_{78}\! \left(x , y\right) &= -\frac{y \left(F_{72}\! \left(x , 1\right)-F_{72}\! \left(x , y\right)\right)}{-1+y}\\ F_{79}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{80}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{37}\! \left(x , y\right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{15}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x , 1\right)\\ F_{85}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{72}\! \left(x , y\right)\\ F_{86}\! \left(x \right) &= F_{45}\! \left(x , 1\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Col Placements Tracked Fusion" and has 24 rules.

Found on June 03, 2021.

Finding the specification took 799 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{7}\! \left(x \right) &= x\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y , 1\right)\\ F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y z , z\right)\\ F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(x , y\right)+F_{18}\! \left(x , y , z\right)\\ F_{12}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{15}\! \left(x , y\right) &= -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}\\ F_{16}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= y x\\ F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , z\right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\ F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\ F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\ F_{22}\! \left(x , y , z\right) &= -\frac{z \left(F_{18}\! \left(x , y , 1\right)-F_{18}\! \left(x , y , z\right)\right)}{-1+z}\\ F_{23}\! \left(x , y , z\right) &= F_{17}\! \left(x , y\right) F_{18}\! \left(x , y , z\right)\\ \end{align*}\)