02143_02413_02431_20143_20413_20431_21043

Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3129, 17442, 99574, 579108, 3419056, 20440024, 123494294, 752913720, 4626460910, 28623829932, 178166605469, 1114930402440, 7010385859241, 44268641757686, 280626420185957, 1785180266234336, 11392541408667527, 72916422219043686, 467941980829808259, 3010430527688012228, 19411255413676902257, 125427990832979822646, 812056475420723211783, 5267089205038358557792, 34221205347220552639329, 222696131439707551192690, 1451375382406498882058182, 9472342505150837980903252, 61902740691871232108044808, 405046171027094337860731016, 2653452918572449121584479218, 17402149338897585751600805720, 114249329148950156856234234746, 750827625471004622211463752436, 4939021884727022458842867544952, 32518886411316671674479523832840, 214291873751757716767485377868124, 1413297776087416103371614244161400, 9328318771999552335668313231280520, 61616876783670657420750133354448784, 407294397185839959305030086486523312, 2694116644458775819191900360249028160, 17832454952556194793063448702441218878, 118108456133224054896712281881294073504, 782735441038084181873376174571921204798, 5190423904758211714925623093159987529940, 34437748604324370602921443095806124348670, 228613348802761193819299056898251103103520, 1518429584878699452758715737965618159089146, 10090339156041997714448904165769656482808836, 67085265469182269096371940696225176709087018, 446222470771400760685028301475826338589370968, 2969420268403659855286401721764792630621190430, 19768841311537724731476668187817715104569054612, 131666042922449537951834621280520110053303471010, 877290424015865818346880465873212379701063241152, 5847689920102773395759414557652760546802232350510, 38993408419116618105542020519109120925093028526268, 260111052357004245660027670908389957512466820743597, 1735730220114040026340897099386922165391833947865432, 11586619493088057882327621252793168906633250938259721, 77370938845319382687142128852935924146408932629941190, 516822353108239057057029437902042842148514674662419773, 3453368290932589431853552021684476899062661662140650512, 23082282473781244452295005277856353187419679309190452031, 154328124984472507651335696388666980554258774573424627974, 1032139183592163087017533898200918421374692470046418839071, 6904859429601032747058582816164952948679433476446939199924, 46205266536320181426487310344988988269089878831043923591709, 309275121223940447159630036857060836913341464544421031517550, 2070676670974641920906501287320278905499315655042971674572323, 13867253178811249227450625186077796703068596490980137353842544, 92891635992394003458122289441506064871757100155365375339409781, 622397819827856475992653514365555537205877166359004019148819498, 4171211114683363427571940726311192393941688810523954035950009817, 27961238701882598679447834359486732630441844324338482564095564756, 187477145923724981612292903698648795608425282097227497205342107555, 1257290403354177037223612728961396659821227768162891862633256099738, 8433657178969410678131440011101868721692491889501994028286162049357, 56583157089508627243158990205965857000513916886620191564623491222248, 379705761920781999657270131090422845850991964973181396964885522557739, 2548554599043140363443231873509704126193769692611360247388224330790142, 17109033305191955618097654053809021898880593578369070022649093578663029, 114878795834488059089903096169421685021220278083636011885606402267845476, 771498902416377410624559072179342466876146574738360664788940250559675835, 5182150333600908292783706121488990170282871900048595239396338176644084322, 34814666560135972710263317246810153243233673189827274867799009911758078385, 233932383133868249797258682403495809787396329184028403812999095922175026288, 1572145407395045149670521466060147900287845853819939769693645445770608553567, 10567391028374042932499173915192456572349859271146334217119048908545002501422, 71041812502192814388078254150442949034695626021661148811669323709035335648075, 477672249204505045222596299584128022762033334726637681936105232438962474568012, 3212286643394146533079755798626935388948238393497282286492182058292664002271913, 21605558511504029545830813337448516283122899753151114737788606128423697402175422

Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24777/
System of equations in Maple syntax:
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[4,x]+F[83,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[6,x]+F[66,x]+F[82,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[62,x,k[0]]+F[64,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[41,x,k[0]]+F[47,x,k[0]]+F[60,x,k[0]]+F[61,x,k[0]]
F[14,x,k[0]] = F[15,x,1,k[0]]
F[15,x,k[0],k[1]] = F[11,x]*F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = 1/(-1+k[1])*(F[17,x,k[0],k[1]]*k[1]-F[17,x,k[0],1])
F[17,x,k[0],k[1]] = F[18,x,k[0],k[0]*k[1]]
F[18,x,k[0],k[1]] = 1/(-1+k[0])*(F[19,x,k[0],k[1]]*k[0]-F[19,x,1,k[1]])
F[19,x,k[0],k[1]] = (F[20,x,k[0]]*k[0]-F[20,x,k[1]]*k[1])/(-k[1]+k[0])
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[39,x,k[0]]+F[7,x,k[0]]
F[21,x,k[0]] = F[11,x]*F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,1,k[0]]
F[23,x,k[0],k[1]] = F[1,x]+F[24,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[35,x,k[0],k[1]]+F[37,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[11,x]*F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = 1/(-1+k[0])*(F[19,x,k[0],k[1]]*k[0]-F[19,x,1,k[1]])
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[33,x,k[0]]
F[27,x,k[0],k[1]] = 1/(-1+k[1])*(F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])
F[28,x,k[0],k[1]] = (F[29,x,k[0],1]*k[0]-F[29,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[29,x,k[0],k[1]] = F[30,x,k[0],k[0]*k[1]]
F[30,x,k[0],k[1]] = F[1,x]+F[31,x,k[0],k[1]]+F[32,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[11,x]*F[19,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[28,x,k[0],k[1]]*F[33,x,k[0]]
F[33,x,k[0]] = k[0]*x
F[34,x,k[0],k[1]] = F[30,x,k[0],k[1]]*F[33,x,k[1]]
F[35,x,k[0],k[1]] = F[11,x]*F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = (F[23,x,k[0],k[1]]*k[0]-F[23,x,1,k[1]])/(-1+k[0])
F[37,x,k[0],k[1]] = F[33,x,k[1]]*F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = (F[30,x,k[0],k[1]]*k[0]-F[30,x,1,k[1]])/(-1+k[0])
F[39,x,k[0]] = F[33,x,k[0]]*F[40,x,k[0]]
F[40,x,k[0]] = F[29,x,1,k[0]]
F[41,x,k[0]] = F[42,x,1,k[0]]
F[42,x,k[0],k[1]] = F[11,x]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = 1/(-1+k[1])*(F[44,x,k[0],k[1]]*k[1]-F[44,x,k[0],1])
F[44,x,k[0],k[1]] = F[45,x,k[0],k[0]*k[1]]
F[45,x,k[0],k[1]] = 1/(-1+k[0])*(F[46,x,k[0],k[1]]*k[0]-F[46,x,1,k[1]])
F[46,x,k[0],k[1]] = (F[40,x,k[0]]*k[0]-F[40,x,k[1]]*k[1])/(-k[1]+k[0])
F[47,x,k[0]] = F[11,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,1,k[0]]
F[49,x,k[0],k[1]] = (F[50,x,k[0],k[1]]*k[0]-F[50,x,1,k[1]])/(-1+k[0])
F[50,x,k[0],k[1]] = F[1,x]+F[51,x,k[0],k[1]]+F[53,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[56,x,k[0],k[1]]+F[58,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[11,x]*F[52,x,k[0],k[1]]
F[52,x,k[0],k[1]] = (F[25,x,k[0],k[1]]*k[0]-F[25,x,1,k[1]])/(-1+k[0])
F[53,x,k[0],k[1]] = F[33,x,k[0]]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = 1/(-1+k[1])*(F[27,x,k[0],k[1]]*k[1]-F[27,x,k[0],1])
F[55,x,k[0],k[1]] = F[11,x]*F[49,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[11,x]*F[57,x,k[0],k[1]]
F[57,x,k[0],k[1]] = (F[36,x,k[0],k[1]]*k[0]-F[36,x,1,k[1]])/(-1+k[0])
F[58,x,k[0],k[1]] = F[33,x,k[1]]*F[59,x,k[0],k[1]]
F[59,x,k[0],k[1]] = (F[38,x,k[0],k[1]]*k[0]-F[38,x,1,k[1]])/(-1+k[0])
F[60,x,k[0]] = F[56,x,1,k[0]]
F[61,x,k[0]] = F[58,x,1,k[0]]
F[62,x,k[0]] = F[11,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[36,x,1,k[0]]
F[64,x,k[0]] = F[33,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[38,x,1,k[0]]
F[66,x] = F[11,x]*F[67,x]
F[67,x] = F[68,x,1]
F[68,x,k[0]] = (F[69,x,k[0]]*k[0]-F[69,x,1])/(-1+k[0])
F[69,x,k[0]] = F[1,x]+F[70,x,k[0]]+F[72,x,k[0]]+F[74,x,k[0]]
F[70,x,k[0]] = F[11,x]*F[71,x,k[0]]
F[71,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[72,x,k[0]] = F[11,x]*F[73,x,k[0]]
F[73,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[74,x,k[0]] = F[33,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,1,k[0]]
F[76,x,k[0],k[1]] = (-F[77,x,1,k[1]]*k[1]+F[77,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[77,x,k[0],k[1]] = F[1,x]+F[78,x,k[0],k[1]]+F[79,x,k[0],k[1]]+F[80,x,k[0],k[1]]
F[78,x,k[0],k[1]] = F[31,x,k[0]*k[1],k[1]]
F[79,x,k[0],k[1]] = F[32,x,k[0]*k[1],k[1]]
F[80,x,k[0],k[1]] = F[33,x,k[1]]*F[81,x,k[0],k[1]]
F[81,x,k[0],k[1]] = (F[77,x,k[0],k[1]]*k[0]-F[77,x,1,k[1]])/(-1+k[0])
F[82,x] = F[74,x,1]
F[83,x] = F[11,x]*F[84,x]
F[84,x] = F[69,x,1]
System of equations in latex syntax:
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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{83}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{66}\! \left(x \right)+F_{82}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{64}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , 1, y\right)
F_{15}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{16}\! \left(x , y , z\right)
F_{16}\! \left(x , y , z\right) = -\frac{-F_{17}\! \left(x , y , z\right) z +F_{17}\! \left(x , y , 1\right)}{-1+z}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , y z \right)
F_{18}\! \left(x , y , z\right) = -\frac{-F_{19}\! \left(x , y , z\right) y +F_{19}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = \frac{F_{20}\! \left(x , y\right) y -F_{20}\! \left(x , z\right) z}{-z +y}
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , 1, y\right)
F_{23}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = -\frac{-F_{19}\! \left(x , y , z\right) y +F_{19}\! \left(x , 1, z\right)}{-1+y}
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y , z\right) F_{33}\! \left(x , y\right)
F_{27}\! \left(x , y , z\right) = -\frac{-z F_{28}\! \left(x , y , z\right)+F_{28}\! \left(x , y , 1\right)}{-1+z}
F_{28}\! \left(x , y , z\right) = \frac{F_{29}\! \left(x , y , 1\right) y -F_{29}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , y , y z \right)
F_{30}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)
F_{31}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{19}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = y x
F_{34}\! \left(x , y , z\right) = F_{30}\! \left(x , y , z\right) F_{33}\! \left(x , z\right)
F_{35}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{36}\! \left(x , y , z\right)
F_{36}\! \left(x , y , z\right) = -\frac{-F_{23}\! \left(x , y , z\right) y +F_{23}\! \left(x , 1, z\right)}{-1+y}
F_{37}\! \left(x , y , z\right) = F_{33}\! \left(x , z\right) F_{38}\! \left(x , y , z\right)
F_{38}\! \left(x , y , z\right) = -\frac{-F_{30}\! \left(x , y , z\right) y +F_{30}\! \left(x , 1, z\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{29}\! \left(x , 1, y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , 1, y\right)
F_{42}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{43}\! \left(x , y , z\right)
F_{43}\! \left(x , y , z\right) = -\frac{-F_{44}\! \left(x , y , z\right) z +F_{44}\! \left(x , y , 1\right)}{-1+z}
F_{44}\! \left(x , y , z\right) = F_{45}\! \left(x , y , y z \right)
F_{45}\! \left(x , y , z\right) = -\frac{-F_{46}\! \left(x , y , z\right) y +F_{46}\! \left(x , 1, z\right)}{-1+y}
F_{46}\! \left(x , y , z\right) = \frac{F_{40}\! \left(x , y\right) y -F_{40}\! \left(x , z\right) z}{-z +y}
F_{47}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , 1, y\right)
F_{49}\! \left(x , y , z\right) = -\frac{-F_{50}\! \left(x , y , z\right) y +F_{50}\! \left(x , 1, z\right)}{-1+y}
F_{50}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{51}\! \left(x , y , z\right)+F_{53}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)+F_{56}\! \left(x , y , z\right)+F_{58}\! \left(x , y , z\right)
F_{51}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{52}\! \left(x , y , z\right)
F_{52}\! \left(x , y , z\right) = -\frac{-y F_{25}\! \left(x , y , z\right)+F_{25}\! \left(x , 1, z\right)}{-1+y}
F_{53}\! \left(x , y , z\right) = F_{33}\! \left(x , y\right) F_{54}\! \left(x , y , z\right)
F_{54}\! \left(x , y , z\right) = -\frac{-F_{27}\! \left(x , y , z\right) z +F_{27}\! \left(x , y , 1\right)}{-1+z}
F_{55}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{49}\! \left(x , y , z\right)
F_{56}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{57}\! \left(x , y , z\right)
F_{57}\! \left(x , y , z\right) = -\frac{-F_{36}\! \left(x , y , z\right) y +F_{36}\! \left(x , 1, z\right)}{-1+y}
F_{58}\! \left(x , y , z\right) = F_{33}\! \left(x , z\right) F_{59}\! \left(x , y , z\right)
F_{59}\! \left(x , y , z\right) = -\frac{-F_{38}\! \left(x , y , z\right) y +F_{38}\! \left(x , 1, z\right)}{-1+y}
F_{60}\! \left(x , y\right) = F_{56}\! \left(x , 1, y\right)
F_{61}\! \left(x , y\right) = F_{58}\! \left(x , 1, y\right)
F_{62}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{36}\! \left(x , 1, y\right)
F_{64}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{38}\! \left(x , 1, y\right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x , 1\right)
F_{68}\! \left(x , y\right) = -\frac{-F_{69}\! \left(x , y\right) y +F_{69}\! \left(x , 1\right)}{-1+y}
F_{69}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = -\frac{-F_{20}\! \left(x , y\right) y +F_{20}\! \left(x , 1\right)}{-1+y}
F_{72}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{74}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , 1, y\right)
F_{76}\! \left(x , y , z\right) = -\frac{F_{77}\! \left(x , 1, z\right) z -y F_{77}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{77}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{78}\! \left(x , y , z\right)+F_{79}\! \left(x , y , z\right)+F_{80}\! \left(x , y , z\right)
F_{78}\! \left(x , y , z\right) = F_{31}\! \left(x , y z , z\right)
F_{79}\! \left(x , y , z\right) = F_{32}\! \left(x , y z , z\right)
F_{80}\! \left(x , y , z\right) = F_{33}\! \left(x , z\right) F_{81}\! \left(x , y , z\right)
F_{81}\! \left(x , y , z\right) = -\frac{-y F_{77}\! \left(x , y , z\right)+F_{77}\! \left(x , 1, z\right)}{-1+y}
F_{82}\! \left(x \right) = F_{74}\! \left(x , 1\right)
F_{83}\! \left(x \right) = F_{11}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{69}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_83(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_6(x) + F_66(x) + F_82(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_62(x, k_0) + F_64(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0) + F_41(x, k_0) + F_47(x, k_0) + F_60(x, k_0) + F_61(x, k_0))
Eq(F_14(x, k_0), F_15(x, 1, k_0))
Eq(F_15(x, k_0, k_1), F_11(x)*F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), (k_1*F_17(x, k_0, k_1) - F_17(x, k_0, 1))/(k_1 - 1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_0*k_1))
Eq(F_18(x, k_0, k_1), (k_0*F_19(x, k_0, k_1) - F_19(x, 1, k_1))/(k_0 - 1))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0) + k_1*F_20(x, k_1))/(-k_0 + k_1))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_39(x, k_0) + F_7(x, k_0))
Eq(F_21(x, k_0), F_11(x)*F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, 1, k_0))
Eq(F_23(x, k_0, k_1), F_1(x) + F_24(x, k_0, k_1) + F_26(x, k_0, k_1) + F_35(x, k_0, k_1) + F_37(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_11(x)*F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), (-k_0*F_19(x, k_0, k_1) + F_19(x, 1, k_1))/(1 - k_0))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_33(x, k_0))
Eq(F_27(x, k_0, k_1), (k_1*F_28(x, k_0, k_1) - F_28(x, k_0, 1))/(k_1 - 1))
Eq(F_28(x, k_0, k_1), (-k_0*F_29(x, k_0, 1) + k_1*F_29(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_29(x, k_0, k_1), F_30(x, k_0, k_0*k_1))
Eq(F_30(x, k_0, k_1), F_1(x) + F_31(x, k_0, k_1) + F_32(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_11(x)*F_19(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_28(x, k_0, k_1)*F_33(x, k_0))
Eq(F_33(x, k_0), k_0*x)
Eq(F_34(x, k_0, k_1), F_30(x, k_0, k_1)*F_33(x, k_1))
Eq(F_35(x, k_0, k_1), F_11(x)*F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), (-k_0*F_23(x, k_0, k_1) + F_23(x, 1, k_1))/(1 - k_0))
Eq(F_37(x, k_0, k_1), F_33(x, k_1)*F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), (-k_0*F_30(x, k_0, k_1) + F_30(x, 1, k_1))/(1 - k_0))
Eq(F_39(x, k_0), F_33(x, k_0)*F_40(x, k_0))
Eq(F_40(x, k_0), F_29(x, 1, k_0))
Eq(F_41(x, k_0), F_42(x, 1, k_0))
Eq(F_42(x, k_0, k_1), F_11(x)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), (k_1*F_44(x, k_0, k_1) - F_44(x, k_0, 1))/(k_1 - 1))
Eq(F_44(x, k_0, k_1), F_45(x, k_0, k_0*k_1))
Eq(F_45(x, k_0, k_1), (k_0*F_46(x, k_0, k_1) - F_46(x, 1, k_1))/(k_0 - 1))
Eq(F_46(x, k_0, k_1), (-k_0*F_40(x, k_0) + k_1*F_40(x, k_1))/(-k_0 + k_1))
Eq(F_47(x, k_0), F_11(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, 1, k_0))
Eq(F_49(x, k_0, k_1), (-k_0*F_50(x, k_0, k_1) + F_50(x, 1, k_1))/(1 - k_0))
Eq(F_50(x, k_0, k_1), F_1(x) + F_51(x, k_0, k_1) + F_53(x, k_0, k_1) + F_55(x, k_0, k_1) + F_56(x, k_0, k_1) + F_58(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_11(x)*F_52(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), (-k_0*F_25(x, k_0, k_1) + F_25(x, 1, k_1))/(1 - k_0))
Eq(F_53(x, k_0, k_1), F_33(x, k_0)*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), (k_1*F_27(x, k_0, k_1) - F_27(x, k_0, 1))/(k_1 - 1))
Eq(F_55(x, k_0, k_1), F_11(x)*F_49(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_11(x)*F_57(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), (-k_0*F_36(x, k_0, k_1) + F_36(x, 1, k_1))/(1 - k_0))
Eq(F_58(x, k_0, k_1), F_33(x, k_1)*F_59(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), (-k_0*F_38(x, k_0, k_1) + F_38(x, 1, k_1))/(1 - k_0))
Eq(F_60(x, k_0), F_56(x, 1, k_0))
Eq(F_61(x, k_0), F_58(x, 1, k_0))
Eq(F_62(x, k_0), F_11(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_36(x, 1, k_0))
Eq(F_64(x, k_0), F_33(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_38(x, 1, k_0))
Eq(F_66(x), F_11(x)*F_67(x))
Eq(F_67(x), F_68(x, 1))
Eq(F_68(x, k_0), (-k_0*F_69(x, k_0) + F_69(x, 1))/(1 - k_0))
Eq(F_69(x, k_0), F_1(x) + F_70(x, k_0) + F_72(x, k_0) + F_74(x, k_0))
Eq(F_70(x, k_0), F_11(x)*F_71(x, k_0))
Eq(F_71(x, k_0), (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_72(x, k_0), F_11(x)*F_73(x, k_0))
Eq(F_73(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_74(x, k_0), F_33(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, 1, k_0))
Eq(F_76(x, k_0, k_1), (-k_0*F_77(x, k_0/k_1, k_1) + k_1*F_77(x, 1, k_1))/(-k_0 + k_1))
Eq(F_77(x, k_0, k_1), F_1(x) + F_78(x, k_0, k_1) + F_79(x, k_0, k_1) + F_80(x, k_0, k_1))
Eq(F_78(x, k_0, k_1), F_31(x, k_0*k_1, k_1))
Eq(F_79(x, k_0, k_1), F_32(x, k_0*k_1, k_1))
Eq(F_80(x, k_0, k_1), F_33(x, k_1)*F_81(x, k_0, k_1))
Eq(F_81(x, k_0, k_1), (-k_0*F_77(x, k_0, k_1) + F_77(x, 1, k_1))/(1 - k_0))
Eq(F_82(x), F_74(x, 1))
Eq(F_83(x), F_11(x)*F_84(x))
Eq(F_84(x), F_69(x, 1))
Pack JSON:
{"name": "row_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": 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[[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}

Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24816/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[226,x]+F[8,x]
F[8,x] = F[224,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[18,x]
F[12,x] = F[13,x]+F[189,x]
F[13,x] = F[14,x]+F[223,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[18,x]*F[21,x]
F[21,x] = F[14,x]+F[22,x]
F[22,x] = F[23,x]+F[28,x]
F[23,x] = F[2,x]+F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[0,x]+F[26,x]
F[26,x] = 1/F[18,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = 1/F[110,x]*F[29,x]
F[29,x] = -F[222,x]+F[30,x]
F[30,x] = 1/F[15,x]*F[31,x]
F[31,x] = -F[174,x]+F[32,x]
F[32,x] = 1/F[18,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[39,x]+F[35,x]
F[35,x] = -F[38,x]+F[36,x]
F[36,x] = 1/F[18,x]*F[37,x]
F[37,x] = F[24,x]
F[38,x] = F[2,x]*F[26,x]
F[39,x] = F[10,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[18,x]*F[42,x]
F[42,x] = F[43,x]+F[50,x]
F[43,x] = F[2,x]*F[44,x]
F[44,x] = 1/F[18,x]/F[47,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[18,x]*F[47,x]
F[47,x] = F[1,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[47,x]^2*F[18,x]
F[50,x] = F[51,x]
F[51,x] = F[18,x]*F[52,x]
F[52,x] = F[53,x]+F[62,x]
F[53,x] = F[54,x]*F[58,x]
F[54,x] = 1/F[18,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[9,x]+F[13,x]
F[58,x] = 1/F[18,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[2,x]+F[61,x]
F[61,x] = -F[2,x]+F[5,x]
F[62,x] = F[63,x]*F[64,x]
F[63,x] = -F[54,x]+F[44,x]
F[64,x] = F[138,x]+F[65,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[0,x]*F[67,x]
F[67,x] = -1+(x^2-2*x)*F[67,x]^2+(2+x)*F[67,x]
F[68,x] = 1/F[88,x]*F[69,x]
F[69,x] = -F[173,x]+F[70,x]
F[70,x] = -F[120,x]+F[71,x]
F[71,x] = F[72,x]+F[93,x]
F[72,x] = F[73,x]+F[87,x]
F[73,x] = F[15,x]*F[74,x]
F[74,x] = F[60,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[18,x]^2*F[77,x]
F[77,x] = F[65,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[18,x]*F[77,x]*F[80,x]
F[80,x] = F[47,x]+F[81,x]
F[81,x] = F[16,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[18,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[47,x]*F[81,x]
F[86,x] = F[80,x]*F[81,x]
F[87,x] = F[60,x]*F[88,x]
F[88,x] = F[18,x]+F[89,x]
F[89,x] = F[90,x]+F[91,x]+F[92,x]
F[90,x] = 0
F[91,x] = F[16,x]*F[18,x]
F[92,x] = F[18,x]*F[88,x]
F[93,x] = -F[172,x]+F[94,x]
F[94,x] = 1/F[18,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[99,x]+F[97,x]
F[97,x] = 1/F[18,x]*F[98,x]
F[98,x] = F[61,x]
F[99,x] = F[100,x]+F[113,x]
F[100,x] = -F[101,x]+F[8,x]
F[101,x] = F[0,x]+F[102,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[18,x]
F[104,x] = F[105,x]+F[109,x]
F[105,x] = F[106,x]*F[15,x]
F[106,x] = F[0,x]+F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[18,x]*F[58,x]
F[109,x] = F[110,x]*F[88,x]
F[110,x] = F[0,x]+F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[18,x]*F[77,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[2,x]*F[60,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[18,x]
F[117,x] = F[118,x]+F[164,x]
F[118,x] = F[119,x]+F[142,x]
F[119,x] = F[120,x]*F[2,x]
F[120,x] = F[121,x]+F[129,x]
F[121,x] = F[122,x]*F[15,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[0,x]*F[124,x]
F[124,x] = (x*F[124,x]+x-2*F[124,x])*(x*F[124,x]+x-1)
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[18,x]*F[58,x]
F[127,x] = F[128,x]+F[81,x]
F[128,x] = F[48,x]
F[129,x] = F[130,x]*F[88,x]
F[130,x] = 1/F[16,x]*F[131,x]
F[131,x] = -F[122,x]+F[132,x]
F[132,x] = -F[140,x]+F[133,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[0,x]*F[15,x]*F[67,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[107,x]+F[125,x]
F[137,x] = F[138,x]*F[16,x]
F[138,x] = F[139,x]
F[139,x] = F[18,x]*F[77,x]*F[80,x]
F[140,x] = F[106,x]+F[141,x]
F[141,x] = F[110,x]*F[16,x]
F[142,x] = -F[163,x]+F[143,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[122,x]*F[54,x]
F[145,x] = F[130,x]*F[146,x]
F[146,x] = F[147,x]+F[153,x]
F[147,x] = F[148,x]+F[88,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[18,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[147,x]*F[80,x]
F[152,x] = F[147,x]*F[80,x]
F[153,x] = -F[158,x]+F[154,x]
F[154,x] = -F[157,x]+F[155,x]
F[155,x] = 1/F[18,x]/F[47,x]*F[156,x]
F[156,x] = F[46,x]
F[157,x] = F[147,x]+F[80,x]
F[158,x] = -F[63,x]+F[159,x]
F[159,x] = F[160,x]+F[161,x]
F[160,x] = F[16,x]*F[80,x]
F[161,x] = -F[162,x]+F[44,x]
F[162,x] = F[15,x]*F[80,x]
F[163,x] = F[0,x]*F[120,x]
F[164,x] = F[165,x]+F[170,x]
F[165,x] = F[166,x]*F[168,x]
F[166,x] = F[158,x]+F[167,x]
F[167,x] = F[128,x]+F[82,x]
F[168,x] = -F[169,x]+F[58,x]
F[169,x] = F[106,x]+F[122,x]
F[170,x] = F[171,x]*F[68,x]
F[171,x] = F[148,x]+F[153,x]
F[172,x] = F[104,x]+F[72,x]
F[173,x] = F[15,x]*F[168,x]
F[174,x] = F[175,x]
F[175,x] = F[15,x]*F[176,x]*F[18,x]
F[176,x] = 1/F[18,x]*F[177,x]
F[177,x] = F[178,x]
F[178,x] = -F[219,x]+F[179,x]
F[179,x] = 1/F[18,x]*F[180,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[24,x]
F[183,x] = F[184,x]
F[184,x] = -F[24,x]+F[185,x]
F[185,x] = -F[25,x]+F[186,x]
F[186,x] = -F[189,x]+F[187,x]
F[187,x] = 1/F[18,x]*F[188,x]
F[188,x] = F[24,x]
F[189,x] = F[190,x]
F[190,x] = F[18,x]*F[191,x]
F[191,x] = 1/F[18,x]*F[192,x]
F[192,x] = F[193,x]
F[193,x] = -F[194,x]+F[36,x]
F[194,x] = F[195,x]
F[195,x] = F[18,x]*F[196,x]
F[196,x] = F[197,x]+F[217,x]
F[197,x] = 1/F[18,x]*F[198,x]
F[198,x] = F[199,x]
F[199,x] = -F[202,x]+F[200,x]
F[200,x] = 1/F[18,x]*F[201,x]
F[201,x] = F[24,x]
F[202,x] = -F[205,x]+F[203,x]
F[203,x] = 1/F[18,x]*F[204,x]
F[204,x] = F[23,x]
F[205,x] = F[206,x]+F[26,x]
F[206,x] = -F[209,x]+F[207,x]
F[207,x] = 1/F[18,x]*F[208,x]
F[208,x] = F[61,x]
F[209,x] = F[210,x]
F[210,x] = F[18,x]*F[211,x]
F[211,x] = F[212,x]+F[215,x]
F[212,x] = F[213,x]+F[214,x]
F[213,x] = F[0,x]*F[58,x]
F[214,x] = F[56,x]*F[64,x]
F[215,x] = F[216,x]
F[216,x] = F[18,x]*F[52,x]
F[217,x] = F[218,x]
F[218,x] = F[193,x]*F[4,x]
F[219,x] = F[2,x]*F[220,x]
F[220,x] = F[189,x]+F[221,x]
F[221,x] = F[186,x]+F[26,x]
F[222,x] = F[106,x]*F[23,x]
F[223,x] = F[10,x]
F[224,x] = F[225,x]+F[40,x]
F[225,x] = F[0,x]*F[2,x]
F[226,x] = F[224,x]+F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[18,x]*F[229,x]
F[229,x] = F[230,x]+F[238,x]
F[230,x] = F[231,x]+F[236,x]
F[231,x] = F[232,x]
F[232,x] = F[18,x]*F[233,x]
F[233,x] = F[234,x]+F[235,x]
F[234,x] = F[15,x]*F[211,x]
F[235,x] = F[14,x]*F[64,x]*F[88,x]
F[236,x] = F[237,x]
F[237,x] = F[10,x]*F[96,x]
F[238,x] = F[239,x]
F[239,x] = F[18,x]*F[240,x]
F[240,x] = 1/F[18,x]*F[241,x]
F[241,x] = F[242,x]
F[242,x] = F[243,x]+F[255,x]
F[243,x] = -F[251,x]+F[244,x]
F[244,x] = 1/F[18,x]*F[245,x]
F[245,x] = F[246,x]
F[246,x] = -F[5,x]+F[247,x]
F[247,x] = F[248,x]
F[248,x] = F[18,x]*F[249,x]
F[249,x] = 1/F[18,x]*F[250,x]
F[250,x] = F[99,x]
F[251,x] = F[252,x]
F[252,x] = F[18,x]*F[253,x]
F[253,x] = 1/F[18,x]*F[254,x]
F[254,x] = F[231,x]
F[255,x] = F[256,x]
F[256,x] = F[10,x]*F[247,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{226}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{224}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{189}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{223}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{110}\! \left(x \right)}
F_{29}\! \left(x \right) = -F_{222}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{31}\! \left(x \right) = -F_{174}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{24}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{18}\! \left(x \right) F_{47}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47} \left(x \right)^{2} F_{18}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{13}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{44}\! \left(x \right)
F_{64}\! \left(x \right) = F_{138}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{0}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = x^{2} F_{67} \left(x \right)^{2}-2 x F_{67} \left(x \right)^{2}+F_{67}\! \left(x \right) x +2 F_{67}\! \left(x \right)-1
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{88}\! \left(x \right)}
F_{69}\! \left(x \right) = -F_{173}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{93}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{87}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{60}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{65}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{47}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{16}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{47}\! \left(x \right) F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{80}\! \left(x \right) F_{81}\! \left(x \right)
F_{87}\! \left(x \right) = F_{60}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{92}\! \left(x \right) = F_{18}\! \left(x \right) F_{88}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{172}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{61}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{113}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{101}\! \left(x \right)+F_{8}\! \left(x \right)
F_{101}\! \left(x \right) = F_{0}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{18}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{109}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{15}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{88}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right) F_{60}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{18}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{164}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{142}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{2}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{129}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{15}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{0}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = x^{2} F_{124} \left(x \right)^{2}+2 x^{2} F_{124}\! \left(x \right)-2 x F_{124} \left(x \right)^{2}+x^{2}-3 x F_{124}\! \left(x \right)-x +2 F_{124}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{81}\! \left(x \right)
F_{128}\! \left(x \right) = F_{48}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{88}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{131}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{67}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{107}\! \left(x \right)+F_{125}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{16}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right) F_{80}\! \left(x \right)
F_{140}\! \left(x \right) = F_{106}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{110}\! \left(x \right) F_{16}\! \left(x \right)
F_{142}\! \left(x \right) = -F_{163}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{122}\! \left(x \right) F_{54}\! \left(x \right)
F_{145}\! \left(x \right) = F_{130}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{153}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{88}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{18}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right) F_{80}\! \left(x \right)
F_{152}\! \left(x \right) = F_{147}\! \left(x \right) F_{80}\! \left(x \right)
F_{153}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{157}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = \frac{F_{156}\! \left(x \right)}{F_{18}\! \left(x \right) F_{47}\! \left(x \right)}
F_{156}\! \left(x \right) = F_{46}\! \left(x \right)
F_{157}\! \left(x \right) = F_{147}\! \left(x \right)+F_{80}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{16}\! \left(x \right) F_{80}\! \left(x \right)
F_{161}\! \left(x \right) = -F_{162}\! \left(x \right)+F_{44}\! \left(x \right)
F_{162}\! \left(x \right) = F_{15}\! \left(x \right) F_{80}\! \left(x \right)
F_{163}\! \left(x \right) = F_{0}\! \left(x \right) F_{120}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{170}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{168}\! \left(x \right)
F_{166}\! \left(x \right) = F_{158}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{128}\! \left(x \right)+F_{82}\! \left(x \right)
F_{168}\! \left(x \right) = -F_{169}\! \left(x \right)+F_{58}\! \left(x \right)
F_{169}\! \left(x \right) = F_{106}\! \left(x \right)+F_{122}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{68}\! \left(x \right)
F_{171}\! \left(x \right) = F_{148}\! \left(x \right)+F_{153}\! \left(x \right)
F_{172}\! \left(x \right) = F_{104}\! \left(x \right)+F_{72}\! \left(x \right)
F_{173}\! \left(x \right) = F_{15}\! \left(x \right) F_{168}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{15}\! \left(x \right) F_{176}\! \left(x \right) F_{18}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = -F_{219}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = \frac{F_{180}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{24}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = \frac{F_{188}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{188}\! \left(x \right) = F_{24}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{18}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = \frac{F_{192}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = -F_{194}\! \left(x \right)+F_{36}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{18}\! \left(x \right) F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{217}\! \left(x \right)
F_{197}\! \left(x \right) = \frac{F_{198}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = -F_{202}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{24}\! \left(x \right)
F_{202}\! \left(x \right) = -F_{205}\! \left(x \right)+F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = \frac{F_{204}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{204}\! \left(x \right) = F_{23}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{26}\! \left(x \right)
F_{206}\! \left(x \right) = -F_{209}\! \left(x \right)+F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = \frac{F_{208}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{208}\! \left(x \right) = F_{61}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{18}\! \left(x \right) F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{215}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)+F_{214}\! \left(x \right)
F_{213}\! \left(x \right) = F_{0}\! \left(x \right) F_{58}\! \left(x \right)
F_{214}\! \left(x \right) = F_{56}\! \left(x \right) F_{64}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{193}\! \left(x \right) F_{4}\! \left(x \right)
F_{219}\! \left(x \right) = F_{2}\! \left(x \right) F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{189}\! \left(x \right)+F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{186}\! \left(x \right)+F_{26}\! \left(x \right)
F_{222}\! \left(x \right) = F_{106}\! \left(x \right) F_{23}\! \left(x \right)
F_{223}\! \left(x \right) = F_{10}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)+F_{40}\! \left(x \right)
F_{225}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{226}\! \left(x \right) = F_{224}\! \left(x \right)+F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{18}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{238}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{236}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{18}\! \left(x \right) F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{235}\! \left(x \right)
F_{234}\! \left(x \right) = F_{15}\! \left(x \right) F_{211}\! \left(x \right)
F_{235}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right) F_{88}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{10}\! \left(x \right) F_{96}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{18}\! \left(x \right) F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = \frac{F_{241}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{255}\! \left(x \right)
F_{243}\! \left(x \right) = -F_{251}\! \left(x \right)+F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = \frac{F_{245}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{18}\! \left(x \right) F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = \frac{F_{250}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{250}\! \left(x \right) = F_{99}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{18}\! \left(x \right) F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = \frac{F_{254}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{254}\! \left(x \right) = F_{231}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{10}\! \left(x \right) F_{247}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_226(x) + F_8(x))
Eq(F_8(x), F_224(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_18(x))
Eq(F_12(x), F_13(x) + F_189(x))
Eq(F_13(x), F_14(x) + F_223(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_18(x)*F_21(x))
Eq(F_21(x), F_14(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_28(x))
Eq(F_23(x), F_2(x) + F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), -F_0(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_18(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), F_29(x)/F_110(x))
Eq(F_29(x), -F_222(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_15(x))
Eq(F_31(x), -F_174(x) + F_32(x))
Eq(F_32(x), F_33(x)/F_18(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_39(x))
Eq(F_35(x), F_36(x) - F_38(x))
Eq(F_36(x), F_37(x)/F_18(x))
Eq(F_37(x), F_24(x))
Eq(F_38(x), F_2(x)*F_26(x))
Eq(F_39(x), F_10(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_18(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_50(x))
Eq(F_43(x), F_2(x)*F_44(x))
Eq(F_44(x), F_45(x)/(F_18(x)*F_47(x)))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_18(x)*F_47(x))
Eq(F_47(x), F_1(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_18(x)*F_47(x)**2)
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_18(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_62(x))
Eq(F_53(x), F_54(x)*F_58(x))
Eq(F_54(x), F_55(x)/F_18(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_13(x) - F_9(x))
Eq(F_58(x), F_59(x)/F_18(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_2(x) + F_61(x))
Eq(F_61(x), -F_2(x) + F_5(x))
Eq(F_62(x), F_63(x)*F_64(x))
Eq(F_63(x), F_44(x) - F_54(x))
Eq(F_64(x), F_138(x) + F_65(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_0(x)*F_67(x))
Eq(F_67(x), x*(x - 2)*F_67(x)**2 + (x + 2)*F_67(x) - 1)
Eq(F_68(x), F_69(x)/F_88(x))
Eq(F_69(x), -F_173(x) + F_70(x))
Eq(F_70(x), -F_120(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_93(x))
Eq(F_72(x), F_73(x) + F_87(x))
Eq(F_73(x), F_15(x)*F_74(x))
Eq(F_74(x), F_60(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_18(x)**2*F_77(x))
Eq(F_77(x), F_65(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_18(x)*F_77(x)*F_80(x))
Eq(F_80(x), F_47(x) + F_81(x))
Eq(F_81(x), F_16(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_18(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_47(x)*F_81(x))
Eq(F_86(x), F_80(x)*F_81(x))
Eq(F_87(x), F_60(x)*F_88(x))
Eq(F_88(x), F_18(x) + F_89(x))
Eq(F_89(x), F_90(x) + F_91(x) + F_92(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_16(x)*F_18(x))
Eq(F_92(x), F_18(x)*F_88(x))
Eq(F_93(x), -F_172(x) + F_94(x))
Eq(F_94(x), F_95(x)/F_18(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x) - F_99(x))
Eq(F_97(x), F_98(x)/F_18(x))
Eq(F_98(x), F_61(x))
Eq(F_99(x), F_100(x) + F_113(x))
Eq(F_100(x), -F_101(x) + F_8(x))
Eq(F_101(x), F_0(x) + F_102(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_18(x))
Eq(F_104(x), F_105(x) + F_109(x))
Eq(F_105(x), F_106(x)*F_15(x))
Eq(F_106(x), F_0(x) + F_107(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_18(x)*F_58(x))
Eq(F_109(x), F_110(x)*F_88(x))
Eq(F_110(x), F_0(x) + F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_18(x)*F_77(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_2(x)*F_60(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_18(x))
Eq(F_117(x), F_118(x) + F_164(x))
Eq(F_118(x), F_119(x) + F_142(x))
Eq(F_119(x), F_120(x)*F_2(x))
Eq(F_120(x), F_121(x) + F_129(x))
Eq(F_121(x), F_122(x)*F_15(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_0(x)*F_124(x))
Eq(F_124(x), x*(x - 2)*(F_124(x) + 1)**2 + (x + 1)*(F_124(x) + 1) + F_124(x) - 1)
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_18(x)*F_58(x))
Eq(F_127(x), F_128(x) + F_81(x))
Eq(F_128(x), F_48(x))
Eq(F_129(x), F_130(x)*F_88(x))
Eq(F_130(x), F_131(x)/F_16(x))
Eq(F_131(x), -F_122(x) + F_132(x))
Eq(F_132(x), F_133(x) - F_140(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_0(x)*F_15(x)*F_67(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_107(x) + F_125(x))
Eq(F_137(x), F_138(x)*F_16(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_18(x)*F_77(x)*F_80(x))
Eq(F_140(x), F_106(x) + F_141(x))
Eq(F_141(x), F_110(x)*F_16(x))
Eq(F_142(x), F_143(x) - F_163(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_122(x)*F_54(x))
Eq(F_145(x), F_130(x)*F_146(x))
Eq(F_146(x), F_147(x) + F_153(x))
Eq(F_147(x), F_148(x) + F_88(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_18(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_147(x)*F_80(x))
Eq(F_152(x), F_147(x)*F_80(x))
Eq(F_153(x), F_154(x) - F_158(x))
Eq(F_154(x), F_155(x) - F_157(x))
Eq(F_155(x), F_156(x)/(F_18(x)*F_47(x)))
Eq(F_156(x), F_46(x))
Eq(F_157(x), F_147(x) + F_80(x))
Eq(F_158(x), F_159(x) - F_63(x))
Eq(F_159(x), F_160(x) + F_161(x))
Eq(F_160(x), F_16(x)*F_80(x))
Eq(F_161(x), -F_162(x) + F_44(x))
Eq(F_162(x), F_15(x)*F_80(x))
Eq(F_163(x), F_0(x)*F_120(x))
Eq(F_164(x), F_165(x) + F_170(x))
Eq(F_165(x), F_166(x)*F_168(x))
Eq(F_166(x), F_158(x) + F_167(x))
Eq(F_167(x), F_128(x) + F_82(x))
Eq(F_168(x), -F_169(x) + F_58(x))
Eq(F_169(x), F_106(x) + F_122(x))
Eq(F_170(x), F_171(x)*F_68(x))
Eq(F_171(x), F_148(x) + F_153(x))
Eq(F_172(x), F_104(x) + F_72(x))
Eq(F_173(x), F_15(x)*F_168(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_15(x)*F_176(x)*F_18(x))
Eq(F_176(x), F_177(x)/F_18(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_179(x) - F_219(x))
Eq(F_179(x), F_180(x)/F_18(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_24(x))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_185(x) - F_24(x))
Eq(F_185(x), F_186(x) - F_25(x))
Eq(F_186(x), F_187(x) - F_189(x))
Eq(F_187(x), F_188(x)/F_18(x))
Eq(F_188(x), F_24(x))
Eq(F_189(x), F_190(x))
Eq(F_190(x), F_18(x)*F_191(x))
Eq(F_191(x), F_192(x)/F_18(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), -F_194(x) + F_36(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_18(x)*F_196(x))
Eq(F_196(x), F_197(x) + F_217(x))
Eq(F_197(x), F_198(x)/F_18(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x) - F_202(x))
Eq(F_200(x), F_201(x)/F_18(x))
Eq(F_201(x), F_24(x))
Eq(F_202(x), F_203(x) - F_205(x))
Eq(F_203(x), F_204(x)/F_18(x))
Eq(F_204(x), F_23(x))
Eq(F_205(x), F_206(x) + F_26(x))
Eq(F_206(x), F_207(x) - F_209(x))
Eq(F_207(x), F_208(x)/F_18(x))
Eq(F_208(x), F_61(x))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_18(x)*F_211(x))
Eq(F_211(x), F_212(x) + F_215(x))
Eq(F_212(x), F_213(x) + F_214(x))
Eq(F_213(x), F_0(x)*F_58(x))
Eq(F_214(x), F_56(x)*F_64(x))
Eq(F_215(x), F_216(x))
Eq(F_216(x), F_18(x)*F_52(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_193(x)*F_4(x))
Eq(F_219(x), F_2(x)*F_220(x))
Eq(F_220(x), F_189(x) + F_221(x))
Eq(F_221(x), F_186(x) + F_26(x))
Eq(F_222(x), F_106(x)*F_23(x))
Eq(F_223(x), F_10(x))
Eq(F_224(x), F_225(x) + F_40(x))
Eq(F_225(x), F_0(x)*F_2(x))
Eq(F_226(x), F_224(x) + F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_18(x)*F_229(x))
Eq(F_229(x), F_230(x) + F_238(x))
Eq(F_230(x), F_231(x) + F_236(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_18(x)*F_233(x))
Eq(F_233(x), F_234(x) + F_235(x))
Eq(F_234(x), F_15(x)*F_211(x))
Eq(F_235(x), F_14(x)*F_64(x)*F_88(x))
Eq(F_236(x), F_237(x))
Eq(F_237(x), F_10(x)*F_96(x))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_18(x)*F_240(x))
Eq(F_240(x), F_241(x)/F_18(x))
Eq(F_241(x), F_242(x))
Eq(F_242(x), F_243(x) + F_255(x))
Eq(F_243(x), F_244(x) - F_251(x))
Eq(F_244(x), F_245(x)/F_18(x))
Eq(F_245(x), F_246(x))
Eq(F_246(x), F_247(x) - F_5(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_18(x)*F_249(x))
Eq(F_249(x), F_250(x)/F_18(x))
Eq(F_250(x), F_99(x))
Eq(F_251(x), F_252(x))
Eq(F_252(x), F_18(x)*F_253(x))
Eq(F_253(x), F_254(x)/F_18(x))
Eq(F_254(x), F_231(x))
Eq(F_255(x), F_256(x))
Eq(F_256(x), F_10(x)*F_247(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 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"tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 4]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 6], [1, 6]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 6]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 5], [0, 5], [0, 5]]}, {"patt": [0, 2, 1], "pos": [[2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 6]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25115/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[208,x]+F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[0,x]^2
F[10,x] = F[11,x]+F[203,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[14,x]+F[54,x]
F[14,x] = F[15,x]+F[202,x]
F[15,x] = F[16,x]+F[20,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[19,x]
F[19,x] = x
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[19,x]*F[22,x]
F[22,x] = F[15,x]+F[23,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = -F[0,x]+F[25,x]
F[25,x] = 1/F[19,x]*F[26,x]
F[26,x] = F[2,x]
F[27,x] = 1/F[110,x]*F[28,x]
F[28,x] = -F[201,x]+F[29,x]
F[29,x] = 1/F[16,x]*F[30,x]
F[30,x] = -F[39,x]+F[31,x]
F[31,x] = 1/F[19,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[10,x]+F[34,x]
F[34,x] = -F[38,x]+F[35,x]
F[35,x] = 1/F[19,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[2,x]+F[24,x]
F[38,x] = F[2,x]*F[25,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[19,x]*F[41,x]
F[41,x] = 1/F[19,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[198,x]+F[44,x]
F[44,x] = 1/F[19,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[37,x]
F[48,x] = F[49,x]
F[49,x] = -F[37,x]+F[50,x]
F[50,x] = -F[197,x]+F[51,x]
F[51,x] = -F[54,x]+F[52,x]
F[52,x] = 1/F[19,x]*F[53,x]
F[53,x] = F[37,x]
F[54,x] = F[55,x]
F[55,x] = F[19,x]*F[56,x]
F[56,x] = 1/F[19,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = -F[59,x]+F[35,x]
F[59,x] = F[60,x]
F[60,x] = F[19,x]*F[61,x]
F[61,x] = F[195,x]+F[62,x]
F[62,x] = 1/F[19,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = -F[67,x]+F[65,x]
F[65,x] = 1/F[19,x]*F[66,x]
F[66,x] = F[37,x]
F[67,x] = -F[70,x]+F[68,x]
F[68,x] = 1/F[19,x]*F[69,x]
F[69,x] = F[24,x]
F[70,x] = F[25,x]+F[71,x]
F[71,x] = -F[76,x]+F[72,x]
F[72,x] = 1/F[19,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[2,x]+F[75,x]
F[75,x] = -F[0,x]+F[4,x]
F[76,x] = F[77,x]
F[77,x] = F[19,x]*F[78,x]
F[78,x] = F[190,x]+F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[0,x]*F[81,x]
F[81,x] = 1/F[19,x]*F[82,x]
F[82,x] = F[75,x]
F[83,x] = F[84,x]*F[87,x]
F[84,x] = F[85,x]
F[85,x] = -F[86,x]+F[14,x]
F[86,x] = F[0,x]+F[11,x]
F[87,x] = F[153,x]+F[88,x]
F[88,x] = F[89,x]+F[91,x]
F[89,x] = F[0,x]*F[90,x]
F[90,x] = -1+(x^2-2*x)*F[90,x]^2+(2+x)*F[90,x]
F[91,x] = 1/F[140,x]*F[92,x]
F[92,x] = -F[189,x]+F[93,x]
F[93,x] = -F[120,x]+F[94,x]
F[94,x] = 1/F[19,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[103,x]+F[97,x]
F[97,x] = -F[100,x]+F[98,x]
F[98,x] = 1/F[19,x]*F[99,x]
F[99,x] = F[74,x]
F[100,x] = F[101,x]+F[113,x]
F[101,x] = -F[102,x]+F[8,x]
F[102,x] = F[0,x]+F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[16,x]*F[19,x]
F[105,x] = F[106,x]+F[109,x]
F[106,x] = F[0,x]+F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[19,x]*F[81,x]
F[109,x] = F[110,x]*F[17,x]
F[110,x] = F[0,x]+F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[19,x]*F[87,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[2,x]*F[75,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[19,x]
F[117,x] = F[118,x]+F[166,x]
F[118,x] = F[119,x]+F[155,x]
F[119,x] = F[120,x]*F[2,x]
F[120,x] = F[121,x]+F[139,x]
F[121,x] = F[122,x]*F[16,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[0,x]*F[124,x]
F[124,x] = (x*F[124,x]+x-1)*(x*F[124,x]+x-2*F[124,x])
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[19,x]*F[81,x]
F[127,x] = F[128,x]+F[132,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]^2*F[19,x]
F[131,x] = F[1,x]+F[129,x]
F[132,x] = F[133,x]+F[17,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[19,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[131,x]*F[132,x]
F[137,x] = F[132,x]*F[138,x]
F[138,x] = F[131,x]+F[132,x]
F[139,x] = F[140,x]*F[145,x]
F[140,x] = F[141,x]+F[19,x]
F[141,x] = F[142,x]+F[143,x]+F[144,x]
F[142,x] = 0
F[143,x] = F[17,x]*F[19,x]
F[144,x] = F[140,x]*F[19,x]
F[145,x] = 1/F[17,x]*F[146,x]
F[146,x] = -F[122,x]+F[147,x]
F[147,x] = -F[105,x]+F[148,x]
F[148,x] = F[149,x]+F[150,x]
F[149,x] = F[0,x]*F[16,x]*F[90,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[107,x]+F[125,x]
F[152,x] = F[153,x]*F[17,x]
F[153,x] = F[154,x]
F[154,x] = F[138,x]*F[19,x]*F[87,x]
F[155,x] = -F[165,x]+F[156,x]
F[156,x] = F[157,x]+F[160,x]
F[157,x] = F[122,x]*F[158,x]
F[158,x] = 1/F[19,x]*F[159,x]
F[159,x] = F[84,x]
F[160,x] = F[145,x]*F[161,x]
F[161,x] = -F[158,x]+F[162,x]
F[162,x] = 1/F[131,x]/F[19,x]*F[163,x]
F[163,x] = F[164,x]
F[164,x] = F[13,x]*F[131,x]*F[19,x]
F[165,x] = F[0,x]*F[120,x]
F[166,x] = F[167,x]+F[180,x]
F[167,x] = F[168,x]*F[178,x]
F[168,x] = F[169,x]+F[170,x]
F[169,x] = F[128,x]+F[133,x]
F[170,x] = -F[177,x]+F[171,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[138,x]*F[17,x]
F[173,x] = -F[176,x]+F[174,x]
F[174,x] = 1/F[131,x]/F[19,x]*F[175,x]
F[175,x] = F[164,x]
F[176,x] = F[138,x]*F[16,x]
F[177,x] = -F[158,x]+F[174,x]
F[178,x] = -F[179,x]+F[81,x]
F[179,x] = F[106,x]+F[122,x]
F[180,x] = F[181,x]*F[91,x]
F[181,x] = F[182,x]+F[188,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]*F[19,x]
F[184,x] = F[185,x]+F[187,x]
F[185,x] = F[138,x]*F[186,x]
F[186,x] = F[140,x]+F[182,x]
F[187,x] = F[138,x]*F[186,x]
F[188,x] = -F[186,x]+F[161,x]
F[189,x] = F[16,x]*F[178,x]
F[190,x] = F[191,x]
F[191,x] = F[19,x]*F[192,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[158,x]*F[81,x]
F[194,x] = F[177,x]*F[87,x]
F[195,x] = F[196,x]
F[196,x] = F[4,x]*F[58,x]
F[197,x] = F[2,x]+F[37,x]
F[198,x] = F[199,x]*F[2,x]
F[199,x] = F[200,x]+F[54,x]
F[200,x] = F[25,x]+F[51,x]
F[201,x] = F[106,x]*F[24,x]
F[202,x] = F[11,x]
F[203,x] = F[204,x]
F[204,x] = F[19,x]*F[205,x]
F[205,x] = F[206,x]+F[207,x]
F[206,x] = F[11,x]*F[4,x]
F[207,x] = F[191,x]
F[208,x] = F[209,x]+F[211,x]
F[209,x] = F[203,x]+F[210,x]
F[210,x] = F[0,x]*F[2,x]
F[211,x] = F[212,x]
F[212,x] = F[19,x]*F[213,x]
F[213,x] = F[214,x]+F[234,x]
F[214,x] = F[215,x]+F[232,x]
F[215,x] = -F[223,x]+F[216,x]
F[216,x] = 1/F[19,x]*F[217,x]
F[217,x] = F[218,x]
F[218,x] = -F[5,x]+F[219,x]
F[219,x] = F[220,x]
F[220,x] = F[19,x]*F[221,x]
F[221,x] = 1/F[19,x]*F[222,x]
F[222,x] = F[100,x]
F[223,x] = F[224,x]
F[224,x] = F[19,x]*F[225,x]
F[225,x] = 1/F[19,x]*F[226,x]
F[226,x] = F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[19,x]*F[229,x]
F[229,x] = F[230,x]+F[231,x]
F[230,x] = F[16,x]*F[78,x]
F[231,x] = F[140,x]*F[15,x]*F[87,x]
F[232,x] = F[233,x]
F[233,x] = F[11,x]*F[219,x]
F[234,x] = F[235,x]
F[235,x] = F[19,x]*F[236,x]
F[236,x] = 1/F[19,x]*F[237,x]
F[237,x] = F[238,x]
F[238,x] = F[227,x]+F[239,x]
F[239,x] = F[240,x]
F[240,x] = F[11,x]*F[97,x]
System of equations in latex syntax:
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_{19}\! \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_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{208}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{203}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{54}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{202}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{110}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{201}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{30}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{25}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{198}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{37}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{197}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{37}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{35}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{195}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{37}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{70}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{24}\! \left(x \right)
F_{70}\! \left(x \right) = F_{25}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{19}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{190}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{0}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{75}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right) F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{14}\! \left(x \right)
F_{86}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{87}\! \left(x \right) = F_{153}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{0}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = x^{2} F_{90} \left(x \right)^{2}-2 x F_{90} \left(x \right)^{2}+F_{90}\! \left(x \right) x +2 F_{90}\! \left(x \right)-1
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{140}\! \left(x \right)}
F_{92}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{74}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{113}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{102}\! \left(x \right)+F_{8}\! \left(x \right)
F_{102}\! \left(x \right) = F_{0}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{17}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{19}\! \left(x \right) F_{87}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right) F_{75}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{19}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{166}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{155}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{2}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{139}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{16}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{0}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = x^{2} F_{124} \left(x \right)^{2}+2 x^{2} F_{124}\! \left(x \right)-2 x F_{124} \left(x \right)^{2}+x^{2}-3 x F_{124}\! \left(x \right)-x +2 F_{124}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{132}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131} \left(x \right)^{2} F_{19}\! \left(x \right)
F_{131}\! \left(x \right) = F_{1}\! \left(x \right)+F_{129}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{17}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{19}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{131}\! \left(x \right) F_{132}\! \left(x \right)
F_{137}\! \left(x \right) = F_{132}\! \left(x \right) F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{145}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{19}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{142}\! \left(x \right) = 0
F_{143}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{144}\! \left(x \right) = F_{140}\! \left(x \right) F_{19}\! \left(x \right)
F_{145}\! \left(x \right) = \frac{F_{146}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{146}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = -F_{105}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{150}\! \left(x \right)
F_{149}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{90}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{107}\! \left(x \right)+F_{125}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{17}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{138}\! \left(x \right) F_{19}\! \left(x \right) F_{87}\! \left(x \right)
F_{155}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{160}\! \left(x \right)
F_{157}\! \left(x \right) = F_{122}\! \left(x \right) F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{84}\! \left(x \right)
F_{160}\! \left(x \right) = F_{145}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = \frac{F_{163}\! \left(x \right)}{F_{131}\! \left(x \right) F_{19}\! \left(x \right)}
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{13}\! \left(x \right) F_{131}\! \left(x \right) F_{19}\! \left(x \right)
F_{165}\! \left(x \right) = F_{0}\! \left(x \right) F_{120}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{180}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{178}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{170}\! \left(x \right)
F_{169}\! \left(x \right) = F_{128}\! \left(x \right)+F_{133}\! \left(x \right)
F_{170}\! \left(x \right) = -F_{177}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{138}\! \left(x \right) F_{17}\! \left(x \right)
F_{173}\! \left(x \right) = -F_{176}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = \frac{F_{175}\! \left(x \right)}{F_{131}\! \left(x \right) F_{19}\! \left(x \right)}
F_{175}\! \left(x \right) = F_{164}\! \left(x \right)
F_{176}\! \left(x \right) = F_{138}\! \left(x \right) F_{16}\! \left(x \right)
F_{177}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{174}\! \left(x \right)
F_{178}\! \left(x \right) = -F_{179}\! \left(x \right)+F_{81}\! \left(x \right)
F_{179}\! \left(x \right) = F_{106}\! \left(x \right)+F_{122}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{91}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{188}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{19}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{187}\! \left(x \right)
F_{185}\! \left(x \right) = F_{138}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{140}\! \left(x \right)+F_{182}\! \left(x \right)
F_{187}\! \left(x \right) = F_{138}\! \left(x \right) F_{186}\! \left(x \right)
F_{188}\! \left(x \right) = -F_{186}\! \left(x \right)+F_{161}\! \left(x \right)
F_{189}\! \left(x \right) = F_{16}\! \left(x \right) F_{178}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{19}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{158}\! \left(x \right) F_{81}\! \left(x \right)
F_{194}\! \left(x \right) = F_{177}\! \left(x \right) F_{87}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{197}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{2}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{54}\! \left(x \right)
F_{200}\! \left(x \right) = F_{25}\! \left(x \right)+F_{51}\! \left(x \right)
F_{201}\! \left(x \right) = F_{106}\! \left(x \right) F_{24}\! \left(x \right)
F_{202}\! \left(x \right) = F_{11}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{19}\! \left(x \right) F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{207}\! \left(x \right)
F_{206}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{207}\! \left(x \right) = F_{191}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{211}\! \left(x \right)
F_{209}\! \left(x \right) = F_{203}\! \left(x \right)+F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{19}\! \left(x \right) F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{234}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)+F_{232}\! \left(x \right)
F_{215}\! \left(x \right) = -F_{223}\! \left(x \right)+F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = \frac{F_{217}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{19}\! \left(x \right) F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = \frac{F_{222}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{222}\! \left(x \right) = F_{100}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{19}\! \left(x \right) F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = \frac{F_{226}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{19}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{231}\! \left(x \right)
F_{230}\! \left(x \right) = F_{16}\! \left(x \right) F_{78}\! \left(x \right)
F_{231}\! \left(x \right) = F_{140}\! \left(x \right) F_{15}\! \left(x \right) F_{87}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{11}\! \left(x \right) F_{219}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{19}\! \left(x \right) F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = \frac{F_{237}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{227}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{11}\! \left(x \right) F_{97}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_208(x) + F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_0(x)**2)
Eq(F_10(x), F_11(x) + F_203(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_19(x))
Eq(F_13(x), F_14(x) + F_54(x))
Eq(F_14(x), F_15(x) + F_202(x))
Eq(F_15(x), F_16(x) + F_20(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_19(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_19(x)*F_22(x))
Eq(F_22(x), F_15(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), -F_0(x) + F_25(x))
Eq(F_25(x), F_26(x)/F_19(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), F_28(x)/F_110(x))
Eq(F_28(x), -F_201(x) + F_29(x))
Eq(F_29(x), F_30(x)/F_16(x))
Eq(F_30(x), F_31(x) - F_39(x))
Eq(F_31(x), F_32(x)/F_19(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_10(x) + F_34(x))
Eq(F_34(x), F_35(x) - F_38(x))
Eq(F_35(x), F_36(x)/F_19(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), -F_2(x) + F_24(x))
Eq(F_38(x), F_2(x)*F_25(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_19(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_19(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), -F_198(x) + F_44(x))
Eq(F_44(x), F_45(x)/F_19(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_37(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), -F_37(x) + F_50(x))
Eq(F_50(x), -F_197(x) + F_51(x))
Eq(F_51(x), F_52(x) - F_54(x))
Eq(F_52(x), F_53(x)/F_19(x))
Eq(F_53(x), F_37(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_19(x)*F_56(x))
Eq(F_56(x), F_57(x)/F_19(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_35(x) - F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x)*F_61(x))
Eq(F_61(x), F_195(x) + F_62(x))
Eq(F_62(x), F_63(x)/F_19(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x) - F_67(x))
Eq(F_65(x), F_66(x)/F_19(x))
Eq(F_66(x), F_37(x))
Eq(F_67(x), F_68(x) - F_70(x))
Eq(F_68(x), F_69(x)/F_19(x))
Eq(F_69(x), F_24(x))
Eq(F_70(x), F_25(x) + F_71(x))
Eq(F_71(x), F_72(x) - F_76(x))
Eq(F_72(x), F_73(x)/F_19(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), -F_2(x) + F_75(x))
Eq(F_75(x), -F_0(x) + F_4(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_19(x)*F_78(x))
Eq(F_78(x), F_190(x) + F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_0(x)*F_81(x))
Eq(F_81(x), F_82(x)/F_19(x))
Eq(F_82(x), F_75(x))
Eq(F_83(x), F_84(x)*F_87(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_14(x) - F_86(x))
Eq(F_86(x), F_0(x) + F_11(x))
Eq(F_87(x), F_153(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_91(x))
Eq(F_89(x), F_0(x)*F_90(x))
Eq(F_90(x), x*(x - 2)*F_90(x)**2 + (x + 2)*F_90(x) - 1)
Eq(F_91(x), F_92(x)/F_140(x))
Eq(F_92(x), -F_189(x) + F_93(x))
Eq(F_93(x), -F_120(x) + F_94(x))
Eq(F_94(x), F_95(x)/F_19(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), -F_103(x) + F_97(x))
Eq(F_97(x), -F_100(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_19(x))
Eq(F_99(x), F_74(x))
Eq(F_100(x), F_101(x) + F_113(x))
Eq(F_101(x), -F_102(x) + F_8(x))
Eq(F_102(x), F_0(x) + F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_16(x)*F_19(x))
Eq(F_105(x), F_106(x) + F_109(x))
Eq(F_106(x), F_0(x) + F_107(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_19(x)*F_81(x))
Eq(F_109(x), F_110(x)*F_17(x))
Eq(F_110(x), F_0(x) + F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_19(x)*F_87(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_2(x)*F_75(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_19(x))
Eq(F_117(x), F_118(x) + F_166(x))
Eq(F_118(x), F_119(x) + F_155(x))
Eq(F_119(x), F_120(x)*F_2(x))
Eq(F_120(x), F_121(x) + F_139(x))
Eq(F_121(x), F_122(x)*F_16(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_0(x)*F_124(x))
Eq(F_124(x), x*(x - 2)*(F_124(x) + 1)**2 + (x + 1)*(F_124(x) + 1) + F_124(x) - 1)
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_19(x)*F_81(x))
Eq(F_127(x), F_128(x) + F_132(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x)**2*F_19(x))
Eq(F_131(x), F_1(x) + F_129(x))
Eq(F_132(x), F_133(x) + F_17(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_19(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_131(x)*F_132(x))
Eq(F_137(x), F_132(x)*F_138(x))
Eq(F_138(x), F_131(x) + F_132(x))
Eq(F_139(x), F_140(x)*F_145(x))
Eq(F_140(x), F_141(x) + F_19(x))
Eq(F_141(x), F_142(x) + F_143(x) + F_144(x))
Eq(F_142(x), 0)
Eq(F_143(x), F_17(x)*F_19(x))
Eq(F_144(x), F_140(x)*F_19(x))
Eq(F_145(x), F_146(x)/F_17(x))
Eq(F_146(x), -F_122(x) + F_147(x))
Eq(F_147(x), -F_105(x) + F_148(x))
Eq(F_148(x), F_149(x) + F_150(x))
Eq(F_149(x), F_0(x)*F_16(x)*F_90(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_107(x) + F_125(x))
Eq(F_152(x), F_153(x)*F_17(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_138(x)*F_19(x)*F_87(x))
Eq(F_155(x), F_156(x) - F_165(x))
Eq(F_156(x), F_157(x) + F_160(x))
Eq(F_157(x), F_122(x)*F_158(x))
Eq(F_158(x), F_159(x)/F_19(x))
Eq(F_159(x), F_84(x))
Eq(F_160(x), F_145(x)*F_161(x))
Eq(F_161(x), -F_158(x) + F_162(x))
Eq(F_162(x), F_163(x)/(F_131(x)*F_19(x)))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_13(x)*F_131(x)*F_19(x))
Eq(F_165(x), F_0(x)*F_120(x))
Eq(F_166(x), F_167(x) + F_180(x))
Eq(F_167(x), F_168(x)*F_178(x))
Eq(F_168(x), F_169(x) + F_170(x))
Eq(F_169(x), F_128(x) + F_133(x))
Eq(F_170(x), F_171(x) - F_177(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_138(x)*F_17(x))
Eq(F_173(x), F_174(x) - F_176(x))
Eq(F_174(x), F_175(x)/(F_131(x)*F_19(x)))
Eq(F_175(x), F_164(x))
Eq(F_176(x), F_138(x)*F_16(x))
Eq(F_177(x), -F_158(x) + F_174(x))
Eq(F_178(x), -F_179(x) + F_81(x))
Eq(F_179(x), F_106(x) + F_122(x))
Eq(F_180(x), F_181(x)*F_91(x))
Eq(F_181(x), F_182(x) + F_188(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x)*F_19(x))
Eq(F_184(x), F_185(x) + F_187(x))
Eq(F_185(x), F_138(x)*F_186(x))
Eq(F_186(x), F_140(x) + F_182(x))
Eq(F_187(x), F_138(x)*F_186(x))
Eq(F_188(x), F_161(x) - F_186(x))
Eq(F_189(x), F_16(x)*F_178(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_19(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_158(x)*F_81(x))
Eq(F_194(x), F_177(x)*F_87(x))
Eq(F_195(x), F_196(x))
Eq(F_196(x), F_4(x)*F_58(x))
Eq(F_197(x), F_2(x) + F_37(x))
Eq(F_198(x), F_199(x)*F_2(x))
Eq(F_199(x), F_200(x) + F_54(x))
Eq(F_200(x), F_25(x) + F_51(x))
Eq(F_201(x), F_106(x)*F_24(x))
Eq(F_202(x), F_11(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_19(x)*F_205(x))
Eq(F_205(x), F_206(x) + F_207(x))
Eq(F_206(x), F_11(x)*F_4(x))
Eq(F_207(x), F_191(x))
Eq(F_208(x), F_209(x) + F_211(x))
Eq(F_209(x), F_203(x) + F_210(x))
Eq(F_210(x), F_0(x)*F_2(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_19(x)*F_213(x))
Eq(F_213(x), F_214(x) + F_234(x))
Eq(F_214(x), F_215(x) + F_232(x))
Eq(F_215(x), F_216(x) - F_223(x))
Eq(F_216(x), F_217(x)/F_19(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_219(x) - F_5(x))
Eq(F_219(x), F_220(x))
Eq(F_220(x), F_19(x)*F_221(x))
Eq(F_221(x), F_222(x)/F_19(x))
Eq(F_222(x), F_100(x))
Eq(F_223(x), F_224(x))
Eq(F_224(x), F_19(x)*F_225(x))
Eq(F_225(x), F_226(x)/F_19(x))
Eq(F_226(x), F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_19(x)*F_229(x))
Eq(F_229(x), F_230(x) + F_231(x))
Eq(F_230(x), F_16(x)*F_78(x))
Eq(F_231(x), F_140(x)*F_15(x)*F_87(x))
Eq(F_232(x), F_233(x))
Eq(F_233(x), F_11(x)*F_219(x))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_19(x)*F_236(x))
Eq(F_236(x), F_237(x)/F_19(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_227(x) + F_239(x))
Eq(F_239(x), F_240(x))
Eq(F_240(x), F_11(x)*F_97(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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{"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 4]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 6], [1, 6]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 6]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 5], [0, 5], [0, 5]]}, {"patt": [0, 2, 1], "pos": [[2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 6]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25613/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[208,x]+F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[0,x]^2
F[10,x] = F[11,x]+F[203,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[14,x]+F[54,x]
F[14,x] = F[15,x]+F[202,x]
F[15,x] = F[16,x]+F[20,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[19,x]
F[19,x] = x
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[19,x]*F[22,x]
F[22,x] = F[15,x]+F[23,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = -F[0,x]+F[25,x]
F[25,x] = 1/F[19,x]*F[26,x]
F[26,x] = F[2,x]
F[27,x] = 1/F[110,x]*F[28,x]
F[28,x] = -F[201,x]+F[29,x]
F[29,x] = 1/F[16,x]*F[30,x]
F[30,x] = -F[39,x]+F[31,x]
F[31,x] = 1/F[19,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[10,x]+F[34,x]
F[34,x] = -F[38,x]+F[35,x]
F[35,x] = 1/F[19,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[2,x]+F[24,x]
F[38,x] = F[2,x]*F[25,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[19,x]*F[41,x]
F[41,x] = 1/F[19,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[198,x]+F[44,x]
F[44,x] = 1/F[19,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[37,x]
F[48,x] = F[49,x]
F[49,x] = -F[37,x]+F[50,x]
F[50,x] = -F[197,x]+F[51,x]
F[51,x] = -F[54,x]+F[52,x]
F[52,x] = 1/F[19,x]*F[53,x]
F[53,x] = F[37,x]
F[54,x] = F[55,x]
F[55,x] = F[19,x]*F[56,x]
F[56,x] = 1/F[19,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = -F[59,x]+F[35,x]
F[59,x] = F[60,x]
F[60,x] = F[19,x]*F[61,x]
F[61,x] = F[195,x]+F[62,x]
F[62,x] = 1/F[19,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = -F[67,x]+F[65,x]
F[65,x] = 1/F[19,x]*F[66,x]
F[66,x] = F[37,x]
F[67,x] = -F[70,x]+F[68,x]
F[68,x] = 1/F[19,x]*F[69,x]
F[69,x] = F[24,x]
F[70,x] = F[25,x]+F[71,x]
F[71,x] = -F[76,x]+F[72,x]
F[72,x] = 1/F[19,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[2,x]+F[75,x]
F[75,x] = -F[0,x]+F[4,x]
F[76,x] = F[77,x]
F[77,x] = F[19,x]*F[78,x]
F[78,x] = F[190,x]+F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[0,x]*F[81,x]
F[81,x] = 1/F[19,x]*F[82,x]
F[82,x] = F[75,x]
F[83,x] = F[84,x]*F[87,x]
F[84,x] = F[85,x]
F[85,x] = -F[86,x]+F[14,x]
F[86,x] = F[0,x]+F[11,x]
F[87,x] = F[153,x]+F[88,x]
F[88,x] = F[89,x]+F[91,x]
F[89,x] = F[0,x]*F[90,x]
F[90,x] = -1+(x^2-2*x)*F[90,x]^2+(2+x)*F[90,x]
F[91,x] = 1/F[140,x]*F[92,x]
F[92,x] = -F[189,x]+F[93,x]
F[93,x] = -F[120,x]+F[94,x]
F[94,x] = 1/F[19,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[103,x]+F[97,x]
F[97,x] = -F[100,x]+F[98,x]
F[98,x] = 1/F[19,x]*F[99,x]
F[99,x] = F[74,x]
F[100,x] = F[101,x]+F[113,x]
F[101,x] = -F[102,x]+F[8,x]
F[102,x] = F[0,x]+F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[16,x]*F[19,x]
F[105,x] = F[106,x]+F[109,x]
F[106,x] = F[0,x]+F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[19,x]*F[81,x]
F[109,x] = F[110,x]*F[17,x]
F[110,x] = F[0,x]+F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[19,x]*F[87,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[2,x]*F[75,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[19,x]
F[117,x] = F[118,x]+F[166,x]
F[118,x] = F[119,x]+F[155,x]
F[119,x] = F[120,x]*F[2,x]
F[120,x] = F[121,x]+F[139,x]
F[121,x] = F[122,x]*F[16,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[0,x]*F[124,x]
F[124,x] = (x*F[124,x]+x-1)*(x*F[124,x]+x-2*F[124,x])
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[19,x]*F[81,x]
F[127,x] = F[128,x]+F[132,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]^2*F[19,x]
F[131,x] = F[1,x]+F[129,x]
F[132,x] = F[133,x]+F[17,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[19,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[131,x]*F[132,x]
F[137,x] = F[132,x]*F[138,x]
F[138,x] = F[131,x]+F[132,x]
F[139,x] = F[140,x]*F[145,x]
F[140,x] = F[141,x]+F[19,x]
F[141,x] = F[142,x]+F[143,x]+F[144,x]
F[142,x] = 0
F[143,x] = F[17,x]*F[19,x]
F[144,x] = F[140,x]*F[19,x]
F[145,x] = 1/F[17,x]*F[146,x]
F[146,x] = -F[122,x]+F[147,x]
F[147,x] = -F[105,x]+F[148,x]
F[148,x] = F[149,x]+F[150,x]
F[149,x] = F[0,x]*F[16,x]*F[90,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[107,x]+F[125,x]
F[152,x] = F[153,x]*F[17,x]
F[153,x] = F[154,x]
F[154,x] = F[138,x]*F[19,x]*F[87,x]
F[155,x] = -F[165,x]+F[156,x]
F[156,x] = F[157,x]+F[160,x]
F[157,x] = F[122,x]*F[158,x]
F[158,x] = 1/F[19,x]*F[159,x]
F[159,x] = F[84,x]
F[160,x] = F[145,x]*F[161,x]
F[161,x] = -F[158,x]+F[162,x]
F[162,x] = 1/F[131,x]/F[19,x]*F[163,x]
F[163,x] = F[164,x]
F[164,x] = F[13,x]*F[131,x]*F[19,x]
F[165,x] = F[0,x]*F[120,x]
F[166,x] = F[167,x]+F[180,x]
F[167,x] = F[168,x]*F[178,x]
F[168,x] = F[169,x]+F[170,x]
F[169,x] = F[128,x]+F[133,x]
F[170,x] = -F[177,x]+F[171,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[138,x]*F[17,x]
F[173,x] = -F[176,x]+F[174,x]
F[174,x] = 1/F[131,x]/F[19,x]*F[175,x]
F[175,x] = F[164,x]
F[176,x] = F[138,x]*F[16,x]
F[177,x] = -F[158,x]+F[174,x]
F[178,x] = -F[179,x]+F[81,x]
F[179,x] = F[106,x]+F[122,x]
F[180,x] = F[181,x]*F[91,x]
F[181,x] = F[182,x]+F[188,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]*F[19,x]
F[184,x] = F[185,x]+F[187,x]
F[185,x] = F[138,x]*F[186,x]
F[186,x] = F[140,x]+F[182,x]
F[187,x] = F[138,x]*F[186,x]
F[188,x] = -F[186,x]+F[161,x]
F[189,x] = F[16,x]*F[178,x]
F[190,x] = F[191,x]
F[191,x] = F[19,x]*F[192,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[158,x]*F[81,x]
F[194,x] = F[177,x]*F[87,x]
F[195,x] = F[196,x]
F[196,x] = F[4,x]*F[58,x]
F[197,x] = F[2,x]+F[37,x]
F[198,x] = F[199,x]*F[2,x]
F[199,x] = F[200,x]+F[54,x]
F[200,x] = F[25,x]+F[51,x]
F[201,x] = F[106,x]*F[24,x]
F[202,x] = F[11,x]
F[203,x] = F[204,x]
F[204,x] = F[19,x]*F[205,x]
F[205,x] = F[206,x]+F[207,x]
F[206,x] = F[11,x]*F[4,x]
F[207,x] = F[191,x]
F[208,x] = F[209,x]+F[211,x]
F[209,x] = F[203,x]+F[210,x]
F[210,x] = F[0,x]*F[2,x]
F[211,x] = F[212,x]
F[212,x] = F[19,x]*F[213,x]
F[213,x] = F[214,x]+F[234,x]
F[214,x] = F[215,x]+F[232,x]
F[215,x] = -F[223,x]+F[216,x]
F[216,x] = 1/F[19,x]*F[217,x]
F[217,x] = F[218,x]
F[218,x] = -F[5,x]+F[219,x]
F[219,x] = F[220,x]
F[220,x] = F[19,x]*F[221,x]
F[221,x] = 1/F[19,x]*F[222,x]
F[222,x] = F[100,x]
F[223,x] = F[224,x]
F[224,x] = F[19,x]*F[225,x]
F[225,x] = 1/F[19,x]*F[226,x]
F[226,x] = F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[19,x]*F[229,x]
F[229,x] = F[230,x]+F[231,x]
F[230,x] = F[16,x]*F[78,x]
F[231,x] = F[140,x]*F[15,x]*F[87,x]
F[232,x] = F[233,x]
F[233,x] = F[11,x]*F[219,x]
F[234,x] = F[235,x]
F[235,x] = F[19,x]*F[236,x]
F[236,x] = 1/F[19,x]*F[237,x]
F[237,x] = F[238,x]
F[238,x] = F[227,x]+F[239,x]
F[239,x] = F[240,x]
F[240,x] = F[11,x]*F[97,x]
System of equations in latex syntax:
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_{19}\! \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_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{208}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{203}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{54}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{202}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{110}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{201}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{30}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{25}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{198}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{37}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{197}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{37}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{35}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{195}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{37}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{70}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{24}\! \left(x \right)
F_{70}\! \left(x \right) = F_{25}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{19}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{190}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{0}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{75}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right) F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{14}\! \left(x \right)
F_{86}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{87}\! \left(x \right) = F_{153}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{0}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = x^{2} F_{90} \left(x \right)^{2}-2 x F_{90} \left(x \right)^{2}+F_{90}\! \left(x \right) x +2 F_{90}\! \left(x \right)-1
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{140}\! \left(x \right)}
F_{92}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{74}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{113}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{102}\! \left(x \right)+F_{8}\! \left(x \right)
F_{102}\! \left(x \right) = F_{0}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{17}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{19}\! \left(x \right) F_{87}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right) F_{75}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{19}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{166}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{155}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{2}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{139}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{16}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{0}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = x^{2} F_{124} \left(x \right)^{2}+2 x^{2} F_{124}\! \left(x \right)-2 x F_{124} \left(x \right)^{2}+x^{2}-3 x F_{124}\! \left(x \right)-x +2 F_{124}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{132}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131} \left(x \right)^{2} F_{19}\! \left(x \right)
F_{131}\! \left(x \right) = F_{1}\! \left(x \right)+F_{129}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{17}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{19}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{131}\! \left(x \right) F_{132}\! \left(x \right)
F_{137}\! \left(x \right) = F_{132}\! \left(x \right) F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{145}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{19}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{142}\! \left(x \right) = 0
F_{143}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{144}\! \left(x \right) = F_{140}\! \left(x \right) F_{19}\! \left(x \right)
F_{145}\! \left(x \right) = \frac{F_{146}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{146}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = -F_{105}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{150}\! \left(x \right)
F_{149}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{90}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{107}\! \left(x \right)+F_{125}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{17}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{138}\! \left(x \right) F_{19}\! \left(x \right) F_{87}\! \left(x \right)
F_{155}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{160}\! \left(x \right)
F_{157}\! \left(x \right) = F_{122}\! \left(x \right) F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{84}\! \left(x \right)
F_{160}\! \left(x \right) = F_{145}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = \frac{F_{163}\! \left(x \right)}{F_{131}\! \left(x \right) F_{19}\! \left(x \right)}
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{13}\! \left(x \right) F_{131}\! \left(x \right) F_{19}\! \left(x \right)
F_{165}\! \left(x \right) = F_{0}\! \left(x \right) F_{120}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{180}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{178}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{170}\! \left(x \right)
F_{169}\! \left(x \right) = F_{128}\! \left(x \right)+F_{133}\! \left(x \right)
F_{170}\! \left(x \right) = -F_{177}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{138}\! \left(x \right) F_{17}\! \left(x \right)
F_{173}\! \left(x \right) = -F_{176}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = \frac{F_{175}\! \left(x \right)}{F_{131}\! \left(x \right) F_{19}\! \left(x \right)}
F_{175}\! \left(x \right) = F_{164}\! \left(x \right)
F_{176}\! \left(x \right) = F_{138}\! \left(x \right) F_{16}\! \left(x \right)
F_{177}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{174}\! \left(x \right)
F_{178}\! \left(x \right) = -F_{179}\! \left(x \right)+F_{81}\! \left(x \right)
F_{179}\! \left(x \right) = F_{106}\! \left(x \right)+F_{122}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{91}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{188}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{19}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{187}\! \left(x \right)
F_{185}\! \left(x \right) = F_{138}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{140}\! \left(x \right)+F_{182}\! \left(x \right)
F_{187}\! \left(x \right) = F_{138}\! \left(x \right) F_{186}\! \left(x \right)
F_{188}\! \left(x \right) = -F_{186}\! \left(x \right)+F_{161}\! \left(x \right)
F_{189}\! \left(x \right) = F_{16}\! \left(x \right) F_{178}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{19}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{158}\! \left(x \right) F_{81}\! \left(x \right)
F_{194}\! \left(x \right) = F_{177}\! \left(x \right) F_{87}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{197}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{2}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{54}\! \left(x \right)
F_{200}\! \left(x \right) = F_{25}\! \left(x \right)+F_{51}\! \left(x \right)
F_{201}\! \left(x \right) = F_{106}\! \left(x \right) F_{24}\! \left(x \right)
F_{202}\! \left(x \right) = F_{11}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{19}\! \left(x \right) F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{207}\! \left(x \right)
F_{206}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{207}\! \left(x \right) = F_{191}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{211}\! \left(x \right)
F_{209}\! \left(x \right) = F_{203}\! \left(x \right)+F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{19}\! \left(x \right) F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{234}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)+F_{232}\! \left(x \right)
F_{215}\! \left(x \right) = -F_{223}\! \left(x \right)+F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = \frac{F_{217}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{19}\! \left(x \right) F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = \frac{F_{222}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{222}\! \left(x \right) = F_{100}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{19}\! \left(x \right) F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = \frac{F_{226}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{19}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{231}\! \left(x \right)
F_{230}\! \left(x \right) = F_{16}\! \left(x \right) F_{78}\! \left(x \right)
F_{231}\! \left(x \right) = F_{140}\! \left(x \right) F_{15}\! \left(x \right) F_{87}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{11}\! \left(x \right) F_{219}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{19}\! \left(x \right) F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = \frac{F_{237}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{227}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{11}\! \left(x \right) F_{97}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_208(x) + F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_0(x)**2)
Eq(F_10(x), F_11(x) + F_203(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_19(x))
Eq(F_13(x), F_14(x) + F_54(x))
Eq(F_14(x), F_15(x) + F_202(x))
Eq(F_15(x), F_16(x) + F_20(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_19(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_19(x)*F_22(x))
Eq(F_22(x), F_15(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), -F_0(x) + F_25(x))
Eq(F_25(x), F_26(x)/F_19(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), F_28(x)/F_110(x))
Eq(F_28(x), -F_201(x) + F_29(x))
Eq(F_29(x), F_30(x)/F_16(x))
Eq(F_30(x), F_31(x) - F_39(x))
Eq(F_31(x), F_32(x)/F_19(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_10(x) + F_34(x))
Eq(F_34(x), F_35(x) - F_38(x))
Eq(F_35(x), F_36(x)/F_19(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), -F_2(x) + F_24(x))
Eq(F_38(x), F_2(x)*F_25(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_19(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_19(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), -F_198(x) + F_44(x))
Eq(F_44(x), F_45(x)/F_19(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_37(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), -F_37(x) + F_50(x))
Eq(F_50(x), -F_197(x) + F_51(x))
Eq(F_51(x), F_52(x) - F_54(x))
Eq(F_52(x), F_53(x)/F_19(x))
Eq(F_53(x), F_37(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_19(x)*F_56(x))
Eq(F_56(x), F_57(x)/F_19(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_35(x) - F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x)*F_61(x))
Eq(F_61(x), F_195(x) + F_62(x))
Eq(F_62(x), F_63(x)/F_19(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x) - F_67(x))
Eq(F_65(x), F_66(x)/F_19(x))
Eq(F_66(x), F_37(x))
Eq(F_67(x), F_68(x) - F_70(x))
Eq(F_68(x), F_69(x)/F_19(x))
Eq(F_69(x), F_24(x))
Eq(F_70(x), F_25(x) + F_71(x))
Eq(F_71(x), F_72(x) - F_76(x))
Eq(F_72(x), F_73(x)/F_19(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), -F_2(x) + F_75(x))
Eq(F_75(x), -F_0(x) + F_4(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_19(x)*F_78(x))
Eq(F_78(x), F_190(x) + F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_0(x)*F_81(x))
Eq(F_81(x), F_82(x)/F_19(x))
Eq(F_82(x), F_75(x))
Eq(F_83(x), F_84(x)*F_87(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_14(x) - F_86(x))
Eq(F_86(x), F_0(x) + F_11(x))
Eq(F_87(x), F_153(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_91(x))
Eq(F_89(x), F_0(x)*F_90(x))
Eq(F_90(x), x*(x - 2)*F_90(x)**2 + (x + 2)*F_90(x) - 1)
Eq(F_91(x), F_92(x)/F_140(x))
Eq(F_92(x), -F_189(x) + F_93(x))
Eq(F_93(x), -F_120(x) + F_94(x))
Eq(F_94(x), F_95(x)/F_19(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), -F_103(x) + F_97(x))
Eq(F_97(x), -F_100(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_19(x))
Eq(F_99(x), F_74(x))
Eq(F_100(x), F_101(x) + F_113(x))
Eq(F_101(x), -F_102(x) + F_8(x))
Eq(F_102(x), F_0(x) + F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_16(x)*F_19(x))
Eq(F_105(x), F_106(x) + F_109(x))
Eq(F_106(x), F_0(x) + F_107(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_19(x)*F_81(x))
Eq(F_109(x), F_110(x)*F_17(x))
Eq(F_110(x), F_0(x) + F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_19(x)*F_87(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_2(x)*F_75(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_19(x))
Eq(F_117(x), F_118(x) + F_166(x))
Eq(F_118(x), F_119(x) + F_155(x))
Eq(F_119(x), F_120(x)*F_2(x))
Eq(F_120(x), F_121(x) + F_139(x))
Eq(F_121(x), F_122(x)*F_16(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_0(x)*F_124(x))
Eq(F_124(x), x*(x - 2)*(F_124(x) + 1)**2 + (x + 1)*(F_124(x) + 1) + F_124(x) - 1)
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_19(x)*F_81(x))
Eq(F_127(x), F_128(x) + F_132(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x)**2*F_19(x))
Eq(F_131(x), F_1(x) + F_129(x))
Eq(F_132(x), F_133(x) + F_17(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_19(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_131(x)*F_132(x))
Eq(F_137(x), F_132(x)*F_138(x))
Eq(F_138(x), F_131(x) + F_132(x))
Eq(F_139(x), F_140(x)*F_145(x))
Eq(F_140(x), F_141(x) + F_19(x))
Eq(F_141(x), F_142(x) + F_143(x) + F_144(x))
Eq(F_142(x), 0)
Eq(F_143(x), F_17(x)*F_19(x))
Eq(F_144(x), F_140(x)*F_19(x))
Eq(F_145(x), F_146(x)/F_17(x))
Eq(F_146(x), -F_122(x) + F_147(x))
Eq(F_147(x), -F_105(x) + F_148(x))
Eq(F_148(x), F_149(x) + F_150(x))
Eq(F_149(x), F_0(x)*F_16(x)*F_90(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_107(x) + F_125(x))
Eq(F_152(x), F_153(x)*F_17(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_138(x)*F_19(x)*F_87(x))
Eq(F_155(x), F_156(x) - F_165(x))
Eq(F_156(x), F_157(x) + F_160(x))
Eq(F_157(x), F_122(x)*F_158(x))
Eq(F_158(x), F_159(x)/F_19(x))
Eq(F_159(x), F_84(x))
Eq(F_160(x), F_145(x)*F_161(x))
Eq(F_161(x), -F_158(x) + F_162(x))
Eq(F_162(x), F_163(x)/(F_131(x)*F_19(x)))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_13(x)*F_131(x)*F_19(x))
Eq(F_165(x), F_0(x)*F_120(x))
Eq(F_166(x), F_167(x) + F_180(x))
Eq(F_167(x), F_168(x)*F_178(x))
Eq(F_168(x), F_169(x) + F_170(x))
Eq(F_169(x), F_128(x) + F_133(x))
Eq(F_170(x), F_171(x) - F_177(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_138(x)*F_17(x))
Eq(F_173(x), F_174(x) - F_176(x))
Eq(F_174(x), F_175(x)/(F_131(x)*F_19(x)))
Eq(F_175(x), F_164(x))
Eq(F_176(x), F_138(x)*F_16(x))
Eq(F_177(x), -F_158(x) + F_174(x))
Eq(F_178(x), -F_179(x) + F_81(x))
Eq(F_179(x), F_106(x) + F_122(x))
Eq(F_180(x), F_181(x)*F_91(x))
Eq(F_181(x), F_182(x) + F_188(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x)*F_19(x))
Eq(F_184(x), F_185(x) + F_187(x))
Eq(F_185(x), F_138(x)*F_186(x))
Eq(F_186(x), F_140(x) + F_182(x))
Eq(F_187(x), F_138(x)*F_186(x))
Eq(F_188(x), F_161(x) - F_186(x))
Eq(F_189(x), F_16(x)*F_178(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_19(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_158(x)*F_81(x))
Eq(F_194(x), F_177(x)*F_87(x))
Eq(F_195(x), F_196(x))
Eq(F_196(x), F_4(x)*F_58(x))
Eq(F_197(x), F_2(x) + F_37(x))
Eq(F_198(x), F_199(x)*F_2(x))
Eq(F_199(x), F_200(x) + F_54(x))
Eq(F_200(x), F_25(x) + F_51(x))
Eq(F_201(x), F_106(x)*F_24(x))
Eq(F_202(x), F_11(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_19(x)*F_205(x))
Eq(F_205(x), F_206(x) + F_207(x))
Eq(F_206(x), F_11(x)*F_4(x))
Eq(F_207(x), F_191(x))
Eq(F_208(x), F_209(x) + F_211(x))
Eq(F_209(x), F_203(x) + F_210(x))
Eq(F_210(x), F_0(x)*F_2(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_19(x)*F_213(x))
Eq(F_213(x), F_214(x) + F_234(x))
Eq(F_214(x), F_215(x) + F_232(x))
Eq(F_215(x), F_216(x) - F_223(x))
Eq(F_216(x), F_217(x)/F_19(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_219(x) - F_5(x))
Eq(F_219(x), F_220(x))
Eq(F_220(x), F_19(x)*F_221(x))
Eq(F_221(x), F_222(x)/F_19(x))
Eq(F_222(x), F_100(x))
Eq(F_223(x), F_224(x))
Eq(F_224(x), F_19(x)*F_225(x))
Eq(F_225(x), F_226(x)/F_19(x))
Eq(F_226(x), F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_19(x)*F_229(x))
Eq(F_229(x), F_230(x) + F_231(x))
Eq(F_230(x), F_16(x)*F_78(x))
Eq(F_231(x), F_140(x)*F_15(x)*F_87(x))
Eq(F_232(x), F_233(x))
Eq(F_233(x), F_11(x)*F_219(x))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_19(x)*F_236(x))
Eq(F_236(x), F_237(x)/F_19(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_227(x) + F_239(x))
Eq(F_239(x), F_240(x))
Eq(F_240(x), F_11(x)*F_97(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, 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3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 6], [1, 6]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 6]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 5], [0, 5], [0, 5]]}, {"patt": [0, 2, 1], "pos": [[2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 6]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25734/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[226,x]+F[8,x]
F[8,x] = F[224,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[18,x]
F[12,x] = F[13,x]+F[189,x]
F[13,x] = F[14,x]+F[223,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[18,x]*F[21,x]
F[21,x] = F[14,x]+F[22,x]
F[22,x] = F[23,x]+F[28,x]
F[23,x] = F[2,x]+F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[0,x]+F[26,x]
F[26,x] = 1/F[18,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = 1/F[110,x]*F[29,x]
F[29,x] = -F[222,x]+F[30,x]
F[30,x] = 1/F[15,x]*F[31,x]
F[31,x] = -F[174,x]+F[32,x]
F[32,x] = 1/F[18,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[39,x]+F[35,x]
F[35,x] = -F[38,x]+F[36,x]
F[36,x] = 1/F[18,x]*F[37,x]
F[37,x] = F[24,x]
F[38,x] = F[2,x]*F[26,x]
F[39,x] = F[10,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[18,x]*F[42,x]
F[42,x] = F[43,x]+F[50,x]
F[43,x] = F[2,x]*F[44,x]
F[44,x] = 1/F[18,x]/F[47,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[18,x]*F[47,x]
F[47,x] = F[1,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[47,x]^2*F[18,x]
F[50,x] = F[51,x]
F[51,x] = F[18,x]*F[52,x]
F[52,x] = F[53,x]+F[62,x]
F[53,x] = F[54,x]*F[58,x]
F[54,x] = 1/F[18,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[9,x]+F[13,x]
F[58,x] = 1/F[18,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[2,x]+F[61,x]
F[61,x] = -F[2,x]+F[5,x]
F[62,x] = F[63,x]*F[64,x]
F[63,x] = -F[54,x]+F[44,x]
F[64,x] = F[138,x]+F[65,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[0,x]*F[67,x]
F[67,x] = -1+(x^2-2*x)*F[67,x]^2+(2+x)*F[67,x]
F[68,x] = 1/F[88,x]*F[69,x]
F[69,x] = -F[173,x]+F[70,x]
F[70,x] = -F[120,x]+F[71,x]
F[71,x] = F[72,x]+F[93,x]
F[72,x] = F[73,x]+F[87,x]
F[73,x] = F[15,x]*F[74,x]
F[74,x] = F[60,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[18,x]^2*F[77,x]
F[77,x] = F[65,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[18,x]*F[77,x]*F[80,x]
F[80,x] = F[47,x]+F[81,x]
F[81,x] = F[16,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[18,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[47,x]*F[81,x]
F[86,x] = F[80,x]*F[81,x]
F[87,x] = F[60,x]*F[88,x]
F[88,x] = F[18,x]+F[89,x]
F[89,x] = F[90,x]+F[91,x]+F[92,x]
F[90,x] = 0
F[91,x] = F[16,x]*F[18,x]
F[92,x] = F[18,x]*F[88,x]
F[93,x] = -F[172,x]+F[94,x]
F[94,x] = 1/F[18,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[99,x]+F[97,x]
F[97,x] = 1/F[18,x]*F[98,x]
F[98,x] = F[61,x]
F[99,x] = F[100,x]+F[113,x]
F[100,x] = -F[101,x]+F[8,x]
F[101,x] = F[0,x]+F[102,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[18,x]
F[104,x] = F[105,x]+F[109,x]
F[105,x] = F[106,x]*F[15,x]
F[106,x] = F[0,x]+F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[18,x]*F[58,x]
F[109,x] = F[110,x]*F[88,x]
F[110,x] = F[0,x]+F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[18,x]*F[77,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[2,x]*F[60,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[18,x]
F[117,x] = F[118,x]+F[164,x]
F[118,x] = F[119,x]+F[142,x]
F[119,x] = F[120,x]*F[2,x]
F[120,x] = F[121,x]+F[129,x]
F[121,x] = F[122,x]*F[15,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[0,x]*F[124,x]
F[124,x] = (x*F[124,x]+x-2*F[124,x])*(x*F[124,x]+x-1)
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[18,x]*F[58,x]
F[127,x] = F[128,x]+F[81,x]
F[128,x] = F[48,x]
F[129,x] = F[130,x]*F[88,x]
F[130,x] = 1/F[16,x]*F[131,x]
F[131,x] = -F[122,x]+F[132,x]
F[132,x] = -F[140,x]+F[133,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[0,x]*F[15,x]*F[67,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[107,x]+F[125,x]
F[137,x] = F[138,x]*F[16,x]
F[138,x] = F[139,x]
F[139,x] = F[18,x]*F[77,x]*F[80,x]
F[140,x] = F[106,x]+F[141,x]
F[141,x] = F[110,x]*F[16,x]
F[142,x] = -F[163,x]+F[143,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[122,x]*F[54,x]
F[145,x] = F[130,x]*F[146,x]
F[146,x] = F[147,x]+F[153,x]
F[147,x] = F[148,x]+F[88,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[18,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[147,x]*F[80,x]
F[152,x] = F[147,x]*F[80,x]
F[153,x] = -F[158,x]+F[154,x]
F[154,x] = -F[157,x]+F[155,x]
F[155,x] = 1/F[18,x]/F[47,x]*F[156,x]
F[156,x] = F[46,x]
F[157,x] = F[147,x]+F[80,x]
F[158,x] = -F[63,x]+F[159,x]
F[159,x] = F[160,x]+F[161,x]
F[160,x] = F[16,x]*F[80,x]
F[161,x] = -F[162,x]+F[44,x]
F[162,x] = F[15,x]*F[80,x]
F[163,x] = F[0,x]*F[120,x]
F[164,x] = F[165,x]+F[170,x]
F[165,x] = F[166,x]*F[168,x]
F[166,x] = F[158,x]+F[167,x]
F[167,x] = F[128,x]+F[82,x]
F[168,x] = -F[169,x]+F[58,x]
F[169,x] = F[106,x]+F[122,x]
F[170,x] = F[171,x]*F[68,x]
F[171,x] = F[148,x]+F[153,x]
F[172,x] = F[104,x]+F[72,x]
F[173,x] = F[15,x]*F[168,x]
F[174,x] = F[175,x]
F[175,x] = F[15,x]*F[176,x]*F[18,x]
F[176,x] = 1/F[18,x]*F[177,x]
F[177,x] = F[178,x]
F[178,x] = -F[219,x]+F[179,x]
F[179,x] = 1/F[18,x]*F[180,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[24,x]
F[183,x] = F[184,x]
F[184,x] = -F[24,x]+F[185,x]
F[185,x] = -F[25,x]+F[186,x]
F[186,x] = -F[189,x]+F[187,x]
F[187,x] = 1/F[18,x]*F[188,x]
F[188,x] = F[24,x]
F[189,x] = F[190,x]
F[190,x] = F[18,x]*F[191,x]
F[191,x] = 1/F[18,x]*F[192,x]
F[192,x] = F[193,x]
F[193,x] = -F[194,x]+F[36,x]
F[194,x] = F[195,x]
F[195,x] = F[18,x]*F[196,x]
F[196,x] = F[197,x]+F[217,x]
F[197,x] = 1/F[18,x]*F[198,x]
F[198,x] = F[199,x]
F[199,x] = -F[202,x]+F[200,x]
F[200,x] = 1/F[18,x]*F[201,x]
F[201,x] = F[24,x]
F[202,x] = -F[205,x]+F[203,x]
F[203,x] = 1/F[18,x]*F[204,x]
F[204,x] = F[23,x]
F[205,x] = F[206,x]+F[26,x]
F[206,x] = -F[209,x]+F[207,x]
F[207,x] = 1/F[18,x]*F[208,x]
F[208,x] = F[61,x]
F[209,x] = F[210,x]
F[210,x] = F[18,x]*F[211,x]
F[211,x] = F[212,x]+F[215,x]
F[212,x] = F[213,x]+F[214,x]
F[213,x] = F[0,x]*F[58,x]
F[214,x] = F[56,x]*F[64,x]
F[215,x] = F[216,x]
F[216,x] = F[18,x]*F[52,x]
F[217,x] = F[218,x]
F[218,x] = F[193,x]*F[4,x]
F[219,x] = F[2,x]*F[220,x]
F[220,x] = F[189,x]+F[221,x]
F[221,x] = F[186,x]+F[26,x]
F[222,x] = F[106,x]*F[23,x]
F[223,x] = F[10,x]
F[224,x] = F[225,x]+F[40,x]
F[225,x] = F[0,x]*F[2,x]
F[226,x] = F[224,x]+F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[18,x]*F[229,x]
F[229,x] = F[230,x]+F[238,x]
F[230,x] = F[231,x]+F[236,x]
F[231,x] = F[232,x]
F[232,x] = F[18,x]*F[233,x]
F[233,x] = F[234,x]+F[235,x]
F[234,x] = F[15,x]*F[211,x]
F[235,x] = F[14,x]*F[64,x]*F[88,x]
F[236,x] = F[237,x]
F[237,x] = F[10,x]*F[96,x]
F[238,x] = F[239,x]
F[239,x] = F[18,x]*F[240,x]
F[240,x] = 1/F[18,x]*F[241,x]
F[241,x] = F[242,x]
F[242,x] = F[243,x]+F[255,x]
F[243,x] = -F[251,x]+F[244,x]
F[244,x] = 1/F[18,x]*F[245,x]
F[245,x] = F[246,x]
F[246,x] = -F[5,x]+F[247,x]
F[247,x] = F[248,x]
F[248,x] = F[18,x]*F[249,x]
F[249,x] = 1/F[18,x]*F[250,x]
F[250,x] = F[99,x]
F[251,x] = F[252,x]
F[252,x] = F[18,x]*F[253,x]
F[253,x] = 1/F[18,x]*F[254,x]
F[254,x] = F[231,x]
F[255,x] = F[256,x]
F[256,x] = F[10,x]*F[247,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{226}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{224}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{189}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{223}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{110}\! \left(x \right)}
F_{29}\! \left(x \right) = -F_{222}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{31}\! \left(x \right) = -F_{174}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{24}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{18}\! \left(x \right) F_{47}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47} \left(x \right)^{2} F_{18}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{13}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{44}\! \left(x \right)
F_{64}\! \left(x \right) = F_{138}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{0}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = x^{2} F_{67} \left(x \right)^{2}-2 x F_{67} \left(x \right)^{2}+F_{67}\! \left(x \right) x +2 F_{67}\! \left(x \right)-1
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{88}\! \left(x \right)}
F_{69}\! \left(x \right) = -F_{173}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{93}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{87}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{60}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{65}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{47}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{16}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{47}\! \left(x \right) F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{80}\! \left(x \right) F_{81}\! \left(x \right)
F_{87}\! \left(x \right) = F_{60}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{92}\! \left(x \right) = F_{18}\! \left(x \right) F_{88}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{172}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{61}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{113}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{101}\! \left(x \right)+F_{8}\! \left(x \right)
F_{101}\! \left(x \right) = F_{0}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{18}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{109}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{15}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{88}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right) F_{60}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{18}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{164}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{142}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{2}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{129}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{15}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{0}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = x^{2} F_{124} \left(x \right)^{2}+2 x^{2} F_{124}\! \left(x \right)-2 x F_{124} \left(x \right)^{2}+x^{2}-3 x F_{124}\! \left(x \right)-x +2 F_{124}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{81}\! \left(x \right)
F_{128}\! \left(x \right) = F_{48}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{88}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{131}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{67}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{107}\! \left(x \right)+F_{125}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{16}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right) F_{80}\! \left(x \right)
F_{140}\! \left(x \right) = F_{106}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{110}\! \left(x \right) F_{16}\! \left(x \right)
F_{142}\! \left(x \right) = -F_{163}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{122}\! \left(x \right) F_{54}\! \left(x \right)
F_{145}\! \left(x \right) = F_{130}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{153}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{88}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{18}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right) F_{80}\! \left(x \right)
F_{152}\! \left(x \right) = F_{147}\! \left(x \right) F_{80}\! \left(x \right)
F_{153}\! \left(x \right) = -F_{158}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{157}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = \frac{F_{156}\! \left(x \right)}{F_{18}\! \left(x \right) F_{47}\! \left(x \right)}
F_{156}\! \left(x \right) = F_{46}\! \left(x \right)
F_{157}\! \left(x \right) = F_{147}\! \left(x \right)+F_{80}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{16}\! \left(x \right) F_{80}\! \left(x \right)
F_{161}\! \left(x \right) = -F_{162}\! \left(x \right)+F_{44}\! \left(x \right)
F_{162}\! \left(x \right) = F_{15}\! \left(x \right) F_{80}\! \left(x \right)
F_{163}\! \left(x \right) = F_{0}\! \left(x \right) F_{120}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{170}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{168}\! \left(x \right)
F_{166}\! \left(x \right) = F_{158}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{128}\! \left(x \right)+F_{82}\! \left(x \right)
F_{168}\! \left(x \right) = -F_{169}\! \left(x \right)+F_{58}\! \left(x \right)
F_{169}\! \left(x \right) = F_{106}\! \left(x \right)+F_{122}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{68}\! \left(x \right)
F_{171}\! \left(x \right) = F_{148}\! \left(x \right)+F_{153}\! \left(x \right)
F_{172}\! \left(x \right) = F_{104}\! \left(x \right)+F_{72}\! \left(x \right)
F_{173}\! \left(x \right) = F_{15}\! \left(x \right) F_{168}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{15}\! \left(x \right) F_{176}\! \left(x \right) F_{18}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = -F_{219}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = \frac{F_{180}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{24}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = \frac{F_{188}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{188}\! \left(x \right) = F_{24}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{18}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = \frac{F_{192}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = -F_{194}\! \left(x \right)+F_{36}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{18}\! \left(x \right) F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{217}\! \left(x \right)
F_{197}\! \left(x \right) = \frac{F_{198}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = -F_{202}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{24}\! \left(x \right)
F_{202}\! \left(x \right) = -F_{205}\! \left(x \right)+F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = \frac{F_{204}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{204}\! \left(x \right) = F_{23}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{26}\! \left(x \right)
F_{206}\! \left(x \right) = -F_{209}\! \left(x \right)+F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = \frac{F_{208}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{208}\! \left(x \right) = F_{61}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{18}\! \left(x \right) F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{215}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)+F_{214}\! \left(x \right)
F_{213}\! \left(x \right) = F_{0}\! \left(x \right) F_{58}\! \left(x \right)
F_{214}\! \left(x \right) = F_{56}\! \left(x \right) F_{64}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{193}\! \left(x \right) F_{4}\! \left(x \right)
F_{219}\! \left(x \right) = F_{2}\! \left(x \right) F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{189}\! \left(x \right)+F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{186}\! \left(x \right)+F_{26}\! \left(x \right)
F_{222}\! \left(x \right) = F_{106}\! \left(x \right) F_{23}\! \left(x \right)
F_{223}\! \left(x \right) = F_{10}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)+F_{40}\! \left(x \right)
F_{225}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{226}\! \left(x \right) = F_{224}\! \left(x \right)+F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{18}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{238}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{236}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{18}\! \left(x \right) F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{235}\! \left(x \right)
F_{234}\! \left(x \right) = F_{15}\! \left(x \right) F_{211}\! \left(x \right)
F_{235}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right) F_{88}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{10}\! \left(x \right) F_{96}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{18}\! \left(x \right) F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = \frac{F_{241}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{255}\! \left(x \right)
F_{243}\! \left(x \right) = -F_{251}\! \left(x \right)+F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = \frac{F_{245}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{18}\! \left(x \right) F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = \frac{F_{250}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{250}\! \left(x \right) = F_{99}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{18}\! \left(x \right) F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = \frac{F_{254}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{254}\! \left(x \right) = F_{231}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{10}\! \left(x \right) F_{247}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_226(x) + F_8(x))
Eq(F_8(x), F_224(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_18(x))
Eq(F_12(x), F_13(x) + F_189(x))
Eq(F_13(x), F_14(x) + F_223(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_18(x)*F_21(x))
Eq(F_21(x), F_14(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_28(x))
Eq(F_23(x), F_2(x) + F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), -F_0(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_18(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), F_29(x)/F_110(x))
Eq(F_29(x), -F_222(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_15(x))
Eq(F_31(x), -F_174(x) + F_32(x))
Eq(F_32(x), F_33(x)/F_18(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_39(x))
Eq(F_35(x), F_36(x) - F_38(x))
Eq(F_36(x), F_37(x)/F_18(x))
Eq(F_37(x), F_24(x))
Eq(F_38(x), F_2(x)*F_26(x))
Eq(F_39(x), F_10(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_18(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_50(x))
Eq(F_43(x), F_2(x)*F_44(x))
Eq(F_44(x), F_45(x)/(F_18(x)*F_47(x)))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_18(x)*F_47(x))
Eq(F_47(x), F_1(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_18(x)*F_47(x)**2)
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_18(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_62(x))
Eq(F_53(x), F_54(x)*F_58(x))
Eq(F_54(x), F_55(x)/F_18(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_13(x) - F_9(x))
Eq(F_58(x), F_59(x)/F_18(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_2(x) + F_61(x))
Eq(F_61(x), -F_2(x) + F_5(x))
Eq(F_62(x), F_63(x)*F_64(x))
Eq(F_63(x), F_44(x) - F_54(x))
Eq(F_64(x), F_138(x) + F_65(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_0(x)*F_67(x))
Eq(F_67(x), x*(x - 2)*F_67(x)**2 + (x + 2)*F_67(x) - 1)
Eq(F_68(x), F_69(x)/F_88(x))
Eq(F_69(x), -F_173(x) + F_70(x))
Eq(F_70(x), -F_120(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_93(x))
Eq(F_72(x), F_73(x) + F_87(x))
Eq(F_73(x), F_15(x)*F_74(x))
Eq(F_74(x), F_60(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_18(x)**2*F_77(x))
Eq(F_77(x), F_65(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_18(x)*F_77(x)*F_80(x))
Eq(F_80(x), F_47(x) + F_81(x))
Eq(F_81(x), F_16(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_18(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_47(x)*F_81(x))
Eq(F_86(x), F_80(x)*F_81(x))
Eq(F_87(x), F_60(x)*F_88(x))
Eq(F_88(x), F_18(x) + F_89(x))
Eq(F_89(x), F_90(x) + F_91(x) + F_92(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_16(x)*F_18(x))
Eq(F_92(x), F_18(x)*F_88(x))
Eq(F_93(x), -F_172(x) + F_94(x))
Eq(F_94(x), F_95(x)/F_18(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x) - F_99(x))
Eq(F_97(x), F_98(x)/F_18(x))
Eq(F_98(x), F_61(x))
Eq(F_99(x), F_100(x) + F_113(x))
Eq(F_100(x), -F_101(x) + F_8(x))
Eq(F_101(x), F_0(x) + F_102(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_18(x))
Eq(F_104(x), F_105(x) + F_109(x))
Eq(F_105(x), F_106(x)*F_15(x))
Eq(F_106(x), F_0(x) + F_107(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_18(x)*F_58(x))
Eq(F_109(x), F_110(x)*F_88(x))
Eq(F_110(x), F_0(x) + F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_18(x)*F_77(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_2(x)*F_60(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_18(x))
Eq(F_117(x), F_118(x) + F_164(x))
Eq(F_118(x), F_119(x) + F_142(x))
Eq(F_119(x), F_120(x)*F_2(x))
Eq(F_120(x), F_121(x) + F_129(x))
Eq(F_121(x), F_122(x)*F_15(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_0(x)*F_124(x))
Eq(F_124(x), x*(x - 2)*(F_124(x) + 1)**2 + (x + 1)*(F_124(x) + 1) + F_124(x) - 1)
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_18(x)*F_58(x))
Eq(F_127(x), F_128(x) + F_81(x))
Eq(F_128(x), F_48(x))
Eq(F_129(x), F_130(x)*F_88(x))
Eq(F_130(x), F_131(x)/F_16(x))
Eq(F_131(x), -F_122(x) + F_132(x))
Eq(F_132(x), F_133(x) - F_140(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_0(x)*F_15(x)*F_67(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_107(x) + F_125(x))
Eq(F_137(x), F_138(x)*F_16(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_18(x)*F_77(x)*F_80(x))
Eq(F_140(x), F_106(x) + F_141(x))
Eq(F_141(x), F_110(x)*F_16(x))
Eq(F_142(x), F_143(x) - F_163(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_122(x)*F_54(x))
Eq(F_145(x), F_130(x)*F_146(x))
Eq(F_146(x), F_147(x) + F_153(x))
Eq(F_147(x), F_148(x) + F_88(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_18(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_147(x)*F_80(x))
Eq(F_152(x), F_147(x)*F_80(x))
Eq(F_153(x), F_154(x) - F_158(x))
Eq(F_154(x), F_155(x) - F_157(x))
Eq(F_155(x), F_156(x)/(F_18(x)*F_47(x)))
Eq(F_156(x), F_46(x))
Eq(F_157(x), F_147(x) + F_80(x))
Eq(F_158(x), F_159(x) - F_63(x))
Eq(F_159(x), F_160(x) + F_161(x))
Eq(F_160(x), F_16(x)*F_80(x))
Eq(F_161(x), -F_162(x) + F_44(x))
Eq(F_162(x), F_15(x)*F_80(x))
Eq(F_163(x), F_0(x)*F_120(x))
Eq(F_164(x), F_165(x) + F_170(x))
Eq(F_165(x), F_166(x)*F_168(x))
Eq(F_166(x), F_158(x) + F_167(x))
Eq(F_167(x), F_128(x) + F_82(x))
Eq(F_168(x), -F_169(x) + F_58(x))
Eq(F_169(x), F_106(x) + F_122(x))
Eq(F_170(x), F_171(x)*F_68(x))
Eq(F_171(x), F_148(x) + F_153(x))
Eq(F_172(x), F_104(x) + F_72(x))
Eq(F_173(x), F_15(x)*F_168(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_15(x)*F_176(x)*F_18(x))
Eq(F_176(x), F_177(x)/F_18(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_179(x) - F_219(x))
Eq(F_179(x), F_180(x)/F_18(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_24(x))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_185(x) - F_24(x))
Eq(F_185(x), F_186(x) - F_25(x))
Eq(F_186(x), F_187(x) - F_189(x))
Eq(F_187(x), F_188(x)/F_18(x))
Eq(F_188(x), F_24(x))
Eq(F_189(x), F_190(x))
Eq(F_190(x), F_18(x)*F_191(x))
Eq(F_191(x), F_192(x)/F_18(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), -F_194(x) + F_36(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_18(x)*F_196(x))
Eq(F_196(x), F_197(x) + F_217(x))
Eq(F_197(x), F_198(x)/F_18(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x) - F_202(x))
Eq(F_200(x), F_201(x)/F_18(x))
Eq(F_201(x), F_24(x))
Eq(F_202(x), F_203(x) - F_205(x))
Eq(F_203(x), F_204(x)/F_18(x))
Eq(F_204(x), F_23(x))
Eq(F_205(x), F_206(x) + F_26(x))
Eq(F_206(x), F_207(x) - F_209(x))
Eq(F_207(x), F_208(x)/F_18(x))
Eq(F_208(x), F_61(x))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_18(x)*F_211(x))
Eq(F_211(x), F_212(x) + F_215(x))
Eq(F_212(x), F_213(x) + F_214(x))
Eq(F_213(x), F_0(x)*F_58(x))
Eq(F_214(x), F_56(x)*F_64(x))
Eq(F_215(x), F_216(x))
Eq(F_216(x), F_18(x)*F_52(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_193(x)*F_4(x))
Eq(F_219(x), F_2(x)*F_220(x))
Eq(F_220(x), F_189(x) + F_221(x))
Eq(F_221(x), F_186(x) + F_26(x))
Eq(F_222(x), F_106(x)*F_23(x))
Eq(F_223(x), F_10(x))
Eq(F_224(x), F_225(x) + F_40(x))
Eq(F_225(x), F_0(x)*F_2(x))
Eq(F_226(x), F_224(x) + F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_18(x)*F_229(x))
Eq(F_229(x), F_230(x) + F_238(x))
Eq(F_230(x), F_231(x) + F_236(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_18(x)*F_233(x))
Eq(F_233(x), F_234(x) + F_235(x))
Eq(F_234(x), F_15(x)*F_211(x))
Eq(F_235(x), F_14(x)*F_64(x)*F_88(x))
Eq(F_236(x), F_237(x))
Eq(F_237(x), F_10(x)*F_96(x))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_18(x)*F_240(x))
Eq(F_240(x), F_241(x)/F_18(x))
Eq(F_241(x), F_242(x))
Eq(F_242(x), F_243(x) + F_255(x))
Eq(F_243(x), F_244(x) - F_251(x))
Eq(F_244(x), F_245(x)/F_18(x))
Eq(F_245(x), F_246(x))
Eq(F_246(x), F_247(x) - F_5(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_18(x)*F_249(x))
Eq(F_249(x), F_250(x)/F_18(x))
Eq(F_250(x), F_99(x))
Eq(F_251(x), F_252(x))
Eq(F_252(x), F_18(x)*F_253(x))
Eq(F_253(x), F_254(x)/F_18(x))
Eq(F_254(x), F_231(x))
Eq(F_255(x), F_256(x))
Eq(F_256(x), F_10(x)*F_247(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, 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