0132_2103
Counting sequence:
1, 1, 2, 6, 22, 86, 338, 1318, 5110, 19770, 76466, 295810, 1144530, 4428622, 17136186, 66306722, 256565926, 992749334, 3841316550, 14863484902, 57512368162, 222536820262, 861078033110, 3331832349354, 12892103081874, 49884359171762, 193021206346882, 746871097900286, 2889923068516826, 11182191098038914, 43268071429470230, 167420319399684054, 647811710154532982, 2506625320735008438, 9699069035120090226, 37529318550267201958, 145214942356588872950, 561890817585284684570, 2174165314967239255730, 8412657172652797092770, 32551710864568188822002, 125954720186976689395374, 487365828585306180248314, 1885800313954422290917794, 7296865343295462872586502, 28234295775747372921114070, 109249029610344958428372838, 422725275870143287475635654, 1635681886574557595131667522, 6329063783945522367775932070, 24489510283162834813772770390, 94759056691835747633645460874, 366658161853894858105642499858, 1418737293800645102469965165906, 5489624173763354814326091516194, 21241405086656990456635067880030, 82190925238902803442402382380186, 318027369849951785349507558899714, 1230566606711047596795324576148598, 4761521545352527045679544427733526, 18424104232319710969000768795979926, 71289736595794302140176278239483158, 275846601811036811896229666300528018, 1067353469997049527001975068288099366, 4129988995460449399447507455539543798, 15980469059300066614869740144561372410, 61834399955047614761433725221146616754, 239260374874644561061654900889809770178, 925787701130306297929535564000664427538, 3582218192265175003814640995685970802190, 13860939350704779579817630734069654762938, 53633148337742031713568521809157756563874, 207526671016851415593164689361562124148070, 802998155396924470919603640236870449516950, 3107099605132220494529562606752846051797254, 12022528185560731305166179268614719235771558, 46519649300541608813535103776252125071551074, 180001887926075067926988867650244194285152550, 696494495210523045827275353938107540091377366, 2694997188350539934940846930525168263508330602, 10427950106083741270560710953016903188291177362, 40349631489421707560333921774480661694986144498, 156127785880207730567457374561036558217088974018, 604116682707412466427938684046381771582021475262, 2337552949129946934898615845158506400279580964186, 9044864918310039454297317388407677976557003929218, 34997958622039238881083793217983983395908411484886, 135420165892187302871008332122085682178342671527254, 523991171265605266825204571442965916884903325257142, 2027517436235405249186863142152286667778360186281078, 7845221789347397923804847544941310023088122214609074, 30356091555162934118812986825030369046117784407227558, 117459049501529570351875862538290405430659964758188534, 454492907452582019594888505169017521724977037985225434, 1758602711339081439783500017667225995139178973921585586, 6804690338653597741263315073094043458616983687946892514, 26329886964468371465512118059336193976488229690408711474, 101880161044749782359019423444389524771288760929263513966, 394212372750067581268416942501082464038385644393688427130, 1525354821150890496139565900378797933658067556099707644578, 5902167185106105365225696321430758844062390627225521878982
Generating function in Maple syntax:
(x^5-5*x^4+13*x^3-12*x^2+6*x-1)/(4*x^5-13*x^4+22*x^3-17*x^2+7*x-1)
Generating function in latex syntax:
\frac{x^{5}-5 x^{4}+13 x^{3}-12 x^{2}+6 x -1}{4 x^{5}-13 x^{4}+22 x^{3}-17 x^{2}+7 x -1}
Generating function in sympy syntax:
(x**5 - 5*x**4 + 13*x**3 - 12*x**2 + 6*x - 1)/(4*x**5 - 13*x**4 + 22*x**3 - 17*x**2 + 7*x - 1)
Implicit equation for the generating function in Maple syntax:
(4*x^5-13*x^4+22*x^3-17*x^2+7*x-1)*F(x)-x^5+5*x^4-13*x^3+12*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{5}-13 x^{4}+22 x^{3}-17 x^{2}+7 x -1\right) F \! \left(x \right)-x^{5}+5 x^{4}-13 x^{3}+12 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1/4,0)+28024/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n+3)+28024/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n+3)+28024/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n+3)+28024/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n+3)+28024/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n+3)-128066/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n+2)-128066/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n+2)-128066/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n+2)-128066/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n+2)-128066/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n+2)+240334/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n+1)+240334/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n+1)+240334/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n+1)+240334/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n+1)+240334/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n+1)+23662/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n-1)+23662/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n-1)+23662/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n-1)+23662/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n-1)+23662/377305*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n-1)-21452/75461*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n)-21452/75461*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n)-21452/75461*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n)-21452/75461*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n)-21452/75461*RootOf(4*_Z^5-13*_Z^4+22*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}\frac{1}{4} & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{28024 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{377305}+\frac{28024 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{377305}+\frac{28024 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{377305}+\frac{28024 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{377305}+\frac{28024 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{377305}-\frac{128066 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{377305}-\frac{128066 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{377305}-\frac{128066 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{377305}-\frac{128066 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{377305}-\frac{128066 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{377305}+\frac{240334 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{377305}+\frac{240334 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{377305}+\frac{240334 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{377305}+\frac{240334 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{377305}+\frac{240334 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{377305}+\frac{23662 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{377305}+\frac{23662 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{377305}+\frac{23662 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{377305}+\frac{23662 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{377305}+\frac{23662 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{377305}-\frac{21452 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{75461}-\frac{21452 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{75461}-\frac{21452 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{75461}-\frac{21452 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{75461}-\frac{21452 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+22 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{75461}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 86
a(n+5) = 4*a(n)-13*a(n+1)+22*a(n+2)-17*a(n+3)+7*a(n+4), n >= 6
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 86
a \! \left(n +5\right) = 4 a \! \left(n \right)-13 a \! \left(n +1\right)+22 a \! \left(n +2\right)-17 a \! \left(n +3\right)+7 a \! \left(n +4\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14607/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[28,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]+F[16,x]+F[27,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[22,x]+F[7,x]
F[25,x] = F[26,x]
F[26,x] = F[21,x]*F[4,x]
F[27,x] = F[13,x]*F[4,x]
F[28,x] = F[2,x]+F[29,x]
F[29,x] = F[121,x]+F[15,x]+F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[58,x]
F[32,x] = F[33,x]+F[7,x]
F[33,x] = F[15,x]+F[16,x]+F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[13,x]+F[36,x]
F[36,x] = F[33,x]+F[37,x]
F[37,x] = F[15,x]+F[38,x]+F[49,x]+F[57,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[19,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[40,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[22,x]+F[44,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[43,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[21,x]+F[51,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[33,x]+F[52,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[51,x]
F[57,x] = F[36,x]*F[4,x]
F[58,x] = F[59,x]+F[79,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[2,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[62,x]
F[65,x] = F[59,x]+F[66,x]
F[66,x] = 2*F[15,x]+F[67,x]+F[78,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[63,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[69,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[59,x]+F[73,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[72,x]
F[78,x] = F[4,x]*F[65,x]
F[79,x] = 2*F[15,x]+F[80,x]+F[91,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[63,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[82,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[29,x]+F[86,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[85,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[29,x]+F[94,x]
F[94,x] = 2*F[15,x]+F[80,x]+F[95,x]
F[95,x] = F[4,x]*F[93,x]
F[96,x] = F[79,x]+F[97,x]
F[97,x] = 2*F[15,x]+F[109,x]+F[120,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[103,x]
F[100,x] = F[101,x]+F[70,x]
F[101,x] = F[102,x]
F[102,x] = F[100,x]*F[4,x]
F[103,x] = F[104,x]+F[107,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[104,x]+F[86,x]
F[107,x] = F[108,x]
F[108,x] = F[103,x]*F[4,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[114,x]
F[111,x] = F[112,x]+F[86,x]
F[112,x] = F[113,x]
F[113,x] = F[111,x]*F[4,x]
F[114,x] = F[115,x]+F[118,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[115,x]+F[79,x]
F[118,x] = F[119,x]
F[119,x] = F[114,x]*F[4,x]
F[120,x] = F[4,x]*F[96,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[130,x]
F[123,x] = F[124,x]+F[2,x]
F[124,x] = F[125,x]+F[129,x]+F[15,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[128,x]
F[127,x] = F[11,x]+F[14,x]
F[128,x] = F[63,x]+F[94,x]
F[129,x] = F[123,x]*F[4,x]
F[130,x] = F[131,x]+F[29,x]
F[131,x] = F[132,x]+F[136,x]+F[15,x]+F[80,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[14,x]+F[37,x]
F[135,x] = F[66,x]+F[97,x]
F[136,x] = F[130,x]*F[4,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{28}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{121}\! \left(x \right)+F_{15}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{58}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{7}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)+F_{49}\! \left(x \right)+F_{57}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{21}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{33}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{57}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{79}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{67}\! \left(x \right)+F_{78}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{59}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{80}\! \left(x \right)+F_{91}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{63}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{29}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{29}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{80}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{79}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{109}\! \left(x \right)+F_{120}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{103}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{70}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{107}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{104}\! \left(x \right)+F_{86}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{114}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{86}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{118}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{115}\! \left(x \right)+F_{79}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{130}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{2}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{129}\! \left(x \right)+F_{15}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{128}\! \left(x \right)
F_{127}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{128}\! \left(x \right) = F_{63}\! \left(x \right)+F_{94}\! \left(x \right)
F_{129}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{29}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{136}\! \left(x \right)+F_{15}\! \left(x \right)+F_{80}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{14}\! \left(x \right)+F_{37}\! \left(x \right)
F_{135}\! \left(x \right) = F_{66}\! \left(x \right)+F_{97}\! \left(x \right)
F_{136}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_28(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_27(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_22(x) + F_7(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_21(x)*F_4(x))
Eq(F_27(x), F_13(x)*F_4(x))
Eq(F_28(x), F_2(x) + F_29(x))
Eq(F_29(x), F_121(x) + F_15(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_58(x))
Eq(F_32(x), F_33(x) + F_7(x))
Eq(F_33(x), F_15(x) + F_16(x) + F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_13(x) + F_36(x))
Eq(F_36(x), F_33(x) + F_37(x))
Eq(F_37(x), F_15(x) + F_38(x) + F_49(x) + F_57(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_19(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_40(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_22(x) + F_44(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_43(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_21(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_33(x) + F_52(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_51(x))
Eq(F_57(x), F_36(x)*F_4(x))
Eq(F_58(x), F_59(x) + F_79(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_2(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_62(x))
Eq(F_65(x), F_59(x) + F_66(x))
Eq(F_66(x), 2*F_15(x) + F_67(x) + F_78(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_63(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_69(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_59(x) + F_73(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_72(x))
Eq(F_78(x), F_4(x)*F_65(x))
Eq(F_79(x), 2*F_15(x) + F_80(x) + F_91(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_63(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_82(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_29(x) + F_86(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_85(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_96(x))
Eq(F_93(x), F_29(x) + F_94(x))
Eq(F_94(x), 2*F_15(x) + F_80(x) + F_95(x))
Eq(F_95(x), F_4(x)*F_93(x))
Eq(F_96(x), F_79(x) + F_97(x))
Eq(F_97(x), F_109(x) + F_120(x) + 2*F_15(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_103(x))
Eq(F_100(x), F_101(x) + F_70(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_100(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_107(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_104(x) + F_86(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_103(x)*F_4(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x) + F_114(x))
Eq(F_111(x), F_112(x) + F_86(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_111(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_118(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_115(x) + F_79(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_114(x)*F_4(x))
Eq(F_120(x), F_4(x)*F_96(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_130(x))
Eq(F_123(x), F_124(x) + F_2(x))
Eq(F_124(x), F_125(x) + F_129(x) + F_15(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_128(x))
Eq(F_127(x), F_11(x) + F_14(x))
Eq(F_128(x), F_63(x) + F_94(x))
Eq(F_129(x), F_123(x)*F_4(x))
Eq(F_130(x), F_131(x) + F_29(x))
Eq(F_131(x), F_132(x) + F_136(x) + F_15(x) + F_80(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_14(x) + F_37(x))
Eq(F_135(x), F_66(x) + F_97(x))
Eq(F_136(x), F_130(x)*F_4(x))
Pack JSON:
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Specification JSON:
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"comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 1], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 5]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 1], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[1, 5]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 4]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 1], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[0, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: regular_insertion_encoding_bottom
Tree: http://permpal.com/tree/14608/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[45,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[6,x]
F[14,x] = F[15,x]+F[16,x]+F[37,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[18,x]+F[23,x]
F[18,x] = F[10,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[12,x]+F[22,x]
F[22,x] = F[20,x]
F[23,x] = F[14,x]+F[24,x]
F[24,x] = 2*F[15,x]+F[25,x]+F[29,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[19,x]
F[28,x] = F[24,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[12,x]
F[34,x] = 2*F[15,x]+F[29,x]+F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[22,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[1,x]+F[12,x]
F[42,x] = F[15,x]+F[37,x]+F[43,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[10,x]+F[22,x]
F[45,x] = F[15,x]+F[231,x]+F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[176,x]+F[48,x]
F[48,x] = F[2,x]+F[49,x]
F[49,x] = F[15,x]+F[50,x]+F[51,x]
F[50,x] = F[12,x]*F[48,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[56,x]
F[53,x] = F[12,x]+F[54,x]
F[54,x] = F[15,x]+F[51,x]+F[55,x]
F[55,x] = F[12,x]*F[2,x]
F[56,x] = F[57,x]+F[87,x]
F[57,x] = F[15,x]+F[58,x]+F[59,x]
F[58,x] = F[10,x]*F[12,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[12,x]+F[62,x]
F[62,x] = F[15,x]+F[58,x]+F[63,x]
F[63,x] = F[12,x]*F[61,x]
F[64,x] = F[57,x]+F[65,x]
F[65,x] = F[15,x]+F[66,x]+F[67,x]+F[83,x]
F[66,x] = F[12,x]*F[19,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[69,x]+F[77,x]
F[69,x] = F[62,x]+F[70,x]
F[70,x] = 2*F[15,x]+F[66,x]+F[71,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[73,x]+F[75,x]
F[73,x] = F[74,x]
F[74,x] = x^2
F[75,x] = 2*F[15,x]+F[71,x]+F[76,x]
F[76,x] = F[12,x]*F[22,x]
F[77,x] = F[65,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[70,x]
F[82,x] = F[78,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[74,x]
F[86,x] = 2*F[15,x]+F[76,x]+F[83,x]
F[87,x] = F[15,x]+F[151,x]+F[88,x]+F[89,x]
F[88,x] = F[12,x]*F[49,x]
F[89,x] = F[12,x]*F[90,x]
F[90,x] = F[130,x]+F[91,x]
F[91,x] = F[54,x]+F[92,x]
F[92,x] = F[15,x]+F[88,x]+F[93,x]+F[94,x]
F[93,x] = F[12,x]*F[91,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[96,x]+F[99,x]
F[96,x] = F[73,x]+F[97,x]
F[97,x] = 2*F[15,x]+F[94,x]+F[98,x]
F[98,x] = F[12,x]*F[54,x]
F[99,x] = F[100,x]+F[112,x]
F[100,x] = 2*F[15,x]+F[101,x]+F[76,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]+F[106,x]
F[103,x] = F[104,x]+F[73,x]
F[104,x] = 2*F[15,x]+F[105,x]+F[76,x]
F[105,x] = F[103,x]*F[12,x]
F[106,x] = F[100,x]+F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[104,x]
F[111,x] = F[107,x]
F[112,x] = 2*F[15,x]+F[113,x]+F[117,x]+F[129,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[114,x]+F[54,x]
F[117,x] = F[118,x]*F[12,x]
F[118,x] = F[119,x]+F[123,x]
F[119,x] = F[120,x]+F[97,x]
F[120,x] = 2*F[15,x]+F[113,x]+F[121,x]+F[122,x]
F[121,x] = F[119,x]*F[12,x]
F[122,x] = 0
F[123,x] = F[112,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[12,x]*F[126,x]
F[126,x] = F[127,x]+F[128,x]
F[127,x] = F[120,x]
F[128,x] = F[124,x]
F[129,x] = 0
F[130,x] = F[131,x]+F[87,x]
F[131,x] = F[132,x]+F[134,x]+F[148,x]+F[15,x]+F[173,x]
F[132,x] = F[12,x]*F[133,x]
F[133,x] = F[115,x]
F[134,x] = F[12,x]*F[135,x]
F[135,x] = F[136,x]+F[142,x]
F[136,x] = F[137,x]+F[92,x]
F[137,x] = 2*F[15,x]+F[132,x]+F[138,x]+F[141,x]
F[138,x] = F[12,x]*F[139,x]
F[139,x] = F[140,x]+F[97,x]
F[140,x] = 2*F[15,x]+F[113,x]+F[138,x]+F[141,x]
F[141,x] = 0
F[142,x] = F[131,x]+F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[137,x]
F[147,x] = F[143,x]
F[148,x] = F[12,x]*F[149,x]
F[149,x] = F[150,x]+F[172,x]
F[150,x] = 2*F[15,x]+F[151,x]+F[98,x]
F[151,x] = F[12,x]*F[152,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[150,x]+F[85,x]
F[154,x] = F[155,x]+F[164,x]
F[155,x] = 2*F[15,x]+F[156,x]+F[76,x]
F[156,x] = F[12,x]*F[157,x]
F[157,x] = F[158,x]+F[84,x]
F[158,x] = F[155,x]+F[159,x]
F[159,x] = F[160,x]
F[160,x] = F[12,x]*F[161,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[86,x]
F[163,x] = F[159,x]
F[164,x] = 2*F[15,x]+F[113,x]+F[165,x]+F[175,x]
F[165,x] = F[12,x]*F[166,x]
F[166,x] = F[149,x]+F[167,x]
F[167,x] = F[164,x]+F[168,x]
F[168,x] = F[169,x]
F[169,x] = F[12,x]*F[170,x]
F[170,x] = F[171,x]+F[174,x]
F[171,x] = F[172,x]
F[172,x] = 2*F[15,x]+F[113,x]+F[148,x]+F[173,x]
F[173,x] = 0
F[174,x] = F[168,x]
F[175,x] = 0
F[176,x] = F[177,x]+F[45,x]
F[177,x] = F[15,x]+F[178,x]+F[192,x]+F[226,x]
F[178,x] = F[12,x]*F[179,x]
F[179,x] = F[180,x]+F[181,x]
F[180,x] = F[133,x]+F[49,x]
F[181,x] = F[177,x]+F[182,x]
F[182,x] = 2*F[15,x]+F[183,x]+F[187,x]+F[225,x]
F[183,x] = F[12,x]*F[184,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[133,x]
F[186,x] = F[182,x]
F[187,x] = F[12,x]*F[188,x]
F[188,x] = F[189,x]+F[224,x]
F[189,x] = 2*F[15,x]+F[190,x]+F[192,x]
F[190,x] = F[12,x]*F[191,x]
F[191,x] = F[54,x]
F[192,x] = F[12,x]*F[193,x]
F[193,x] = F[194,x]+F[195,x]
F[194,x] = F[189,x]+F[31,x]
F[195,x] = F[196,x]+F[208,x]
F[196,x] = 2*F[15,x]+F[197,x]+F[35,x]
F[197,x] = F[12,x]*F[198,x]
F[198,x] = F[199,x]+F[202,x]
F[199,x] = F[200,x]+F[31,x]
F[200,x] = 2*F[15,x]+F[201,x]+F[35,x]
F[201,x] = F[12,x]*F[199,x]
F[202,x] = F[196,x]+F[203,x]
F[203,x] = F[204,x]
F[204,x] = F[12,x]*F[205,x]
F[205,x] = F[206,x]+F[207,x]
F[206,x] = F[200,x]
F[207,x] = F[203,x]
F[208,x] = 2*F[15,x]+F[209,x]+F[211,x]+F[223,x]
F[209,x] = F[12,x]*F[210,x]
F[210,x] = F[114,x]
F[211,x] = F[12,x]*F[212,x]
F[212,x] = F[213,x]+F[217,x]
F[213,x] = F[189,x]+F[214,x]
F[214,x] = 2*F[15,x]+F[209,x]+F[215,x]+F[216,x]
F[215,x] = F[12,x]*F[213,x]
F[216,x] = 0
F[217,x] = F[208,x]+F[218,x]
F[218,x] = F[219,x]
F[219,x] = F[12,x]*F[220,x]
F[220,x] = F[221,x]+F[222,x]
F[221,x] = F[214,x]
F[222,x] = F[218,x]
F[223,x] = 0
F[224,x] = 2*F[15,x]+F[187,x]+F[209,x]+F[225,x]
F[225,x] = 0
F[226,x] = F[12,x]*F[227,x]
F[227,x] = F[228,x]+F[268,x]
F[228,x] = F[15,x]+F[229,x]+F[231,x]
F[229,x] = F[12,x]*F[230,x]
F[230,x] = F[2,x]+F[54,x]
F[231,x] = F[12,x]*F[232,x]
F[232,x] = F[233,x]+F[234,x]
F[233,x] = F[228,x]+F[39,x]
F[234,x] = F[235,x]+F[256,x]
F[235,x] = F[15,x]+F[236,x]+F[43,x]
F[236,x] = F[12,x]*F[237,x]
F[237,x] = F[238,x]+F[38,x]
F[238,x] = F[235,x]+F[239,x]
F[239,x] = F[15,x]+F[240,x]+F[242,x]+F[252,x]
F[240,x] = F[12,x]*F[241,x]
F[241,x] = F[19,x]
F[242,x] = F[12,x]*F[243,x]
F[243,x] = F[244,x]+F[246,x]
F[244,x] = F[245,x]+F[42,x]
F[245,x] = 2*F[15,x]+F[240,x]+F[29,x]
F[246,x] = F[239,x]+F[247,x]
F[247,x] = F[248,x]
F[248,x] = F[12,x]*F[249,x]
F[249,x] = F[250,x]+F[251,x]
F[250,x] = F[245,x]
F[251,x] = F[247,x]
F[252,x] = F[12,x]*F[253,x]
F[253,x] = F[254,x]+F[255,x]
F[254,x] = F[32,x]
F[255,x] = 2*F[15,x]+F[252,x]+F[35,x]
F[256,x] = F[15,x]+F[257,x]+F[259,x]+F[279,x]
F[257,x] = F[12,x]*F[258,x]
F[258,x] = F[114,x]+F[49,x]
F[259,x] = F[12,x]*F[260,x]
F[260,x] = F[227,x]+F[261,x]
F[261,x] = F[256,x]+F[262,x]
F[262,x] = F[15,x]+F[263,x]+F[265,x]+F[276,x]+F[301,x]
F[263,x] = F[12,x]*F[264,x]
F[264,x] = F[133,x]
F[265,x] = F[12,x]*F[266,x]
F[266,x] = F[267,x]+F[270,x]
F[267,x] = F[268,x]+F[269,x]
F[268,x] = F[15,x]+F[192,x]+F[226,x]+F[257,x]
F[269,x] = 2*F[15,x]+F[187,x]+F[225,x]+F[263,x]
F[270,x] = F[262,x]+F[271,x]
F[271,x] = F[272,x]
F[272,x] = F[12,x]*F[273,x]
F[273,x] = F[274,x]+F[275,x]
F[274,x] = F[269,x]
F[275,x] = F[271,x]
F[276,x] = F[12,x]*F[277,x]
F[277,x] = F[278,x]+F[300,x]
F[278,x] = 2*F[15,x]+F[190,x]+F[279,x]
F[279,x] = F[12,x]*F[280,x]
F[280,x] = F[281,x]+F[282,x]
F[281,x] = F[254,x]+F[278,x]
F[282,x] = F[283,x]+F[292,x]
F[283,x] = 2*F[15,x]+F[284,x]+F[35,x]
F[284,x] = F[12,x]*F[285,x]
F[285,x] = F[253,x]+F[286,x]
F[286,x] = F[283,x]+F[287,x]
F[287,x] = F[288,x]
F[288,x] = F[12,x]*F[289,x]
F[289,x] = F[290,x]+F[291,x]
F[290,x] = F[255,x]
F[291,x] = F[287,x]
F[292,x] = 2*F[15,x]+F[209,x]+F[293,x]+F[303,x]
F[293,x] = F[12,x]*F[294,x]
F[294,x] = F[277,x]+F[295,x]
F[295,x] = F[292,x]+F[296,x]
F[296,x] = F[297,x]
F[297,x] = F[12,x]*F[298,x]
F[298,x] = F[299,x]+F[302,x]
F[299,x] = F[300,x]
F[300,x] = 2*F[15,x]+F[209,x]+F[276,x]+F[301,x]
F[301,x] = 0
F[302,x] = F[296,x]
F[303,x] = 0
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_{12}\! \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_{45}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \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_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{37}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{22}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{22}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right)+F_{231}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{176}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right)+F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{87}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{57}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right)+F_{66}\! \left(x \right)+F_{67}\! \left(x \right)+F_{83}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{77}\! \left(x \right)
F_{69}\! \left(x \right) = F_{62}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = x^{2}
F_{75}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \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_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{70}\! \left(x \right)
F_{82}\! \left(x \right) = F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \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_{74}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{76}\! \left(x \right)+F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{15}\! \left(x \right)+F_{151}\! \left(x \right)+F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{130}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{54}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right)+F_{88}\! \left(x \right)+F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{96}\! \left(x \right) = F_{73}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{112}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{101}\! \left(x \right)+F_{76}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{106}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{73}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{105}\! \left(x \right)+F_{76}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{100}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{104}\! \left(x \right)
F_{111}\! \left(x \right) = F_{107}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{113}\! \left(x \right)+F_{117}\! \left(x \right)+F_{129}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{54}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{12}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{97}\! \left(x \right)
F_{120}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{113}\! \left(x \right)+F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{122}\! \left(x \right) = 0
F_{123}\! \left(x \right) = F_{112}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{128}\! \left(x \right)
F_{127}\! \left(x \right) = F_{120}\! \left(x \right)
F_{128}\! \left(x \right) = F_{124}\! \left(x \right)
F_{129}\! \left(x \right) = 0
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{87}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{134}\! \left(x \right)+F_{148}\! \left(x \right)+F_{15}\! \left(x \right)+F_{173}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{115}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{142}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{92}\! \left(x \right)
F_{137}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{132}\! \left(x \right)+F_{138}\! \left(x \right)+F_{141}\! \left(x \right)
F_{138}\! \left(x \right) = F_{12}\! \left(x \right) F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{97}\! \left(x \right)
F_{140}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{113}\! \left(x \right)+F_{138}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = 0
F_{142}\! \left(x \right) = F_{131}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{137}\! \left(x \right)
F_{147}\! \left(x \right) = F_{143}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{172}\! \left(x \right)
F_{150}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{151}\! \left(x \right)+F_{98}\! \left(x \right)
F_{151}\! \left(x \right) = F_{12}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{150}\! \left(x \right)+F_{85}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{164}\! \left(x \right)
F_{155}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{156}\! \left(x \right)+F_{76}\! \left(x \right)
F_{156}\! \left(x \right) = F_{12}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{84}\! \left(x \right)
F_{158}\! \left(x \right) = F_{155}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{12}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{86}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{113}\! \left(x \right)+F_{165}\! \left(x \right)+F_{175}\! \left(x \right)
F_{165}\! \left(x \right) = F_{12}\! \left(x \right) F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{149}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{164}\! \left(x \right)+F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{12}\! \left(x \right) F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{174}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{113}\! \left(x \right)+F_{148}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = 0
F_{174}\! \left(x \right) = F_{168}\! \left(x \right)
F_{175}\! \left(x \right) = 0
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{45}\! \left(x \right)
F_{177}\! \left(x \right) = F_{15}\! \left(x \right)+F_{178}\! \left(x \right)+F_{192}\! \left(x \right)+F_{226}\! \left(x \right)
F_{178}\! \left(x \right) = F_{12}\! \left(x \right) F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{181}\! \left(x \right)
F_{180}\! \left(x \right) = F_{133}\! \left(x \right)+F_{49}\! \left(x \right)
F_{181}\! \left(x \right) = F_{177}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{183}\! \left(x \right)+F_{187}\! \left(x \right)+F_{225}\! \left(x \right)
F_{183}\! \left(x \right) = F_{12}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{133}\! \left(x \right)
F_{186}\! \left(x \right) = F_{182}\! \left(x \right)
F_{187}\! \left(x \right) = F_{12}\! \left(x \right) F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{224}\! \left(x \right)
F_{189}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{190}\! \left(x \right)+F_{192}\! \left(x \right)
F_{190}\! \left(x \right) = F_{12}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{54}\! \left(x \right)
F_{192}\! \left(x \right) = F_{12}\! \left(x \right) F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{195}\! \left(x \right)
F_{194}\! \left(x \right) = F_{189}\! \left(x \right)+F_{31}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{208}\! \left(x \right)
F_{196}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{197}\! \left(x \right)+F_{35}\! \left(x \right)
F_{197}\! \left(x \right) = F_{12}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{202}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{31}\! \left(x \right)
F_{200}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{201}\! \left(x \right)+F_{35}\! \left(x \right)
F_{201}\! \left(x \right) = F_{12}\! \left(x \right) F_{199}\! \left(x \right)
F_{202}\! \left(x \right) = F_{196}\! \left(x \right)+F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{12}\! \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_{200}\! \left(x \right)
F_{207}\! \left(x \right) = F_{203}\! \left(x \right)
F_{208}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{209}\! \left(x \right)+F_{211}\! \left(x \right)+F_{223}\! \left(x \right)
F_{209}\! \left(x \right) = F_{12}\! \left(x \right) F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{114}\! \left(x \right)
F_{211}\! \left(x \right) = F_{12}\! \left(x \right) F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)+F_{217}\! \left(x \right)
F_{213}\! \left(x \right) = F_{189}\! \left(x \right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{209}\! \left(x \right)+F_{215}\! \left(x \right)+F_{216}\! \left(x \right)
F_{215}\! \left(x \right) = F_{12}\! \left(x \right) F_{213}\! \left(x \right)
F_{216}\! \left(x \right) = 0
F_{217}\! \left(x \right) = F_{208}\! \left(x \right)+F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = F_{12}\! \left(x \right) F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)+F_{222}\! \left(x \right)
F_{221}\! \left(x \right) = F_{214}\! \left(x \right)
F_{222}\! \left(x \right) = F_{218}\! \left(x \right)
F_{223}\! \left(x \right) = 0
F_{224}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{187}\! \left(x \right)+F_{209}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = 0
F_{226}\! \left(x \right) = F_{12}\! \left(x \right) F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)+F_{268}\! \left(x \right)
F_{228}\! \left(x \right) = F_{15}\! \left(x \right)+F_{229}\! \left(x \right)+F_{231}\! \left(x \right)
F_{229}\! \left(x \right) = F_{12}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{231}\! \left(x \right) = F_{12}\! \left(x \right) F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{234}\! \left(x \right)
F_{233}\! \left(x \right) = F_{228}\! \left(x \right)+F_{39}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)+F_{256}\! \left(x \right)
F_{235}\! \left(x \right) = F_{15}\! \left(x \right)+F_{236}\! \left(x \right)+F_{43}\! \left(x \right)
F_{236}\! \left(x \right) = F_{12}\! \left(x \right) F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)+F_{38}\! \left(x \right)
F_{238}\! \left(x \right) = F_{235}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{15}\! \left(x \right)+F_{240}\! \left(x \right)+F_{242}\! \left(x \right)+F_{252}\! \left(x \right)
F_{240}\! \left(x \right) = F_{12}\! \left(x \right) F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{19}\! \left(x \right)
F_{242}\! \left(x \right) = F_{12}\! \left(x \right) F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{246}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)+F_{42}\! \left(x \right)
F_{245}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{240}\! \left(x \right)+F_{29}\! \left(x \right)
F_{246}\! \left(x \right) = F_{239}\! \left(x \right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{12}\! \left(x \right) F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{251}\! \left(x \right)
F_{250}\! \left(x \right) = F_{245}\! \left(x \right)
F_{251}\! \left(x \right) = F_{247}\! \left(x \right)
F_{252}\! \left(x \right) = F_{12}\! \left(x \right) F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)+F_{255}\! \left(x \right)
F_{254}\! \left(x \right) = F_{32}\! \left(x \right)
F_{255}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{252}\! \left(x \right)+F_{35}\! \left(x \right)
F_{256}\! \left(x \right) = F_{15}\! \left(x \right)+F_{257}\! \left(x \right)+F_{259}\! \left(x \right)+F_{279}\! \left(x \right)
F_{257}\! \left(x \right) = F_{12}\! \left(x \right) F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{114}\! \left(x \right)+F_{49}\! \left(x \right)
F_{259}\! \left(x \right) = F_{12}\! \left(x \right) F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{227}\! \left(x \right)+F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = F_{256}\! \left(x \right)+F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{15}\! \left(x \right)+F_{263}\! \left(x \right)+F_{265}\! \left(x \right)+F_{276}\! \left(x \right)+F_{301}\! \left(x \right)
F_{263}\! \left(x \right) = F_{12}\! \left(x \right) F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{133}\! \left(x \right)
F_{265}\! \left(x \right) = F_{12}\! \left(x \right) F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{270}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)+F_{269}\! \left(x \right)
F_{268}\! \left(x \right) = F_{15}\! \left(x \right)+F_{192}\! \left(x \right)+F_{226}\! \left(x \right)+F_{257}\! \left(x \right)
F_{269}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{187}\! \left(x \right)+F_{225}\! \left(x \right)+F_{263}\! \left(x \right)
F_{270}\! \left(x \right) = F_{262}\! \left(x \right)+F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{12}\! \left(x \right) F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)+F_{275}\! \left(x \right)
F_{274}\! \left(x \right) = F_{269}\! \left(x \right)
F_{275}\! \left(x \right) = F_{271}\! \left(x \right)
F_{276}\! \left(x \right) = F_{12}\! \left(x \right) F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)+F_{300}\! \left(x \right)
F_{278}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{190}\! \left(x \right)+F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = F_{12}\! \left(x \right) F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)+F_{282}\! \left(x \right)
F_{281}\! \left(x \right) = F_{254}\! \left(x \right)+F_{278}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)+F_{292}\! \left(x \right)
F_{283}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{284}\! \left(x \right)+F_{35}\! \left(x \right)
F_{284}\! \left(x \right) = F_{12}\! \left(x \right) F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{253}\! \left(x \right)+F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = F_{283}\! \left(x \right)+F_{287}\! \left(x \right)
F_{287}\! \left(x \right) = F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{12}\! \left(x \right) F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)+F_{291}\! \left(x \right)
F_{290}\! \left(x \right) = F_{255}\! \left(x \right)
F_{291}\! \left(x \right) = F_{287}\! \left(x \right)
F_{292}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{209}\! \left(x \right)+F_{293}\! \left(x \right)+F_{303}\! \left(x \right)
F_{293}\! \left(x \right) = F_{12}\! \left(x \right) F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{277}\! \left(x \right)+F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{292}\! \left(x \right)+F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{12}\! \left(x \right) F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)+F_{302}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{209}\! \left(x \right)+F_{276}\! \left(x \right)+F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = 0
F_{302}\! \left(x \right) = F_{296}\! \left(x \right)
F_{303}\! \left(x \right) = 0
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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_45(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_6(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_37(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_23(x))
Eq(F_18(x), F_10(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_12(x) + F_22(x))
Eq(F_22(x), F_20(x))
Eq(F_23(x), F_14(x) + F_24(x))
Eq(F_24(x), 2*F_15(x) + F_25(x) + F_29(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_19(x))
Eq(F_28(x), F_24(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_12(x))
Eq(F_34(x), 2*F_15(x) + F_29(x) + F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_22(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_1(x) + F_12(x))
Eq(F_42(x), F_15(x) + F_37(x) + F_43(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_10(x) + F_22(x))
Eq(F_45(x), F_15(x) + F_231(x) + F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_176(x) + F_48(x))
Eq(F_48(x), F_2(x) + F_49(x))
Eq(F_49(x), F_15(x) + F_50(x) + F_51(x))
Eq(F_50(x), F_12(x)*F_48(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_56(x))
Eq(F_53(x), F_12(x) + F_54(x))
Eq(F_54(x), F_15(x) + F_51(x) + F_55(x))
Eq(F_55(x), F_12(x)*F_2(x))
Eq(F_56(x), F_57(x) + F_87(x))
Eq(F_57(x), F_15(x) + F_58(x) + F_59(x))
Eq(F_58(x), F_10(x)*F_12(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_12(x) + F_62(x))
Eq(F_62(x), F_15(x) + F_58(x) + F_63(x))
Eq(F_63(x), F_12(x)*F_61(x))
Eq(F_64(x), F_57(x) + F_65(x))
Eq(F_65(x), F_15(x) + F_66(x) + F_67(x) + F_83(x))
Eq(F_66(x), F_12(x)*F_19(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_77(x))
Eq(F_69(x), F_62(x) + F_70(x))
Eq(F_70(x), 2*F_15(x) + F_66(x) + F_71(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_75(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), x**2)
Eq(F_75(x), 2*F_15(x) + F_71(x) + F_76(x))
Eq(F_76(x), F_12(x)*F_22(x))
Eq(F_77(x), F_65(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_70(x))
Eq(F_82(x), F_78(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_74(x))
Eq(F_86(x), 2*F_15(x) + F_76(x) + F_83(x))
Eq(F_87(x), F_15(x) + F_151(x) + F_88(x) + F_89(x))
Eq(F_88(x), F_12(x)*F_49(x))
Eq(F_89(x), F_12(x)*F_90(x))
Eq(F_90(x), F_130(x) + F_91(x))
Eq(F_91(x), F_54(x) + F_92(x))
Eq(F_92(x), F_15(x) + F_88(x) + F_93(x) + F_94(x))
Eq(F_93(x), F_12(x)*F_91(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_99(x))
Eq(F_96(x), F_73(x) + F_97(x))
Eq(F_97(x), 2*F_15(x) + F_94(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_54(x))
Eq(F_99(x), F_100(x) + F_112(x))
Eq(F_100(x), F_101(x) + 2*F_15(x) + F_76(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x) + F_106(x))
Eq(F_103(x), F_104(x) + F_73(x))
Eq(F_104(x), F_105(x) + 2*F_15(x) + F_76(x))
Eq(F_105(x), F_103(x)*F_12(x))
Eq(F_106(x), F_100(x) + F_107(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_104(x))
Eq(F_111(x), F_107(x))
Eq(F_112(x), F_113(x) + F_117(x) + F_129(x) + 2*F_15(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_114(x) + F_54(x))
Eq(F_117(x), F_118(x)*F_12(x))
Eq(F_118(x), F_119(x) + F_123(x))
Eq(F_119(x), F_120(x) + F_97(x))
Eq(F_120(x), F_113(x) + F_121(x) + F_122(x) + 2*F_15(x))
Eq(F_121(x), F_119(x)*F_12(x))
Eq(F_122(x), 0)
Eq(F_123(x), F_112(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_12(x)*F_126(x))
Eq(F_126(x), F_127(x) + F_128(x))
Eq(F_127(x), F_120(x))
Eq(F_128(x), F_124(x))
Eq(F_129(x), 0)
Eq(F_130(x), F_131(x) + F_87(x))
Eq(F_131(x), F_132(x) + F_134(x) + F_148(x) + F_15(x) + F_173(x))
Eq(F_132(x), F_12(x)*F_133(x))
Eq(F_133(x), F_115(x))
Eq(F_134(x), F_12(x)*F_135(x))
Eq(F_135(x), F_136(x) + F_142(x))
Eq(F_136(x), F_137(x) + F_92(x))
Eq(F_137(x), F_132(x) + F_138(x) + F_141(x) + 2*F_15(x))
Eq(F_138(x), F_12(x)*F_139(x))
Eq(F_139(x), F_140(x) + F_97(x))
Eq(F_140(x), F_113(x) + F_138(x) + F_141(x) + 2*F_15(x))
Eq(F_141(x), 0)
Eq(F_142(x), F_131(x) + F_143(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_137(x))
Eq(F_147(x), F_143(x))
Eq(F_148(x), F_12(x)*F_149(x))
Eq(F_149(x), F_150(x) + F_172(x))
Eq(F_150(x), 2*F_15(x) + F_151(x) + F_98(x))
Eq(F_151(x), F_12(x)*F_152(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_150(x) + F_85(x))
Eq(F_154(x), F_155(x) + F_164(x))
Eq(F_155(x), 2*F_15(x) + F_156(x) + F_76(x))
Eq(F_156(x), F_12(x)*F_157(x))
Eq(F_157(x), F_158(x) + F_84(x))
Eq(F_158(x), F_155(x) + F_159(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_12(x)*F_161(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_86(x))
Eq(F_163(x), F_159(x))
Eq(F_164(x), F_113(x) + 2*F_15(x) + F_165(x) + F_175(x))
Eq(F_165(x), F_12(x)*F_166(x))
Eq(F_166(x), F_149(x) + F_167(x))
Eq(F_167(x), F_164(x) + F_168(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_12(x)*F_170(x))
Eq(F_170(x), F_171(x) + F_174(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_113(x) + F_148(x) + 2*F_15(x) + F_173(x))
Eq(F_173(x), 0)
Eq(F_174(x), F_168(x))
Eq(F_175(x), 0)
Eq(F_176(x), F_177(x) + F_45(x))
Eq(F_177(x), F_15(x) + F_178(x) + F_192(x) + F_226(x))
Eq(F_178(x), F_12(x)*F_179(x))
Eq(F_179(x), F_180(x) + F_181(x))
Eq(F_180(x), F_133(x) + F_49(x))
Eq(F_181(x), F_177(x) + F_182(x))
Eq(F_182(x), 2*F_15(x) + F_183(x) + F_187(x) + F_225(x))
Eq(F_183(x), F_12(x)*F_184(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_133(x))
Eq(F_186(x), F_182(x))
Eq(F_187(x), F_12(x)*F_188(x))
Eq(F_188(x), F_189(x) + F_224(x))
Eq(F_189(x), 2*F_15(x) + F_190(x) + F_192(x))
Eq(F_190(x), F_12(x)*F_191(x))
Eq(F_191(x), F_54(x))
Eq(F_192(x), F_12(x)*F_193(x))
Eq(F_193(x), F_194(x) + F_195(x))
Eq(F_194(x), F_189(x) + F_31(x))
Eq(F_195(x), F_196(x) + F_208(x))
Eq(F_196(x), 2*F_15(x) + F_197(x) + F_35(x))
Eq(F_197(x), F_12(x)*F_198(x))
Eq(F_198(x), F_199(x) + F_202(x))
Eq(F_199(x), F_200(x) + F_31(x))
Eq(F_200(x), 2*F_15(x) + F_201(x) + F_35(x))
Eq(F_201(x), F_12(x)*F_199(x))
Eq(F_202(x), F_196(x) + F_203(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_12(x)*F_205(x))
Eq(F_205(x), F_206(x) + F_207(x))
Eq(F_206(x), F_200(x))
Eq(F_207(x), F_203(x))
Eq(F_208(x), 2*F_15(x) + F_209(x) + F_211(x) + F_223(x))
Eq(F_209(x), F_12(x)*F_210(x))
Eq(F_210(x), F_114(x))
Eq(F_211(x), F_12(x)*F_212(x))
Eq(F_212(x), F_213(x) + F_217(x))
Eq(F_213(x), F_189(x) + F_214(x))
Eq(F_214(x), 2*F_15(x) + F_209(x) + F_215(x) + F_216(x))
Eq(F_215(x), F_12(x)*F_213(x))
Eq(F_216(x), 0)
Eq(F_217(x), F_208(x) + F_218(x))
Eq(F_218(x), F_219(x))
Eq(F_219(x), F_12(x)*F_220(x))
Eq(F_220(x), F_221(x) + F_222(x))
Eq(F_221(x), F_214(x))
Eq(F_222(x), F_218(x))
Eq(F_223(x), 0)
Eq(F_224(x), 2*F_15(x) + F_187(x) + F_209(x) + F_225(x))
Eq(F_225(x), 0)
Eq(F_226(x), F_12(x)*F_227(x))
Eq(F_227(x), F_228(x) + F_268(x))
Eq(F_228(x), F_15(x) + F_229(x) + F_231(x))
Eq(F_229(x), F_12(x)*F_230(x))
Eq(F_230(x), F_2(x) + F_54(x))
Eq(F_231(x), F_12(x)*F_232(x))
Eq(F_232(x), F_233(x) + F_234(x))
Eq(F_233(x), F_228(x) + F_39(x))
Eq(F_234(x), F_235(x) + F_256(x))
Eq(F_235(x), F_15(x) + F_236(x) + F_43(x))
Eq(F_236(x), F_12(x)*F_237(x))
Eq(F_237(x), F_238(x) + F_38(x))
Eq(F_238(x), F_235(x) + F_239(x))
Eq(F_239(x), F_15(x) + F_240(x) + F_242(x) + F_252(x))
Eq(F_240(x), F_12(x)*F_241(x))
Eq(F_241(x), F_19(x))
Eq(F_242(x), F_12(x)*F_243(x))
Eq(F_243(x), F_244(x) + F_246(x))
Eq(F_244(x), F_245(x) + F_42(x))
Eq(F_245(x), 2*F_15(x) + F_240(x) + F_29(x))
Eq(F_246(x), F_239(x) + F_247(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_12(x)*F_249(x))
Eq(F_249(x), F_250(x) + F_251(x))
Eq(F_250(x), F_245(x))
Eq(F_251(x), F_247(x))
Eq(F_252(x), F_12(x)*F_253(x))
Eq(F_253(x), F_254(x) + F_255(x))
Eq(F_254(x), F_32(x))
Eq(F_255(x), 2*F_15(x) + F_252(x) + F_35(x))
Eq(F_256(x), F_15(x) + F_257(x) + F_259(x) + F_279(x))
Eq(F_257(x), F_12(x)*F_258(x))
Eq(F_258(x), F_114(x) + F_49(x))
Eq(F_259(x), F_12(x)*F_260(x))
Eq(F_260(x), F_227(x) + F_261(x))
Eq(F_261(x), F_256(x) + F_262(x))
Eq(F_262(x), F_15(x) + F_263(x) + F_265(x) + F_276(x) + F_301(x))
Eq(F_263(x), F_12(x)*F_264(x))
Eq(F_264(x), F_133(x))
Eq(F_265(x), F_12(x)*F_266(x))
Eq(F_266(x), F_267(x) + F_270(x))
Eq(F_267(x), F_268(x) + F_269(x))
Eq(F_268(x), F_15(x) + F_192(x) + F_226(x) + F_257(x))
Eq(F_269(x), 2*F_15(x) + F_187(x) + F_225(x) + F_263(x))
Eq(F_270(x), F_262(x) + F_271(x))
Eq(F_271(x), F_272(x))
Eq(F_272(x), F_12(x)*F_273(x))
Eq(F_273(x), F_274(x) + F_275(x))
Eq(F_274(x), F_269(x))
Eq(F_275(x), F_271(x))
Eq(F_276(x), F_12(x)*F_277(x))
Eq(F_277(x), F_278(x) + F_300(x))
Eq(F_278(x), 2*F_15(x) + F_190(x) + F_279(x))
Eq(F_279(x), F_12(x)*F_280(x))
Eq(F_280(x), F_281(x) + F_282(x))
Eq(F_281(x), F_254(x) + F_278(x))
Eq(F_282(x), F_283(x) + F_292(x))
Eq(F_283(x), 2*F_15(x) + F_284(x) + F_35(x))
Eq(F_284(x), F_12(x)*F_285(x))
Eq(F_285(x), F_253(x) + F_286(x))
Eq(F_286(x), F_283(x) + F_287(x))
Eq(F_287(x), F_288(x))
Eq(F_288(x), F_12(x)*F_289(x))
Eq(F_289(x), F_290(x) + F_291(x))
Eq(F_290(x), F_255(x))
Eq(F_291(x), F_287(x))
Eq(F_292(x), 2*F_15(x) + F_209(x) + F_293(x) + F_303(x))
Eq(F_293(x), F_12(x)*F_294(x))
Eq(F_294(x), F_277(x) + F_295(x))
Eq(F_295(x), F_292(x) + F_296(x))
Eq(F_296(x), F_297(x))
Eq(F_297(x), F_12(x)*F_298(x))
Eq(F_298(x), F_299(x) + F_302(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), 2*F_15(x) + F_209(x) + F_276(x) + F_301(x))
Eq(F_301(x), 0)
Eq(F_302(x), F_296(x))
Eq(F_303(x), 0)
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [1], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "regular_insertion_encoding_bottom", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 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