0132_1203_1230
Counting sequence:
1, 1, 2, 6, 21, 76, 275, 989, 3541, 12660, 45316, 162694, 586506, 2124192, 7730537, 28267633, 103834509, 383040284, 1418613920, 5273119674, 19666526206, 73574387728, 276030734118, 1038300882914, 3915047341826, 14795197571816, 56027909364280, 212581267367244, 808026809184052, 3076490156816512, 11731887458818677, 44804406481543545, 171346683320810813, 656141939033572012, 2515677505860402280, 9656456774189093042, 37107291107251075638, 142742856178230514352, 549642311893201306634, 2118435530516024463654, 8172216915318945779766, 31552638350723287935448, 121922967860629550024408, 471491070250337762136660, 1824671213588181662070988, 7066510976842213823858752, 27385562899312909104570906, 106199453195649474865432346, 412093120692879600858604562, 1600037310815124075094096920, 6216076257930454520267173216, 24162642932999552044769711044, 93973490180493725388157493676, 365671013517881738652321736736, 1423612770036521733005857838540, 5545002029263751392826027979492, 21607910545538274860131267346788, 84239964360191262777290696926672, 328557487695227371873569207629616, 1281994429757660965476391340879768, 5004221989116303658389290808480488, 19541460749056873059397452920256000, 76338240774311171719222859828219917, 298323057060090231576887316868386697, 1166235253833874836995777628372897693, 4560742181285209416617471619683837132, 17841462010547123770047828296326915256, 69817880561564079724995662669534242146, 273300303533212204711412535086077239910, 1070155529909026575420468707465359369456, 4191633318736039253860457223803193065634, 16422742573483576552454203473357048566462, 64362168900014083494016289291545475348462, 252310279335735343070712680900908658411640, 989362265484352868352982741772455747527832, 3880510154244028420273539558724748782806148, 15224129450876959474975046621372978209679964, 59742509815085877794314908975367840619582144, 234497980290542325566782740904894410281541230, 920654740383603830930918995868024958445607294, 3615380553216249109973500776879906545055694726, 14200654543575792624178446886657186354189040328, 55790146167151738355565377929835310264750967168, 219229594922231700155386793077748331434232283660, 861650693015658912652074311548002823227367867908, 3387283821673646016569880927231373675173521440992, 13318588464031175898526634706858446444722949337236, 52378025824654012307940466843187071545797914585756, 206026212552903308950522466547097861635210273373660, 810543703082116899775935406459872963138281764416176, 3189401791087650700012393526695197510624956622171024, 12552180189708239503639843859445622201510969133124392, 49408830946432531029752032006632808756856909200787672, 194519826805228478824581422402121685235198914291825920, 765941328994691618435152419727804979929906879022261442, 3016462751946603182880179967227048543151010105771820938, 11881459949701049259305612205187734899102543490842573234, 46806871917877736730734691341868048003974927931022779384, 184423402080757567316648713672894904670517026250486674640, 726754474365503504807538222284410220858118473614022489044, 2864332204588733751682907965627557325813285994514886676796
Generating function in Maple syntax:
1/2*((-4*x^4+8*x^3-9*x^2+5*x-1)*(1-4*x)^(1/2)-2*x^5+16*x^4-26*x^3+19*x^2-7*x+1)/x^2/(2*x-1)^2
Generating function in latex syntax:
\frac{\left(-4 x^{4}+8 x^{3}-9 x^{2}+5 x -1\right) \sqrt{1-4 x}-2 x^{5}+16 x^{4}-26 x^{3}+19 x^{2}-7 x +1}{2 x^{2} \left(2 x -1\right)^{2}}
Generating function in sympy syntax:
(-x**5 + 8*x**4 - 13*x**3 + 19*x**2/2 - 7*x/2 + sqrt(1 - 4*x)*(-4*x**4 + 8*x**3 - 9*x**2 + 5*x - 1)/2 + 1/2)/(x**2*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
x^2*(2*x-1)^4*F(x)^2+(2*x^5-16*x^4+26*x^3-19*x^2+7*x-1)*(2*x-1)^2*F(x)+x^8+22*x^6-75*x^5+110*x^4-89*x^3+41*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(2 x -1\right)^{4} F \! \left(x \right)^{2}+\left(2 x^{5}-16 x^{4}+26 x^{3}-19 x^{2}+7 x -1\right) \left(2 x -1\right)^{2} F \! \left(x \right)+x^{8}+22 x^{6}-75 x^{5}+110 x^{4}-89 x^{3}+41 x^{2}-10 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 76
a(6) = 275
a(7) = 989
a(n+6) = -16*(-1+2*n)/(8+n)*a(n)-4*(79+31*n)/(8+n)*a(2+n)+8*(10+11*n)/(8+n)*a(n+1)+2*(208+51*n)/(8+n)*a(n+3)-(256+47*n)/(8+n)*a(n+4)+(74+11*n)/(8+n)*a(n+5), n >= 8
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) = 21
a \! \left(5\right) = 76
a \! \left(6\right) = 275
a \! \left(7\right) = 989
a \! \left(n +6\right) = -\frac{16 \left(-1+2 n \right) a \! \left(n \right)}{8+n}-\frac{4 \left(79+31 n \right) a \! \left(2+n \right)}{8+n}+\frac{8 \left(10+11 n \right) a \! \left(n +1\right)}{8+n}+\frac{2 \left(208+51 n \right) a \! \left(n +3\right)}{8+n}-\frac{\left(256+47 n \right) a \! \left(n +4\right)}{8+n}+\frac{\left(74+11 n \right) a \! \left(n +5\right)}{8+n}, \quad n \geq 8
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/287/
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[342,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[14,x]+F[164,x,k[0]]
F[14,x] = F[15,x]+F[80,x]
F[15,x] = F[16,x]+F[42,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[20,x]
F[23,x] = F[24,x]+F[36,x]
F[24,x] = F[25,x]
F[25,x] = F[11,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[11,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[30,x]+F[31,x]+F[35,x]
F[30,x] = 0
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[11,x]
F[34,x] = F[29,x]
F[35,x] = F[11,x]*F[24,x]
F[36,x] = F[30,x]+F[37,x]+F[41,x]
F[37,x] = F[11,x]*F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[21,x]
F[40,x] = F[36,x]
F[41,x] = F[11,x]*F[23,x]
F[42,x] = F[43,x]+F[54,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[45,x]
F[45,x] = F[20,x]+F[46,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = F[1,x]+F[47,x]
F[50,x] = F[30,x]+F[51,x]+F[53,x]
F[51,x] = F[11,x]*F[52,x]
F[52,x] = F[21,x]+F[50,x]
F[53,x] = F[11,x]*F[46,x]
F[54,x] = F[55,x]
F[55,x] = F[11,x]*F[56,x]
F[56,x] = F[57,x]+F[60,x]
F[57,x] = F[47,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[57,x]
F[60,x] = F[61,x]+F[74,x]
F[61,x] = F[62,x]
F[62,x] = F[11,x]*F[63,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[47,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[11,x]*F[47,x]
F[67,x] = F[61,x]+F[68,x]
F[68,x] = 2*F[30,x]+F[69,x]+F[73,x]
F[69,x] = F[11,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[65,x]
F[72,x] = F[68,x]
F[73,x] = F[11,x]*F[61,x]
F[74,x] = 2*F[30,x]+F[75,x]+F[79,x]
F[75,x] = F[11,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[58,x]
F[78,x] = F[74,x]
F[79,x] = F[11,x]*F[60,x]
F[80,x] = F[122,x]+F[81,x]
F[81,x] = F[47,x]+F[82,x]
F[82,x] = F[30,x]+F[83,x]+F[85,x]
F[83,x] = F[11,x]*F[84,x]
F[84,x] = F[17,x]+F[82,x]
F[85,x] = F[11,x]*F[86,x]
F[86,x] = F[46,x]+F[87,x]
F[87,x] = F[111,x]+F[88,x]
F[88,x] = F[30,x]+F[89,x]+F[94,x]
F[89,x] = F[11,x]*F[90,x]
F[90,x] = F[47,x]+F[91,x]
F[91,x] = F[30,x]+F[89,x]+F[92,x]
F[92,x] = F[11,x]*F[93,x]
F[93,x] = F[47,x]+F[91,x]
F[94,x] = F[11,x]*F[95,x]
F[95,x] = F[100,x]+F[96,x]
F[96,x] = F[47,x]+F[97,x]
F[97,x] = F[30,x]+F[66,x]+F[98,x]
F[98,x] = F[11,x]*F[99,x]
F[99,x] = F[11,x]+F[97,x]
F[100,x] = F[101,x]+F[88,x]
F[101,x] = F[102,x]+F[106,x]+F[110,x]+F[30,x]
F[102,x] = F[103,x]*F[11,x]
F[103,x] = F[104,x]+F[65,x]
F[104,x] = 2*F[30,x]+F[102,x]+F[105,x]
F[105,x] = F[11,x]*F[91,x]
F[106,x] = F[107,x]*F[11,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[97,x]
F[109,x] = F[101,x]
F[110,x] = F[11,x]*F[88,x]
F[111,x] = F[112,x]+F[117,x]+F[121,x]+F[30,x]
F[112,x] = F[11,x]*F[113,x]
F[113,x] = F[114,x]+F[58,x]
F[114,x] = 2*F[30,x]+F[112,x]+F[115,x]
F[115,x] = F[11,x]*F[116,x]
F[116,x] = F[114,x]+F[91,x]
F[117,x] = F[11,x]*F[118,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[50,x]
F[120,x] = F[111,x]
F[121,x] = F[11,x]*F[87,x]
F[122,x] = F[123,x]+F[136,x]
F[123,x] = F[124,x]+F[126,x]+F[30,x]
F[124,x] = F[11,x]*F[125,x]
F[125,x] = F[123,x]+F[43,x]
F[126,x] = F[11,x]*F[127,x]
F[127,x] = F[128,x]+F[46,x]
F[128,x] = F[129,x]+F[132,x]
F[129,x] = F[130,x]
F[130,x] = F[11,x]*F[131,x]
F[131,x] = F[129,x]+F[47,x]
F[132,x] = 2*F[30,x]+F[133,x]+F[135,x]
F[133,x] = F[11,x]*F[134,x]
F[134,x] = F[132,x]+F[50,x]
F[135,x] = F[11,x]*F[128,x]
F[136,x] = 2*F[30,x]+F[137,x]+F[139,x]
F[137,x] = F[11,x]*F[138,x]
F[138,x] = F[136,x]+F[54,x]
F[139,x] = F[11,x]*F[140,x]
F[140,x] = F[141,x]+F[144,x]
F[141,x] = F[129,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[11,x]*F[141,x]
F[144,x] = F[145,x]+F[158,x]
F[145,x] = F[146,x]
F[146,x] = F[11,x]*F[147,x]
F[147,x] = F[148,x]+F[151,x]
F[148,x] = F[129,x]+F[149,x]
F[149,x] = F[150,x]
F[150,x] = F[11,x]*F[129,x]
F[151,x] = F[145,x]+F[152,x]
F[152,x] = 3*F[30,x]+F[153,x]+F[157,x]
F[153,x] = F[11,x]*F[154,x]
F[154,x] = F[155,x]+F[156,x]
F[155,x] = F[149,x]
F[156,x] = F[152,x]
F[157,x] = F[11,x]*F[145,x]
F[158,x] = 3*F[30,x]+F[159,x]+F[163,x]
F[159,x] = F[11,x]*F[160,x]
F[160,x] = F[161,x]+F[162,x]
F[161,x] = F[142,x]
F[162,x] = F[158,x]
F[163,x] = F[11,x]*F[144,x]
F[164,x,k[0]] = F[165,x,k[0]]+F[258,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[216,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]+F[170,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[8,x,k[0]]
F[169,x,k[0]] = F[1,x]+F[167,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]+F[173,x,k[0]]+F[30,x]
F[171,x,k[0]] = F[172,x,k[0]]*F[8,x,k[0]]
F[172,x,k[0]] = F[17,x]+F[170,x,k[0]]
F[173,x,k[0]] = F[11,x]*F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]+F[180,x,k[0]]
F[175,x,k[0]] = F[167,x,k[0]]+F[176,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[179,x,k[0]]+F[30,x]
F[177,x,k[0]] = F[178,x,k[0]]*F[8,x,k[0]]
F[178,x,k[0]] = F[176,x,k[0]]+F[21,x]
F[179,x,k[0]] = F[11,x]*F[175,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]+F[205,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[187,x,k[0]]+F[30,x]
F[182,x,k[0]] = F[183,x,k[0]]*F[8,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]+F[47,x]
F[184,x,k[0]] = F[182,x,k[0]]+F[185,x,k[0]]+F[30,x]
F[185,x,k[0]] = F[11,x]*F[186,x,k[0]]
F[186,x,k[0]] = F[167,x,k[0]]+F[184,x,k[0]]
F[187,x,k[0]] = F[11,x]*F[188,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[194,x,k[0]]
F[189,x,k[0]] = F[167,x,k[0]]+F[190,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]+F[193,x,k[0]]+F[30,x]
F[191,x,k[0]] = F[192,x,k[0]]*F[8,x,k[0]]
F[192,x,k[0]] = F[11,x]+F[190,x,k[0]]
F[193,x,k[0]] = F[11,x]*F[167,x,k[0]]
F[194,x,k[0]] = F[181,x,k[0]]+F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]+F[200,x,k[0]]+F[204,x,k[0]]+F[30,x]
F[196,x,k[0]] = F[197,x,k[0]]*F[8,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[65,x]
F[198,x,k[0]] = 2*F[30,x]+F[196,x,k[0]]+F[199,x,k[0]]
F[199,x,k[0]] = F[11,x]*F[184,x,k[0]]
F[200,x,k[0]] = F[11,x]*F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]+F[203,x,k[0]]
F[202,x,k[0]] = F[190,x,k[0]]
F[203,x,k[0]] = F[195,x,k[0]]
F[204,x,k[0]] = F[11,x]*F[181,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]+F[211,x,k[0]]+F[215,x,k[0]]+F[30,x]
F[206,x,k[0]] = F[207,x,k[0]]*F[8,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[58,x]
F[208,x,k[0]] = 2*F[30,x]+F[206,x,k[0]]+F[209,x,k[0]]
F[209,x,k[0]] = F[11,x]*F[210,x,k[0]]
F[210,x,k[0]] = F[184,x,k[0]]+F[208,x,k[0]]
F[211,x,k[0]] = F[11,x]*F[212,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]+F[214,x,k[0]]
F[213,x,k[0]] = F[176,x,k[0]]
F[214,x,k[0]] = F[205,x,k[0]]
F[215,x,k[0]] = F[11,x]*F[180,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[230,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]+F[220,x,k[0]]+F[30,x]
F[218,x,k[0]] = F[219,x,k[0]]*F[8,x,k[0]]
F[219,x,k[0]] = F[217,x,k[0]]+F[43,x]
F[220,x,k[0]] = F[11,x]*F[221,x,k[0]]
F[221,x,k[0]] = F[175,x,k[0]]+F[222,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]+F[226,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]
F[224,x,k[0]] = F[11,x]*F[225,x,k[0]]
F[225,x,k[0]] = F[167,x,k[0]]+F[223,x,k[0]]
F[226,x,k[0]] = 2*F[30,x]+F[227,x,k[0]]+F[229,x,k[0]]
F[227,x,k[0]] = F[11,x]*F[228,x,k[0]]
F[228,x,k[0]] = F[176,x,k[0]]+F[226,x,k[0]]
F[229,x,k[0]] = F[11,x]*F[222,x,k[0]]
F[230,x,k[0]] = 2*F[30,x]+F[231,x,k[0]]+F[233,x,k[0]]
F[231,x,k[0]] = F[232,x,k[0]]*F[8,x,k[0]]
F[232,x,k[0]] = F[230,x,k[0]]+F[54,x]
F[233,x,k[0]] = F[11,x]*F[234,x,k[0]]
F[234,x,k[0]] = F[235,x,k[0]]+F[238,x,k[0]]
F[235,x,k[0]] = F[223,x,k[0]]+F[236,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]
F[237,x,k[0]] = F[11,x]*F[235,x,k[0]]
F[238,x,k[0]] = F[239,x,k[0]]+F[252,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]
F[240,x,k[0]] = F[11,x]*F[241,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]+F[245,x,k[0]]
F[242,x,k[0]] = F[223,x,k[0]]+F[243,x,k[0]]
F[243,x,k[0]] = F[244,x,k[0]]
F[244,x,k[0]] = F[11,x]*F[223,x,k[0]]
F[245,x,k[0]] = F[239,x,k[0]]+F[246,x,k[0]]
F[246,x,k[0]] = 3*F[30,x]+F[247,x,k[0]]+F[251,x,k[0]]
F[247,x,k[0]] = F[11,x]*F[248,x,k[0]]
F[248,x,k[0]] = F[249,x,k[0]]+F[250,x,k[0]]
F[249,x,k[0]] = F[243,x,k[0]]
F[250,x,k[0]] = F[246,x,k[0]]
F[251,x,k[0]] = F[11,x]*F[239,x,k[0]]
F[252,x,k[0]] = 3*F[30,x]+F[253,x,k[0]]+F[257,x,k[0]]
F[253,x,k[0]] = F[11,x]*F[254,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]+F[256,x,k[0]]
F[255,x,k[0]] = F[236,x,k[0]]
F[256,x,k[0]] = F[252,x,k[0]]
F[257,x,k[0]] = F[11,x]*F[238,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[300,x,k[0]]
F[259,x,k[0]] = F[223,x,k[0]]+F[260,x,k[0]]
F[260,x,k[0]] = 2*F[30,x]+F[261,x,k[0]]+F[263,x,k[0]]
F[261,x,k[0]] = F[11,x]*F[262,x,k[0]]
F[262,x,k[0]] = F[170,x,k[0]]+F[260,x,k[0]]
F[263,x,k[0]] = F[11,x]*F[264,x,k[0]]
F[264,x,k[0]] = F[222,x,k[0]]+F[265,x,k[0]]
F[265,x,k[0]] = F[266,x,k[0]]+F[289,x,k[0]]
F[266,x,k[0]] = 2*F[30,x]+F[267,x,k[0]]+F[272,x,k[0]]
F[267,x,k[0]] = F[11,x]*F[268,x,k[0]]
F[268,x,k[0]] = F[184,x,k[0]]+F[269,x,k[0]]
F[269,x,k[0]] = 2*F[30,x]+F[267,x,k[0]]+F[270,x,k[0]]
F[270,x,k[0]] = F[11,x]*F[271,x,k[0]]
F[271,x,k[0]] = F[223,x,k[0]]+F[269,x,k[0]]
F[272,x,k[0]] = F[11,x]*F[273,x,k[0]]
F[273,x,k[0]] = F[274,x,k[0]]+F[278,x,k[0]]
F[274,x,k[0]] = F[223,x,k[0]]+F[275,x,k[0]]
F[275,x,k[0]] = 2*F[30,x]+F[244,x,k[0]]+F[276,x,k[0]]
F[276,x,k[0]] = F[11,x]*F[277,x,k[0]]
F[277,x,k[0]] = F[190,x,k[0]]+F[275,x,k[0]]
F[278,x,k[0]] = F[266,x,k[0]]+F[279,x,k[0]]
F[279,x,k[0]] = 2*F[30,x]+F[280,x,k[0]]+F[284,x,k[0]]+F[288,x,k[0]]
F[280,x,k[0]] = F[11,x]*F[281,x,k[0]]
F[281,x,k[0]] = F[198,x,k[0]]+F[282,x,k[0]]
F[282,x,k[0]] = 3*F[30,x]+F[280,x,k[0]]+F[283,x,k[0]]
F[283,x,k[0]] = F[11,x]*F[269,x,k[0]]
F[284,x,k[0]] = F[11,x]*F[285,x,k[0]]
F[285,x,k[0]] = F[286,x,k[0]]+F[287,x,k[0]]
F[286,x,k[0]] = F[275,x,k[0]]
F[287,x,k[0]] = F[279,x,k[0]]
F[288,x,k[0]] = F[11,x]*F[266,x,k[0]]
F[289,x,k[0]] = 2*F[30,x]+F[290,x,k[0]]+F[295,x,k[0]]+F[299,x,k[0]]
F[290,x,k[0]] = F[11,x]*F[291,x,k[0]]
F[291,x,k[0]] = F[208,x,k[0]]+F[292,x,k[0]]
F[292,x,k[0]] = 3*F[30,x]+F[290,x,k[0]]+F[293,x,k[0]]
F[293,x,k[0]] = F[11,x]*F[294,x,k[0]]
F[294,x,k[0]] = F[269,x,k[0]]+F[292,x,k[0]]
F[295,x,k[0]] = F[11,x]*F[296,x,k[0]]
F[296,x,k[0]] = F[297,x,k[0]]+F[298,x,k[0]]
F[297,x,k[0]] = F[226,x,k[0]]
F[298,x,k[0]] = F[289,x,k[0]]
F[299,x,k[0]] = F[11,x]*F[265,x,k[0]]
F[300,x,k[0]] = F[301,x,k[0]]+F[314,x,k[0]]
F[301,x,k[0]] = 2*F[30,x]+F[302,x,k[0]]+F[304,x,k[0]]
F[302,x,k[0]] = F[11,x]*F[303,x,k[0]]
F[303,x,k[0]] = F[217,x,k[0]]+F[301,x,k[0]]
F[304,x,k[0]] = F[11,x]*F[305,x,k[0]]
F[305,x,k[0]] = F[222,x,k[0]]+F[306,x,k[0]]
F[306,x,k[0]] = F[307,x,k[0]]+F[310,x,k[0]]
F[307,x,k[0]] = F[308,x,k[0]]
F[308,x,k[0]] = F[11,x]*F[309,x,k[0]]
F[309,x,k[0]] = F[223,x,k[0]]+F[307,x,k[0]]
F[310,x,k[0]] = 3*F[30,x]+F[311,x,k[0]]+F[313,x,k[0]]
F[311,x,k[0]] = F[11,x]*F[312,x,k[0]]
F[312,x,k[0]] = F[226,x,k[0]]+F[310,x,k[0]]
F[313,x,k[0]] = F[11,x]*F[306,x,k[0]]
F[314,x,k[0]] = 3*F[30,x]+F[315,x,k[0]]+F[317,x,k[0]]
F[315,x,k[0]] = F[11,x]*F[316,x,k[0]]
F[316,x,k[0]] = F[230,x,k[0]]+F[314,x,k[0]]
F[317,x,k[0]] = F[11,x]*F[318,x,k[0]]
F[318,x,k[0]] = F[319,x,k[0]]+F[322,x,k[0]]
F[319,x,k[0]] = F[307,x,k[0]]+F[320,x,k[0]]
F[320,x,k[0]] = F[321,x,k[0]]
F[321,x,k[0]] = F[11,x]*F[319,x,k[0]]
F[322,x,k[0]] = F[323,x,k[0]]+F[336,x,k[0]]
F[323,x,k[0]] = F[324,x,k[0]]
F[324,x,k[0]] = F[11,x]*F[325,x,k[0]]
F[325,x,k[0]] = F[326,x,k[0]]+F[329,x,k[0]]
F[326,x,k[0]] = F[307,x,k[0]]+F[327,x,k[0]]
F[327,x,k[0]] = F[328,x,k[0]]
F[328,x,k[0]] = F[11,x]*F[307,x,k[0]]
F[329,x,k[0]] = F[323,x,k[0]]+F[330,x,k[0]]
F[330,x,k[0]] = 4*F[30,x]+F[331,x,k[0]]+F[335,x,k[0]]
F[331,x,k[0]] = F[11,x]*F[332,x,k[0]]
F[332,x,k[0]] = F[333,x,k[0]]+F[334,x,k[0]]
F[333,x,k[0]] = F[327,x,k[0]]
F[334,x,k[0]] = F[330,x,k[0]]
F[335,x,k[0]] = F[11,x]*F[323,x,k[0]]
F[336,x,k[0]] = 4*F[30,x]+F[337,x,k[0]]+F[341,x,k[0]]
F[337,x,k[0]] = F[11,x]*F[338,x,k[0]]
F[338,x,k[0]] = F[339,x,k[0]]+F[340,x,k[0]]
F[339,x,k[0]] = F[320,x,k[0]]
F[340,x,k[0]] = F[336,x,k[0]]
F[341,x,k[0]] = F[11,x]*F[322,x,k[0]]
F[342,x] = F[11,x]*F[14,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{342}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \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_{14}\! \left(x \right)+F_{164}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{80}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{42}\! \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_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \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_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{21}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{54}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{30}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{46}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)
F_{57}\! \left(x \right) = F_{47}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{74}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{47}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{47}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{65}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{75}\! \left(x \right)+F_{79}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{58}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{80}\! \left(x \right) = F_{122}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{47}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{30}\! \left(x \right)+F_{83}\! \left(x \right)+F_{85}\! \left(x \right)
F_{83}\! \left(x \right) = F_{11}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{17}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{11}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{46}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{111}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{30}\! \left(x \right)+F_{89}\! \left(x \right)+F_{94}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{47}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{30}\! \left(x \right)+F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{11}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{47}\! \left(x \right)+F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{11}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{47}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{30}\! \left(x \right)+F_{66}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{11}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{11}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{88}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)+F_{110}\! \left(x \right)+F_{30}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{11}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{65}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{102}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{11}\! \left(x \right) F_{91}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{11}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{97}\! \left(x \right)
F_{109}\! \left(x \right) = F_{101}\! \left(x \right)
F_{110}\! \left(x \right) = F_{11}\! \left(x \right) F_{88}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{117}\! \left(x \right)+F_{121}\! \left(x \right)+F_{30}\! \left(x \right)
F_{112}\! \left(x \right) = F_{11}\! \left(x \right) F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{58}\! \left(x \right)
F_{114}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{112}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{91}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{50}\! \left(x \right)
F_{120}\! \left(x \right) = F_{111}\! \left(x \right)
F_{121}\! \left(x \right) = F_{11}\! \left(x \right) F_{87}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{136}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)+F_{30}\! \left(x \right)
F_{124}\! \left(x \right) = F_{11}\! \left(x \right) F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{123}\! \left(x \right)+F_{43}\! \left(x \right)
F_{126}\! \left(x \right) = F_{11}\! \left(x \right) F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{46}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{132}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{11}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{129}\! \left(x \right)+F_{47}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{133}\! \left(x \right)+F_{135}\! \left(x \right)
F_{133}\! \left(x \right) = F_{11}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{132}\! \left(x \right)+F_{50}\! \left(x \right)
F_{135}\! \left(x \right) = F_{11}\! \left(x \right) F_{128}\! \left(x \right)
F_{136}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{137}\! \left(x \right)+F_{139}\! \left(x \right)
F_{137}\! \left(x \right) = F_{11}\! \left(x \right) F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{136}\! \left(x \right)+F_{54}\! \left(x \right)
F_{139}\! \left(x \right) = F_{11}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{144}\! \left(x \right)
F_{141}\! \left(x \right) = F_{129}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{11}\! \left(x \right) F_{141}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{158}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{11}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{151}\! \left(x \right)
F_{148}\! \left(x \right) = F_{129}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{11}\! \left(x \right) F_{129}\! \left(x \right)
F_{151}\! \left(x \right) = F_{145}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = 3 F_{30}\! \left(x \right)+F_{153}\! \left(x \right)+F_{157}\! \left(x \right)
F_{153}\! \left(x \right) = F_{11}\! \left(x \right) F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{156}\! \left(x \right)
F_{155}\! \left(x \right) = F_{149}\! \left(x \right)
F_{156}\! \left(x \right) = F_{152}\! \left(x \right)
F_{157}\! \left(x \right) = F_{11}\! \left(x \right) F_{145}\! \left(x \right)
F_{158}\! \left(x \right) = 3 F_{30}\! \left(x \right)+F_{159}\! \left(x \right)+F_{163}\! \left(x \right)
F_{159}\! \left(x \right) = F_{11}\! \left(x \right) F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{162}\! \left(x \right)
F_{161}\! \left(x \right) = F_{142}\! \left(x \right)
F_{162}\! \left(x \right) = F_{158}\! \left(x \right)
F_{163}\! \left(x \right) = F_{11}\! \left(x \right) F_{144}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{167}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)+F_{173}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{170}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{179}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{21}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{175}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{47}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{185}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{185}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{186}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{193}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{190}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{200}\! \left(x , y\right)+F_{204}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{65}\! \left(x \right)
F_{198}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{196}\! \left(x , y\right)+F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{184}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{181}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{211}\! \left(x , y\right)+F_{215}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{58}\! \left(x \right)
F_{208}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{206}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{208}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{176}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{205}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{180}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{230}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{220}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{43}\! \left(x \right)
F_{220}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{223}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{227}\! \left(x , y\right)+F_{229}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{228}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{222}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{231}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{54}\! \left(x \right)
F_{233}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{234}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{235}\! \left(x , y\right)+F_{238}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{236}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{235}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{252}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{242}\! \left(x , y\right)+F_{245}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{223}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{246}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{247}\! \left(x , y\right)+F_{251}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{249}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{243}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{246}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{239}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{253}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{254}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{256}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{236}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{252}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{238}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{300}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{261}\! \left(x , y\right)+F_{263}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{260}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{264}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{265}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)+F_{289}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{267}\! \left(x , y\right)+F_{272}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{268}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{269}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{267}\! \left(x , y\right)+F_{270}\! \left(x , y\right)
F_{270}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{271}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{269}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{278}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{275}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{244}\! \left(x , y\right)+F_{276}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{277}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{275}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = F_{266}\! \left(x , y\right)+F_{279}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{280}\! \left(x , y\right)+F_{284}\! \left(x , y\right)+F_{288}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{281}\! \left(x , y\right)
F_{281}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{282}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{280}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{269}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{285}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{286}\! \left(x , y\right)+F_{287}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{275}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{279}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{266}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{290}\! \left(x , y\right)+F_{295}\! \left(x , y\right)+F_{299}\! \left(x , y\right)
F_{290}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{291}\! \left(x , y\right)
F_{291}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{292}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{290}\! \left(x , y\right)+F_{293}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{294}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = F_{269}\! \left(x , y\right)+F_{292}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{297}\! \left(x , y\right)+F_{298}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{226}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{289}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{265}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{301}\! \left(x , y\right)+F_{314}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{302}\! \left(x , y\right)+F_{304}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{303}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{301}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{305}\! \left(x , y\right)
F_{305}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{306}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{307}\! \left(x , y\right)+F_{310}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{308}\! \left(x , y\right)
F_{308}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{309}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{307}\! \left(x , y\right)
F_{310}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{311}\! \left(x , y\right)+F_{313}\! \left(x , y\right)
F_{311}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{312}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{226}\! \left(x , y\right)+F_{310}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{306}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{315}\! \left(x , y\right)+F_{317}\! \left(x , y\right)
F_{315}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{316}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{314}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{318}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{319}\! \left(x , y\right)+F_{322}\! \left(x , y\right)
F_{319}\! \left(x , y\right) = F_{307}\! \left(x , y\right)+F_{320}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{321}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{319}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{336}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{324}\! \left(x , y\right)
F_{324}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{325}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{326}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{326}\! \left(x , y\right) = F_{307}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{307}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = 4 F_{30}\! \left(x \right)+F_{331}\! \left(x , y\right)+F_{335}\! \left(x , y\right)
F_{331}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{332}\! \left(x , y\right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y\right)+F_{334}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{327}\! \left(x , y\right)
F_{334}\! \left(x , y\right) = F_{330}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{323}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = 4 F_{30}\! \left(x \right)+F_{337}\! \left(x , y\right)+F_{341}\! \left(x , y\right)
F_{337}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{338}\! \left(x , y\right)
F_{338}\! \left(x , y\right) = F_{339}\! \left(x , y\right)+F_{340}\! \left(x , y\right)
F_{339}\! \left(x , y\right) = F_{320}\! \left(x , y\right)
F_{340}\! \left(x , y\right) = F_{336}\! \left(x , y\right)
F_{341}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{322}\! \left(x , y\right)
F_{342}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_342(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
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_14(x) + F_164(x, k_0))
Eq(F_14(x), F_15(x) + F_80(x))
Eq(F_15(x), F_16(x) + F_42(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_20(x))
Eq(F_23(x), F_24(x) + F_36(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_11(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_31(x) + F_35(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_11(x))
Eq(F_34(x), F_29(x))
Eq(F_35(x), F_11(x)*F_24(x))
Eq(F_36(x), F_30(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_11(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_21(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_11(x)*F_23(x))
Eq(F_42(x), F_43(x) + F_54(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_45(x))
Eq(F_45(x), F_20(x) + F_46(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_1(x) + F_47(x))
Eq(F_50(x), F_30(x) + F_51(x) + F_53(x))
Eq(F_51(x), F_11(x)*F_52(x))
Eq(F_52(x), F_21(x) + F_50(x))
Eq(F_53(x), F_11(x)*F_46(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_11(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_60(x))
Eq(F_57(x), F_47(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_57(x))
Eq(F_60(x), F_61(x) + F_74(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_47(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_11(x)*F_47(x))
Eq(F_67(x), F_61(x) + F_68(x))
Eq(F_68(x), 2*F_30(x) + F_69(x) + F_73(x))
Eq(F_69(x), F_11(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_65(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_11(x)*F_61(x))
Eq(F_74(x), 2*F_30(x) + F_75(x) + F_79(x))
Eq(F_75(x), F_11(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_58(x))
Eq(F_78(x), F_74(x))
Eq(F_79(x), F_11(x)*F_60(x))
Eq(F_80(x), F_122(x) + F_81(x))
Eq(F_81(x), F_47(x) + F_82(x))
Eq(F_82(x), F_30(x) + F_83(x) + F_85(x))
Eq(F_83(x), F_11(x)*F_84(x))
Eq(F_84(x), F_17(x) + F_82(x))
Eq(F_85(x), F_11(x)*F_86(x))
Eq(F_86(x), F_46(x) + F_87(x))
Eq(F_87(x), F_111(x) + F_88(x))
Eq(F_88(x), F_30(x) + F_89(x) + F_94(x))
Eq(F_89(x), F_11(x)*F_90(x))
Eq(F_90(x), F_47(x) + F_91(x))
Eq(F_91(x), F_30(x) + F_89(x) + F_92(x))
Eq(F_92(x), F_11(x)*F_93(x))
Eq(F_93(x), F_47(x) + F_91(x))
Eq(F_94(x), F_11(x)*F_95(x))
Eq(F_95(x), F_100(x) + F_96(x))
Eq(F_96(x), F_47(x) + F_97(x))
Eq(F_97(x), F_30(x) + F_66(x) + F_98(x))
Eq(F_98(x), F_11(x)*F_99(x))
Eq(F_99(x), F_11(x) + F_97(x))
Eq(F_100(x), F_101(x) + F_88(x))
Eq(F_101(x), F_102(x) + F_106(x) + F_110(x) + F_30(x))
Eq(F_102(x), F_103(x)*F_11(x))
Eq(F_103(x), F_104(x) + F_65(x))
Eq(F_104(x), F_102(x) + F_105(x) + 2*F_30(x))
Eq(F_105(x), F_11(x)*F_91(x))
Eq(F_106(x), F_107(x)*F_11(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_97(x))
Eq(F_109(x), F_101(x))
Eq(F_110(x), F_11(x)*F_88(x))
Eq(F_111(x), F_112(x) + F_117(x) + F_121(x) + F_30(x))
Eq(F_112(x), F_11(x)*F_113(x))
Eq(F_113(x), F_114(x) + F_58(x))
Eq(F_114(x), F_112(x) + F_115(x) + 2*F_30(x))
Eq(F_115(x), F_11(x)*F_116(x))
Eq(F_116(x), F_114(x) + F_91(x))
Eq(F_117(x), F_11(x)*F_118(x))
Eq(F_118(x), F_119(x) + F_120(x))
Eq(F_119(x), F_50(x))
Eq(F_120(x), F_111(x))
Eq(F_121(x), F_11(x)*F_87(x))
Eq(F_122(x), F_123(x) + F_136(x))
Eq(F_123(x), F_124(x) + F_126(x) + F_30(x))
Eq(F_124(x), F_11(x)*F_125(x))
Eq(F_125(x), F_123(x) + F_43(x))
Eq(F_126(x), F_11(x)*F_127(x))
Eq(F_127(x), F_128(x) + F_46(x))
Eq(F_128(x), F_129(x) + F_132(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_11(x)*F_131(x))
Eq(F_131(x), F_129(x) + F_47(x))
Eq(F_132(x), F_133(x) + F_135(x) + 2*F_30(x))
Eq(F_133(x), F_11(x)*F_134(x))
Eq(F_134(x), F_132(x) + F_50(x))
Eq(F_135(x), F_11(x)*F_128(x))
Eq(F_136(x), F_137(x) + F_139(x) + 2*F_30(x))
Eq(F_137(x), F_11(x)*F_138(x))
Eq(F_138(x), F_136(x) + F_54(x))
Eq(F_139(x), F_11(x)*F_140(x))
Eq(F_140(x), F_141(x) + F_144(x))
Eq(F_141(x), F_129(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_11(x)*F_141(x))
Eq(F_144(x), F_145(x) + F_158(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_11(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_151(x))
Eq(F_148(x), F_129(x) + F_149(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_11(x)*F_129(x))
Eq(F_151(x), F_145(x) + F_152(x))
Eq(F_152(x), F_153(x) + F_157(x) + 3*F_30(x))
Eq(F_153(x), F_11(x)*F_154(x))
Eq(F_154(x), F_155(x) + F_156(x))
Eq(F_155(x), F_149(x))
Eq(F_156(x), F_152(x))
Eq(F_157(x), F_11(x)*F_145(x))
Eq(F_158(x), F_159(x) + F_163(x) + 3*F_30(x))
Eq(F_159(x), F_11(x)*F_160(x))
Eq(F_160(x), F_161(x) + F_162(x))
Eq(F_161(x), F_142(x))
Eq(F_162(x), F_158(x))
Eq(F_163(x), F_11(x)*F_144(x))
Eq(F_164(x, k_0), F_165(x, k_0) + F_258(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_216(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0) + F_170(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_8(x, k_0))
Eq(F_169(x, k_0), F_1(x) + F_167(x, k_0))
Eq(F_170(x, k_0), F_171(x, k_0) + F_173(x, k_0) + F_30(x))
Eq(F_171(x, k_0), F_172(x, k_0)*F_8(x, k_0))
Eq(F_172(x, k_0), F_17(x) + F_170(x, k_0))
Eq(F_173(x, k_0), F_11(x)*F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0) + F_180(x, k_0))
Eq(F_175(x, k_0), F_167(x, k_0) + F_176(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_179(x, k_0) + F_30(x))
Eq(F_177(x, k_0), F_178(x, k_0)*F_8(x, k_0))
Eq(F_178(x, k_0), F_176(x, k_0) + F_21(x))
Eq(F_179(x, k_0), F_11(x)*F_175(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0) + F_205(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_187(x, k_0) + F_30(x))
Eq(F_182(x, k_0), F_183(x, k_0)*F_8(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0) + F_47(x))
Eq(F_184(x, k_0), F_182(x, k_0) + F_185(x, k_0) + F_30(x))
Eq(F_185(x, k_0), F_11(x)*F_186(x, k_0))
Eq(F_186(x, k_0), F_167(x, k_0) + F_184(x, k_0))
Eq(F_187(x, k_0), F_11(x)*F_188(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_194(x, k_0))
Eq(F_189(x, k_0), F_167(x, k_0) + F_190(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0) + F_193(x, k_0) + F_30(x))
Eq(F_191(x, k_0), F_192(x, k_0)*F_8(x, k_0))
Eq(F_192(x, k_0), F_11(x) + F_190(x, k_0))
Eq(F_193(x, k_0), F_11(x)*F_167(x, k_0))
Eq(F_194(x, k_0), F_181(x, k_0) + F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0) + F_200(x, k_0) + F_204(x, k_0) + F_30(x))
Eq(F_196(x, k_0), F_197(x, k_0)*F_8(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_65(x))
Eq(F_198(x, k_0), F_196(x, k_0) + F_199(x, k_0) + 2*F_30(x))
Eq(F_199(x, k_0), F_11(x)*F_184(x, k_0))
Eq(F_200(x, k_0), F_11(x)*F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0) + F_203(x, k_0))
Eq(F_202(x, k_0), F_190(x, k_0))
Eq(F_203(x, k_0), F_195(x, k_0))
Eq(F_204(x, k_0), F_11(x)*F_181(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0) + F_211(x, k_0) + F_215(x, k_0) + F_30(x))
Eq(F_206(x, k_0), F_207(x, k_0)*F_8(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_58(x))
Eq(F_208(x, k_0), F_206(x, k_0) + F_209(x, k_0) + 2*F_30(x))
Eq(F_209(x, k_0), F_11(x)*F_210(x, k_0))
Eq(F_210(x, k_0), F_184(x, k_0) + F_208(x, k_0))
Eq(F_211(x, k_0), F_11(x)*F_212(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0) + F_214(x, k_0))
Eq(F_213(x, k_0), F_176(x, k_0))
Eq(F_214(x, k_0), F_205(x, k_0))
Eq(F_215(x, k_0), F_11(x)*F_180(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_230(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_220(x, k_0) + F_30(x))
Eq(F_218(x, k_0), F_219(x, k_0)*F_8(x, k_0))
Eq(F_219(x, k_0), F_217(x, k_0) + F_43(x))
Eq(F_220(x, k_0), F_11(x)*F_221(x, k_0))
Eq(F_221(x, k_0), F_175(x, k_0) + F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0) + F_226(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0))
Eq(F_224(x, k_0), F_11(x)*F_225(x, k_0))
Eq(F_225(x, k_0), F_167(x, k_0) + F_223(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0) + F_229(x, k_0) + 2*F_30(x))
Eq(F_227(x, k_0), F_11(x)*F_228(x, k_0))
Eq(F_228(x, k_0), F_176(x, k_0) + F_226(x, k_0))
Eq(F_229(x, k_0), F_11(x)*F_222(x, k_0))
Eq(F_230(x, k_0), F_231(x, k_0) + F_233(x, k_0) + 2*F_30(x))
Eq(F_231(x, k_0), F_232(x, k_0)*F_8(x, k_0))
Eq(F_232(x, k_0), F_230(x, k_0) + F_54(x))
Eq(F_233(x, k_0), F_11(x)*F_234(x, k_0))
Eq(F_234(x, k_0), F_235(x, k_0) + F_238(x, k_0))
Eq(F_235(x, k_0), F_223(x, k_0) + F_236(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0))
Eq(F_237(x, k_0), F_11(x)*F_235(x, k_0))
Eq(F_238(x, k_0), F_239(x, k_0) + F_252(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0))
Eq(F_240(x, k_0), F_11(x)*F_241(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0) + F_245(x, k_0))
Eq(F_242(x, k_0), F_223(x, k_0) + F_243(x, k_0))
Eq(F_243(x, k_0), F_244(x, k_0))
Eq(F_244(x, k_0), F_11(x)*F_223(x, k_0))
Eq(F_245(x, k_0), F_239(x, k_0) + F_246(x, k_0))
Eq(F_246(x, k_0), F_247(x, k_0) + F_251(x, k_0) + 3*F_30(x))
Eq(F_247(x, k_0), F_11(x)*F_248(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0) + F_250(x, k_0))
Eq(F_249(x, k_0), F_243(x, k_0))
Eq(F_250(x, k_0), F_246(x, k_0))
Eq(F_251(x, k_0), F_11(x)*F_239(x, k_0))
Eq(F_252(x, k_0), F_253(x, k_0) + F_257(x, k_0) + 3*F_30(x))
Eq(F_253(x, k_0), F_11(x)*F_254(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0) + F_256(x, k_0))
Eq(F_255(x, k_0), F_236(x, k_0))
Eq(F_256(x, k_0), F_252(x, k_0))
Eq(F_257(x, k_0), F_11(x)*F_238(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_300(x, k_0))
Eq(F_259(x, k_0), F_223(x, k_0) + F_260(x, k_0))
Eq(F_260(x, k_0), F_261(x, k_0) + F_263(x, k_0) + 2*F_30(x))
Eq(F_261(x, k_0), F_11(x)*F_262(x, k_0))
Eq(F_262(x, k_0), F_170(x, k_0) + F_260(x, k_0))
Eq(F_263(x, k_0), F_11(x)*F_264(x, k_0))
Eq(F_264(x, k_0), F_222(x, k_0) + F_265(x, k_0))
Eq(F_265(x, k_0), F_266(x, k_0) + F_289(x, k_0))
Eq(F_266(x, k_0), F_267(x, k_0) + F_272(x, k_0) + 2*F_30(x))
Eq(F_267(x, k_0), F_11(x)*F_268(x, k_0))
Eq(F_268(x, k_0), F_184(x, k_0) + F_269(x, k_0))
Eq(F_269(x, k_0), F_267(x, k_0) + F_270(x, k_0) + 2*F_30(x))
Eq(F_270(x, k_0), F_11(x)*F_271(x, k_0))
Eq(F_271(x, k_0), F_223(x, k_0) + F_269(x, k_0))
Eq(F_272(x, k_0), F_11(x)*F_273(x, k_0))
Eq(F_273(x, k_0), F_274(x, k_0) + F_278(x, k_0))
Eq(F_274(x, k_0), F_223(x, k_0) + F_275(x, k_0))
Eq(F_275(x, k_0), F_244(x, k_0) + F_276(x, k_0) + 2*F_30(x))
Eq(F_276(x, k_0), F_11(x)*F_277(x, k_0))
Eq(F_277(x, k_0), F_190(x, k_0) + F_275(x, k_0))
Eq(F_278(x, k_0), F_266(x, k_0) + F_279(x, k_0))
Eq(F_279(x, k_0), F_280(x, k_0) + F_284(x, k_0) + F_288(x, k_0) + 2*F_30(x))
Eq(F_280(x, k_0), F_11(x)*F_281(x, k_0))
Eq(F_281(x, k_0), F_198(x, k_0) + F_282(x, k_0))
Eq(F_282(x, k_0), F_280(x, k_0) + F_283(x, k_0) + 3*F_30(x))
Eq(F_283(x, k_0), F_11(x)*F_269(x, k_0))
Eq(F_284(x, k_0), F_11(x)*F_285(x, k_0))
Eq(F_285(x, k_0), F_286(x, k_0) + F_287(x, k_0))
Eq(F_286(x, k_0), F_275(x, k_0))
Eq(F_287(x, k_0), F_279(x, k_0))
Eq(F_288(x, k_0), F_11(x)*F_266(x, k_0))
Eq(F_289(x, k_0), F_290(x, k_0) + F_295(x, k_0) + F_299(x, k_0) + 2*F_30(x))
Eq(F_290(x, k_0), F_11(x)*F_291(x, k_0))
Eq(F_291(x, k_0), F_208(x, k_0) + F_292(x, k_0))
Eq(F_292(x, k_0), F_290(x, k_0) + F_293(x, k_0) + 3*F_30(x))
Eq(F_293(x, k_0), F_11(x)*F_294(x, k_0))
Eq(F_294(x, k_0), F_269(x, k_0) + F_292(x, k_0))
Eq(F_295(x, k_0), F_11(x)*F_296(x, k_0))
Eq(F_296(x, k_0), F_297(x, k_0) + F_298(x, k_0))
Eq(F_297(x, k_0), F_226(x, k_0))
Eq(F_298(x, k_0), F_289(x, k_0))
Eq(F_299(x, k_0), F_11(x)*F_265(x, k_0))
Eq(F_300(x, k_0), F_301(x, k_0) + F_314(x, k_0))
Eq(F_301(x, k_0), 2*F_30(x) + F_302(x, k_0) + F_304(x, k_0))
Eq(F_302(x, k_0), F_11(x)*F_303(x, k_0))
Eq(F_303(x, k_0), F_217(x, k_0) + F_301(x, k_0))
Eq(F_304(x, k_0), F_11(x)*F_305(x, k_0))
Eq(F_305(x, k_0), F_222(x, k_0) + F_306(x, k_0))
Eq(F_306(x, k_0), F_307(x, k_0) + F_310(x, k_0))
Eq(F_307(x, k_0), F_308(x, k_0))
Eq(F_308(x, k_0), F_11(x)*F_309(x, k_0))
Eq(F_309(x, k_0), F_223(x, k_0) + F_307(x, k_0))
Eq(F_310(x, k_0), 3*F_30(x) + F_311(x, k_0) + F_313(x, k_0))
Eq(F_311(x, k_0), F_11(x)*F_312(x, k_0))
Eq(F_312(x, k_0), F_226(x, k_0) + F_310(x, k_0))
Eq(F_313(x, k_0), F_11(x)*F_306(x, k_0))
Eq(F_314(x, k_0), 3*F_30(x) + F_315(x, k_0) + F_317(x, k_0))
Eq(F_315(x, k_0), F_11(x)*F_316(x, k_0))
Eq(F_316(x, k_0), F_230(x, k_0) + F_314(x, k_0))
Eq(F_317(x, k_0), F_11(x)*F_318(x, k_0))
Eq(F_318(x, k_0), F_319(x, k_0) + F_322(x, k_0))
Eq(F_319(x, k_0), F_307(x, k_0) + F_320(x, k_0))
Eq(F_320(x, k_0), F_321(x, k_0))
Eq(F_321(x, k_0), F_11(x)*F_319(x, k_0))
Eq(F_322(x, k_0), F_323(x, k_0) + F_336(x, k_0))
Eq(F_323(x, k_0), F_324(x, k_0))
Eq(F_324(x, k_0), F_11(x)*F_325(x, k_0))
Eq(F_325(x, k_0), F_326(x, k_0) + F_329(x, k_0))
Eq(F_326(x, k_0), F_307(x, k_0) + F_327(x, k_0))
Eq(F_327(x, k_0), F_328(x, k_0))
Eq(F_328(x, k_0), F_11(x)*F_307(x, k_0))
Eq(F_329(x, k_0), F_323(x, k_0) + F_330(x, k_0))
Eq(F_330(x, k_0), 4*F_30(x) + F_331(x, k_0) + F_335(x, k_0))
Eq(F_331(x, k_0), F_11(x)*F_332(x, k_0))
Eq(F_332(x, k_0), F_333(x, k_0) + F_334(x, k_0))
Eq(F_333(x, k_0), F_327(x, k_0))
Eq(F_334(x, k_0), F_330(x, k_0))
Eq(F_335(x, k_0), F_11(x)*F_323(x, k_0))
Eq(F_336(x, k_0), 4*F_30(x) + F_337(x, k_0) + F_341(x, k_0))
Eq(F_337(x, k_0), F_11(x)*F_338(x, k_0))
Eq(F_338(x, k_0), F_339(x, k_0) + F_340(x, k_0))
Eq(F_339(x, k_0), F_320(x, k_0))
Eq(F_340(x, k_0), F_336(x, k_0))
Eq(F_341(x, k_0), F_11(x)*F_322(x, k_0))
Eq(F_342(x), F_11(x)*F_14(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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], "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": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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, 0]]}, {"patt": [1, 0], "pos": [[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], "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": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, 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