0132_0213_1230
Counting sequence:
1, 1, 2, 6, 21, 76, 275, 989, 3544, 12696, 45578, 164194, 593966, 2158090, 7875503, 28862235, 106203597, 392291117, 1454239837, 5409048372, 20182045236, 75522431214, 283377791271, 1065990318403, 4019415215923, 15188857311110, 57514327098488, 218201177979480, 829305547436095, 3157180020037927, 12038335208533218, 45970012778497861, 175786753726815475, 673079437848736875, 2580377747635381868, 9903933285497748767, 38055070769967311689, 146376984903052697526, 563592746717733397051, 2172045524567533175767, 8378446807390362614220, 32346754150823669849975, 124983678103753626175275, 483298293538467907416350, 1870258392345399191203753, 7242664101551359823735385, 28066763533382158412452654, 108835676098845115047150593, 422302464991531173512246013, 1639602139675125326009823144, 6369504149114549426373107395, 24757991767206167531382800265, 96285023291855804499074287076, 374651089691453499486346880563, 1458518896437370824066348009629, 5680757082392455367843547074856, 22136154495044817714304602789091, 86296466507699739847612559407081, 336567483106215578812917879385136, 1313207506760750284991235630651067, 5125906483000826775340911635298441, 20016054161094861778380028082873876, 78190022405442737606717877379328232, 305551313200458387716442045482536042, 1194461125913630076084479636439016973, 4671004195057940507901471635212067852, 18272349692051531717341348894865645412, 71502326082864860444339375751208889690, 279887489710539572423655104978732450809, 1095923994178103548766593112975073273249, 4292469992286873493241923134095319594595, 16817459536002180325842351307235482251938, 65907731066761053879048759134840562201450, 258363922830851384145087539242681126976496, 1013080005281484101330606555305806408243373, 3973460802209707708691367104651020059746271, 15588506412965453227371116889558047051349791, 61171290607946082648803492415200250399245278, 240101920069321602285098314868825289396202766, 942639997910030177112334709310880705258792004, 3701653987289093187630569199487599459967079197, 14539286031911085374181383285153384892202972515, 57119619760975786378655054090896397287833868379, 224450330607015240907549218207416876032181234632, 882156690246963086838953454338987062555300802678, 3467844840521997971218973999631751334174325013432, 13635152537830842997594021184697866643638689077647, 53622221691536038044301345165226584408207149003345, 210917286642138179915840652076085288177289495160729, 829774888996775156651750144787830778181415028954434, 3265031473405869902314854288588547754524273374726800, 12849662388982590472395528910115584700036705171777838, 50579166406234969089772054805174766435980378309967045, 199124922423948564434881549772800918469992642158553651, 784064915327118333408803811819303781843868868472706113, 3087801449703487899384285839422528599120837625915941086, 12162313657006420208870166486996268313520804971903352056, 47912750741794798111182550528154926545900969056257983518, 188778579165941910118034352142566214309752929543126446181, 743908795458532232298770353285729473834757426895158544229, 2931910818531753219526609845520177248007463586373839394617
Generating function in Maple syntax:
1/2*((x^2-3*x+1)*(x^5-2*x^4-3*x^3+6*x^2-4*x+1)*(1-4*x)^(1/2)-9*x^7+19*x^6+10*x^5-59*x^4+63*x^3-33*x^2+9*x-1)/x^2/(x^2+x-1)/(x^2-3*x+1)/(x-1)^2
Generating function in latex syntax:
\frac{\left(x^{2}-3 x +1\right) \left(x^{5}-2 x^{4}-3 x^{3}+6 x^{2}-4 x +1\right) \sqrt{1-4 x}-9 x^{7}+19 x^{6}+10 x^{5}-59 x^{4}+63 x^{3}-33 x^{2}+9 x -1}{2 x^{2} \left(x^{2}+x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-9*x**7/2 + 19*x**6/2 + 5*x**5 - 59*x**4/2 + 63*x**3/2 - 33*x**2/2 + 9*x/2 + sqrt(1 - 4*x)*(x**2 - 3*x + 1)*(x**5 - 2*x**4 - 3*x**3 + 6*x**2 - 4*x + 1)/2 - 1/2)/(x**2*(x - 1)**2*(x**2 - 3*x + 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x^2*(x^2-3*x+1)^2*(x^2+x-1)^2*(x-1)^4*F(x)^2+(x^2-3*x+1)*(x^2+x-1)*(9*x^7-19*x^6-10*x^5+59*x^4-63*x^3+33*x^2-9*x+1)*(x-1)^2*F(x)+x^13+10*x^12-50*x^11+23*x^10+200*x^9-386*x^8+119*x^7+464*x^6-774*x^5+614*x^4-292*x^3+85*x^2-14*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(x^{2}-3 x +1\right)^{2} \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)^{2}+\left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(9 x^{7}-19 x^{6}-10 x^{5}+59 x^{4}-63 x^{3}+33 x^{2}-9 x +1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{13}+10 x^{12}-50 x^{11}+23 x^{10}+200 x^{9}-386 x^{8}+119 x^{7}+464 x^{6}-774 x^{5}+614 x^{4}-292 x^{3}+85 x^{2}-14 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(8) = 3544
a(9) = 12696
a(10) = 45578
a(11) = 164194
a(12) = 593966
a(13) = 2158090
a(n+13) = 2*(1+2*n)/(15+n)*a(n)+(217+80*n)/(15+n)*a(2+n)-3*(18+11*n)/(15+n)*a(n+1)+(155+34*n)/(15+n)*a(n+3)-(2277+445*n)/(15+n)*a(n+4)+2*(2071+324*n)/(15+n)*a(n+5)-(794+27*n)/(15+n)*a(n+6)-(7053+959*n)/(15+n)*a(n+7)+(11816+1333*n)/(15+n)*a(n+8)-(9713+955*n)/(15+n)*a(n+9)+2*(2363+207*n)/(15+n)*a(n+10)-(1376+109*n)/(15+n)*a(n+11)+(221+16*n)/(15+n)*a(n+12)+4/(15+n), n >= 14
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(8\right) = 3544
a \! \left(9\right) = 12696
a \! \left(10\right) = 45578
a \! \left(11\right) = 164194
a \! \left(12\right) = 593966
a \! \left(13\right) = 2158090
a \! \left(n +13\right) = \frac{2 \left(1+2 n \right) a \! \left(n \right)}{15+n}+\frac{\left(217+80 n \right) a \! \left(2+n \right)}{15+n}-\frac{3 \left(18+11 n \right) a \! \left(n +1\right)}{15+n}+\frac{\left(155+34 n \right) a \! \left(n +3\right)}{15+n}-\frac{\left(2277+445 n \right) a \! \left(n +4\right)}{15+n}+\frac{2 \left(2071+324 n \right) a \! \left(n +5\right)}{15+n}-\frac{\left(794+27 n \right) a \! \left(n +6\right)}{15+n}-\frac{\left(7053+959 n \right) a \! \left(n +7\right)}{15+n}+\frac{\left(11816+1333 n \right) a \! \left(n +8\right)}{15+n}-\frac{\left(9713+955 n \right) a \! \left(n +9\right)}{15+n}+\frac{2 \left(2363+207 n \right) a \! \left(n +10\right)}{15+n}-\frac{\left(1376+109 n \right) a \! \left(n +11\right)}{15+n}+\frac{\left(221+16 n \right) a \! \left(n +12\right)}{15+n}+\frac{4}{15+n}, \quad n \geq 14
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/256/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[14,x]*F[3,x]
F[3,x] = F[1,x]+F[148,x]+F[4,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[44,x]+F[6,x]
F[6,x] = F[25,x]+F[7,x]
F[7,x] = F[1,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[14,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]+F[23,x]
F[16,x] = F[17,x]
F[17,x] = F[14,x]*F[18,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[1,x]+F[14,x]
F[20,x] = F[16,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[14,x]*F[16,x]
F[23,x] = F[24,x]
F[24,x] = F[14,x]*F[15,x]
F[25,x] = F[12,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[14,x]*F[28,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[14,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[29,x]
F[32,x] = F[33,x]+F[42,x]
F[33,x] = F[34,x]
F[34,x] = F[14,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[14,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = x^2
F[39,x] = F[33,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[33,x]
F[42,x] = F[43,x]
F[43,x] = F[14,x]*F[32,x]
F[44,x] = F[127,x]+F[45,x]
F[45,x] = F[46,x]+F[57,x]
F[46,x] = F[47,x]
F[47,x] = F[14,x]*F[48,x]
F[48,x] = F[19,x]+F[49,x]
F[49,x] = F[46,x]+F[50,x]
F[50,x] = F[51,x]+F[52,x]+F[56,x]
F[51,x] = 0
F[52,x] = F[14,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[14,x]
F[55,x] = F[50,x]
F[56,x] = F[14,x]*F[46,x]
F[57,x] = F[51,x]+F[58,x]+F[90,x]
F[58,x] = F[14,x]*F[59,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = F[61,x]+F[8,x]
F[61,x] = F[27,x]
F[62,x] = F[57,x]+F[63,x]
F[63,x] = 2*F[51,x]+F[64,x]+F[68,x]
F[64,x] = F[14,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[61,x]
F[67,x] = F[63,x]
F[68,x] = F[14,x]*F[69,x]
F[69,x] = F[70,x]+F[78,x]
F[70,x] = F[71,x]+F[76,x]
F[71,x] = F[72,x]
F[72,x] = F[14,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[14,x]*F[75,x]
F[75,x] = F[1,x]+F[73,x]
F[76,x] = F[77,x]
F[77,x] = F[14,x]*F[70,x]
F[78,x] = F[79,x]+F[88,x]
F[79,x] = F[80,x]
F[80,x] = F[14,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[71,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[71,x]
F[85,x] = F[79,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[14,x]*F[79,x]
F[88,x] = F[89,x]
F[89,x] = F[14,x]*F[78,x]
F[90,x] = F[14,x]*F[91,x]
F[91,x] = F[92,x]+F[97,x]
F[92,x] = F[73,x]+F[93,x]
F[93,x] = F[51,x]+F[94,x]+F[96,x]
F[94,x] = F[14,x]*F[95,x]
F[95,x] = F[12,x]+F[93,x]
F[96,x] = F[14,x]*F[92,x]
F[97,x] = F[117,x]+F[98,x]
F[98,x] = F[104,x]+F[51,x]+F[99,x]
F[99,x] = F[100,x]*F[14,x]
F[100,x] = F[101,x]+F[73,x]
F[101,x] = F[102,x]+F[51,x]+F[99,x]
F[102,x] = F[103,x]*F[14,x]
F[103,x] = F[101,x]+F[73,x]
F[104,x] = F[105,x]*F[14,x]
F[105,x] = F[106,x]+F[110,x]
F[106,x] = F[107,x]+F[73,x]
F[107,x] = F[108,x]+F[51,x]+F[72,x]
F[108,x] = F[109,x]*F[14,x]
F[109,x] = F[107,x]+F[14,x]
F[110,x] = F[111,x]+F[98,x]
F[111,x] = 2*F[51,x]+F[112,x]+F[116,x]
F[112,x] = F[113,x]*F[14,x]
F[113,x] = F[114,x]+F[71,x]
F[114,x] = 2*F[51,x]+F[112,x]+F[115,x]
F[115,x] = F[101,x]*F[14,x]
F[116,x] = F[14,x]*F[98,x]
F[117,x] = 2*F[51,x]+F[118,x]+F[126,x]
F[118,x] = F[119,x]*F[14,x]
F[119,x] = F[120,x]+F[123,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[14,x]
F[122,x] = F[120,x]+F[73,x]
F[123,x] = 2*F[51,x]+F[118,x]+F[124,x]
F[124,x] = F[125,x]*F[14,x]
F[125,x] = F[101,x]+F[123,x]
F[126,x] = F[14,x]*F[97,x]
F[127,x] = F[128,x]+F[143,x]
F[128,x] = F[129,x]+F[141,x]+F[51,x]
F[129,x] = F[130,x]*F[14,x]
F[130,x] = F[131,x]+F[134,x]
F[131,x] = F[12,x]+F[132,x]
F[132,x] = F[133,x]
F[133,x] = F[12,x]*F[14,x]
F[134,x] = F[128,x]+F[135,x]
F[135,x] = 2*F[51,x]+F[136,x]+F[140,x]
F[136,x] = F[137,x]*F[14,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[132,x]
F[139,x] = F[135,x]
F[140,x] = F[128,x]*F[14,x]
F[141,x] = F[14,x]*F[142,x]
F[142,x] = F[128,x]+F[46,x]
F[143,x] = 2*F[51,x]+F[144,x]+F[68,x]
F[144,x] = F[14,x]*F[145,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[26,x]
F[147,x] = F[143,x]
F[148,x] = F[14,x]*F[149,x]
F[149,x] = F[150,x,1]
F[150,x,k[0]] = F[1,x]+F[151,x,k[0]]+F[153,x,k[0]]+F[155,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[152,x,k[0]]
F[152,x,k[0]] = k[0]*x
F[153,x,k[0]] = F[14,x]*F[154,x,k[0]]
F[154,x,k[0]] = (F[150,x,k[0]]*k[0]-F[150,x,1])/(-1+k[0])
F[155,x,k[0]] = F[14,x]*F[156,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[5,x]
F[157,x,k[0]] = F[158,x,k[0]]+F[223,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]+F[201,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]+F[163,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[152,x,k[0]]*F[162,x,k[0]]
F[162,x,k[0]] = F[1,x]+F[160,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]+F[166,x,k[0]]+F[51,x]
F[164,x,k[0]] = F[152,x,k[0]]*F[165,x,k[0]]
F[165,x,k[0]] = F[163,x,k[0]]+F[8,x]
F[166,x,k[0]] = F[14,x]*F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[173,x,k[0]]
F[168,x,k[0]] = F[160,x,k[0]]+F[169,x,k[0]]
F[169,x,k[0]] = F[170,x,k[0]]+F[172,x,k[0]]+F[51,x]
F[170,x,k[0]] = F[152,x,k[0]]*F[171,x,k[0]]
F[171,x,k[0]] = F[12,x]+F[169,x,k[0]]
F[172,x,k[0]] = F[14,x]*F[168,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[194,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]+F[180,x,k[0]]+F[51,x]
F[175,x,k[0]] = F[152,x,k[0]]*F[176,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[73,x]
F[177,x,k[0]] = F[175,x,k[0]]+F[178,x,k[0]]+F[51,x]
F[178,x,k[0]] = F[14,x]*F[179,x,k[0]]
F[179,x,k[0]] = F[160,x,k[0]]+F[177,x,k[0]]
F[180,x,k[0]] = F[14,x]*F[181,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[187,x,k[0]]
F[182,x,k[0]] = F[160,x,k[0]]+F[183,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]+F[186,x,k[0]]+F[51,x]
F[184,x,k[0]] = F[152,x,k[0]]*F[185,x,k[0]]
F[185,x,k[0]] = F[14,x]+F[183,x,k[0]]
F[186,x,k[0]] = F[14,x]*F[160,x,k[0]]
F[187,x,k[0]] = F[174,x,k[0]]+F[188,x,k[0]]
F[188,x,k[0]] = 2*F[51,x]+F[189,x,k[0]]+F[193,x,k[0]]
F[189,x,k[0]] = F[152,x,k[0]]*F[190,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]+F[71,x]
F[191,x,k[0]] = 2*F[51,x]+F[189,x,k[0]]+F[192,x,k[0]]
F[192,x,k[0]] = F[14,x]*F[177,x,k[0]]
F[193,x,k[0]] = F[14,x]*F[174,x,k[0]]
F[194,x,k[0]] = 2*F[51,x]+F[195,x,k[0]]+F[200,x,k[0]]
F[195,x,k[0]] = F[152,x,k[0]]*F[196,x,k[0]]
F[196,x,k[0]] = F[120,x]+F[197,x,k[0]]
F[197,x,k[0]] = 2*F[51,x]+F[195,x,k[0]]+F[198,x,k[0]]
F[198,x,k[0]] = F[14,x]*F[199,x,k[0]]
F[199,x,k[0]] = F[177,x,k[0]]+F[197,x,k[0]]
F[200,x,k[0]] = F[14,x]*F[173,x,k[0]]
F[201,x,k[0]] = F[169,x,k[0]]+F[202,x,k[0]]
F[202,x,k[0]] = 2*F[51,x]+F[203,x,k[0]]+F[205,x,k[0]]
F[203,x,k[0]] = F[152,x,k[0]]*F[204,x,k[0]]
F[204,x,k[0]] = F[202,x,k[0]]+F[26,x]
F[205,x,k[0]] = F[14,x]*F[206,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]+F[211,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[209,x,k[0]]
F[208,x,k[0]] = F[186,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[14,x]*F[207,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]+F[221,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[14,x]*F[214,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0]]+F[218,x,k[0]]
F[215,x,k[0]] = F[208,x,k[0]]+F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]
F[217,x,k[0]] = F[14,x]*F[208,x,k[0]]
F[218,x,k[0]] = F[212,x,k[0]]+F[219,x,k[0]]
F[219,x,k[0]] = F[220,x,k[0]]
F[220,x,k[0]] = F[14,x]*F[212,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]
F[222,x,k[0]] = F[14,x]*F[211,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]+F[306,x,k[0]]
F[224,x,k[0]] = F[225,x,k[0]]+F[236,x,k[0]]
F[225,x,k[0]] = F[184,x,k[0]]+F[226,x,k[0]]+F[51,x]
F[226,x,k[0]] = F[14,x]*F[227,x,k[0]]
F[227,x,k[0]] = F[182,x,k[0]]+F[228,x,k[0]]
F[228,x,k[0]] = F[225,x,k[0]]+F[229,x,k[0]]
F[229,x,k[0]] = F[230,x,k[0]]+F[231,x,k[0]]+F[235,x,k[0]]+F[51,x]
F[230,x,k[0]] = 0
F[231,x,k[0]] = F[14,x]*F[232,x,k[0]]
F[232,x,k[0]] = F[233,x,k[0]]+F[234,x,k[0]]
F[233,x,k[0]] = F[183,x,k[0]]
F[234,x,k[0]] = F[229,x,k[0]]
F[235,x,k[0]] = F[14,x]*F[225,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]+F[240,x,k[0]]+F[272,x,k[0]]+F[51,x]
F[237,x,k[0]] = F[152,x,k[0]]*F[238,x,k[0]]
F[238,x,k[0]] = F[239,x,k[0]]+F[61,x]
F[239,x,k[0]] = 2*F[51,x]+F[205,x,k[0]]+F[237,x,k[0]]
F[240,x,k[0]] = F[14,x]*F[241,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]+F[243,x,k[0]]
F[242,x,k[0]] = F[163,x,k[0]]+F[239,x,k[0]]
F[243,x,k[0]] = F[236,x,k[0]]+F[244,x,k[0]]
F[244,x,k[0]] = 2*F[51,x]+F[245,x,k[0]]+F[246,x,k[0]]+F[250,x,k[0]]
F[245,x,k[0]] = 0
F[246,x,k[0]] = F[14,x]*F[247,x,k[0]]
F[247,x,k[0]] = F[248,x,k[0]]+F[249,x,k[0]]
F[248,x,k[0]] = F[239,x,k[0]]
F[249,x,k[0]] = F[244,x,k[0]]
F[250,x,k[0]] = F[14,x]*F[251,x,k[0]]
F[251,x,k[0]] = F[252,x,k[0]]+F[260,x,k[0]]
F[252,x,k[0]] = F[253,x,k[0]]+F[258,x,k[0]]
F[253,x,k[0]] = F[254,x,k[0]]
F[254,x,k[0]] = F[14,x]*F[255,x,k[0]]
F[255,x,k[0]] = F[256,x,k[0]]
F[256,x,k[0]] = F[14,x]*F[257,x,k[0]]
F[257,x,k[0]] = F[160,x,k[0]]+F[255,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]
F[259,x,k[0]] = F[14,x]*F[252,x,k[0]]
F[260,x,k[0]] = F[261,x,k[0]]+F[270,x,k[0]]
F[261,x,k[0]] = F[262,x,k[0]]
F[262,x,k[0]] = F[14,x]*F[263,x,k[0]]
F[263,x,k[0]] = F[264,x,k[0]]+F[267,x,k[0]]
F[264,x,k[0]] = F[253,x,k[0]]+F[265,x,k[0]]
F[265,x,k[0]] = F[266,x,k[0]]
F[266,x,k[0]] = F[14,x]*F[253,x,k[0]]
F[267,x,k[0]] = F[261,x,k[0]]+F[268,x,k[0]]
F[268,x,k[0]] = F[269,x,k[0]]
F[269,x,k[0]] = F[14,x]*F[261,x,k[0]]
F[270,x,k[0]] = F[271,x,k[0]]
F[271,x,k[0]] = F[14,x]*F[260,x,k[0]]
F[272,x,k[0]] = F[14,x]*F[273,x,k[0]]
F[273,x,k[0]] = F[274,x,k[0]]+F[279,x,k[0]]
F[274,x,k[0]] = F[255,x,k[0]]+F[275,x,k[0]]
F[275,x,k[0]] = 2*F[51,x]+F[276,x,k[0]]+F[278,x,k[0]]
F[276,x,k[0]] = F[14,x]*F[277,x,k[0]]
F[277,x,k[0]] = F[169,x,k[0]]+F[275,x,k[0]]
F[278,x,k[0]] = F[14,x]*F[274,x,k[0]]
F[279,x,k[0]] = F[280,x,k[0]]+F[299,x,k[0]]
F[280,x,k[0]] = 2*F[51,x]+F[281,x,k[0]]+F[286,x,k[0]]
F[281,x,k[0]] = F[14,x]*F[282,x,k[0]]
F[282,x,k[0]] = F[177,x,k[0]]+F[283,x,k[0]]
F[283,x,k[0]] = 2*F[51,x]+F[281,x,k[0]]+F[284,x,k[0]]
F[284,x,k[0]] = F[14,x]*F[285,x,k[0]]
F[285,x,k[0]] = F[255,x,k[0]]+F[283,x,k[0]]
F[286,x,k[0]] = F[14,x]*F[287,x,k[0]]
F[287,x,k[0]] = F[288,x,k[0]]+F[292,x,k[0]]
F[288,x,k[0]] = F[255,x,k[0]]+F[289,x,k[0]]
F[289,x,k[0]] = 2*F[51,x]+F[254,x,k[0]]+F[290,x,k[0]]
F[290,x,k[0]] = F[14,x]*F[291,x,k[0]]
F[291,x,k[0]] = F[183,x,k[0]]+F[289,x,k[0]]
F[292,x,k[0]] = F[280,x,k[0]]+F[293,x,k[0]]
F[293,x,k[0]] = 3*F[51,x]+F[294,x,k[0]]+F[298,x,k[0]]
F[294,x,k[0]] = F[14,x]*F[295,x,k[0]]
F[295,x,k[0]] = F[191,x,k[0]]+F[296,x,k[0]]
F[296,x,k[0]] = 3*F[51,x]+F[294,x,k[0]]+F[297,x,k[0]]
F[297,x,k[0]] = F[14,x]*F[283,x,k[0]]
F[298,x,k[0]] = F[14,x]*F[280,x,k[0]]
F[299,x,k[0]] = 3*F[51,x]+F[300,x,k[0]]+F[305,x,k[0]]
F[300,x,k[0]] = F[14,x]*F[301,x,k[0]]
F[301,x,k[0]] = F[197,x,k[0]]+F[302,x,k[0]]
F[302,x,k[0]] = 3*F[51,x]+F[300,x,k[0]]+F[303,x,k[0]]
F[303,x,k[0]] = F[14,x]*F[304,x,k[0]]
F[304,x,k[0]] = F[283,x,k[0]]+F[302,x,k[0]]
F[305,x,k[0]] = F[14,x]*F[279,x,k[0]]
F[306,x,k[0]] = F[307,x,k[0]]+F[325,x,k[0]]
F[307,x,k[0]] = F[308,x,k[0]]+F[312,x,k[0]]+F[323,x,k[0]]+F[51,x]
F[308,x,k[0]] = F[152,x,k[0]]*F[309,x,k[0]]
F[309,x,k[0]] = F[132,x]+F[310,x,k[0]]
F[310,x,k[0]] = 2*F[51,x]+F[308,x,k[0]]+F[311,x,k[0]]
F[311,x,k[0]] = F[14,x]*F[169,x,k[0]]
F[312,x,k[0]] = F[14,x]*F[313,x,k[0]]
F[313,x,k[0]] = F[314,x,k[0]]+F[315,x,k[0]]
F[314,x,k[0]] = F[169,x,k[0]]+F[310,x,k[0]]
F[315,x,k[0]] = F[307,x,k[0]]+F[316,x,k[0]]
F[316,x,k[0]] = 2*F[51,x]+F[317,x,k[0]]+F[318,x,k[0]]+F[322,x,k[0]]
F[317,x,k[0]] = 0
F[318,x,k[0]] = F[14,x]*F[319,x,k[0]]
F[319,x,k[0]] = F[320,x,k[0]]+F[321,x,k[0]]
F[320,x,k[0]] = F[310,x,k[0]]
F[321,x,k[0]] = F[316,x,k[0]]
F[322,x,k[0]] = F[14,x]*F[307,x,k[0]]
F[323,x,k[0]] = F[14,x]*F[324,x,k[0]]
F[324,x,k[0]] = F[225,x,k[0]]+F[307,x,k[0]]
F[325,x,k[0]] = 2*F[51,x]+F[250,x,k[0]]+F[326,x,k[0]]+F[327,x,k[0]]
F[326,x,k[0]] = 0
F[327,x,k[0]] = F[14,x]*F[328,x,k[0]]
F[328,x,k[0]] = F[329,x,k[0]]+F[330,x,k[0]]
F[329,x,k[0]] = F[202,x,k[0]]
F[330,x,k[0]] = F[325,x,k[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_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{148}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{44}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{25}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{23}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \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_{27}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{14}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{42}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = x^{2}
F_{39}\! \left(x \right) = F_{33}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{14}\! \left(x \right) F_{32}\! \left(x \right)
F_{44}\! \left(x \right) = F_{127}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{57}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{19}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{51}\! \left(x \right) = 0
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right)
F_{55}\! \left(x \right) = F_{50}\! \left(x \right)
F_{56}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{57}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)+F_{90}\! \left(x \right)
F_{58}\! \left(x \right) = F_{14}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{8}\! \left(x \right)
F_{61}\! \left(x \right) = F_{27}\! \left(x \right)
F_{62}\! \left(x \right) = F_{57}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{51}\! \left(x \right)+F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{61}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{14}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{78}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{88}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \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_{71}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{85}\! \left(x \right) = F_{79}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{14}\! \left(x \right) F_{79}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{14}\! \left(x \right) F_{78}\! \left(x \right)
F_{90}\! \left(x \right) = F_{14}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{97}\! \left(x \right)
F_{92}\! \left(x \right) = F_{73}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{51}\! \left(x \right)+F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{14}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right)+F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{14}\! \left(x \right) F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{117}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{104}\! \left(x \right)+F_{51}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{14}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{73}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{51}\! \left(x \right)+F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{14}\! \left(x \right)
F_{103}\! \left(x \right) = F_{101}\! \left(x \right)+F_{73}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{14}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{110}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{73}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{51}\! \left(x \right)+F_{72}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{14}\! \left(x \right)
F_{109}\! \left(x \right) = F_{107}\! \left(x \right)+F_{14}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{98}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{51}\! \left(x \right)+F_{112}\! \left(x \right)+F_{116}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{14}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{71}\! \left(x \right)
F_{114}\! \left(x \right) = 2 F_{51}\! \left(x \right)+F_{112}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{101}\! \left(x \right) F_{14}\! \left(x \right)
F_{116}\! \left(x \right) = F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{117}\! \left(x \right) = 2 F_{51}\! \left(x \right)+F_{118}\! \left(x \right)+F_{126}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{14}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{123}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{14}\! \left(x \right)
F_{122}\! \left(x \right) = F_{120}\! \left(x \right)+F_{73}\! \left(x \right)
F_{123}\! \left(x \right) = 2 F_{51}\! \left(x \right)+F_{118}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{14}\! \left(x \right)
F_{125}\! \left(x \right) = F_{101}\! \left(x \right)+F_{123}\! \left(x \right)
F_{126}\! \left(x \right) = F_{14}\! \left(x \right) F_{97}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{143}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{141}\! \left(x \right)+F_{51}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{14}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{134}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{134}\! \left(x \right) = F_{128}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = 2 F_{51}\! \left(x \right)+F_{136}\! \left(x \right)+F_{140}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{14}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{132}\! \left(x \right)
F_{139}\! \left(x \right) = F_{135}\! \left(x \right)
F_{140}\! \left(x \right) = F_{128}\! \left(x \right) F_{14}\! \left(x \right)
F_{141}\! \left(x \right) = F_{14}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{128}\! \left(x \right)+F_{46}\! \left(x \right)
F_{143}\! \left(x \right) = 2 F_{51}\! \left(x \right)+F_{144}\! \left(x \right)+F_{68}\! \left(x \right)
F_{144}\! \left(x \right) = F_{14}\! \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_{26}\! \left(x \right)
F_{147}\! \left(x \right) = F_{143}\! \left(x \right)
F_{148}\! \left(x \right) = F_{14}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x , 1\right)
F_{150}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = y x
F_{153}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = -\frac{-y F_{150}\! \left(x , y\right)+F_{150}\! \left(x , 1\right)}{-1+y}
F_{155}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{223}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{160}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{166}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{172}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{169}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{168}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{180}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{73}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{178}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{178}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{186}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{183}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{160}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{189}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{71}\! \left(x \right)
F_{191}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{189}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{177}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{174}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{120}\! \left(x \right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{173}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{203}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{204}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{202}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{205}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{186}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{207}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{211}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{306}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{236}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{226}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{226}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{230}\! \left(x , y\right)+F_{231}\! \left(x , y\right)+F_{235}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{230}\! \left(x , y\right) = 0
F_{231}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{233}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{183}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{229}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{225}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{240}\! \left(x , y\right)+F_{272}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{237}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{238}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{61}\! \left(x \right)
F_{239}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{205}\! \left(x , y\right)+F_{237}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{241}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{242}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{239}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{236}\! \left(x , y\right)+F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{245}\! \left(x , y\right)+F_{246}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = 0
F_{246}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{247}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{239}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{244}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{251}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)+F_{260}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{253}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{254}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{255}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{257}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{255}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{252}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{261}\! \left(x , y\right)+F_{270}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{263}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{264}\! \left(x , y\right)+F_{267}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{253}\! \left(x , y\right)+F_{265}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{253}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{261}\! \left(x , y\right)+F_{268}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{269}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{261}\! \left(x , y\right)
F_{270}\! \left(x , y\right) = F_{271}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{260}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{279}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{275}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{276}\! \left(x , y\right)+F_{278}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{277}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{275}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{274}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{280}\! \left(x , y\right)+F_{299}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{281}\! \left(x , y\right)+F_{286}\! \left(x , y\right)
F_{281}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{282}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{281}\! \left(x , y\right)+F_{284}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{285}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{287}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{288}\! \left(x , y\right)+F_{292}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{289}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{254}\! \left(x , y\right)+F_{290}\! \left(x , y\right)
F_{290}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{291}\! \left(x , y\right)
F_{291}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{289}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{280}\! \left(x , y\right)+F_{293}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = 3 F_{51}\! \left(x \right)+F_{294}\! \left(x , y\right)+F_{298}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{295}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = 3 F_{51}\! \left(x \right)+F_{294}\! \left(x , y\right)+F_{297}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{283}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{280}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = 3 F_{51}\! \left(x \right)+F_{300}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{301}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{302}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = 3 F_{51}\! \left(x \right)+F_{300}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{304}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{283}\! \left(x , y\right)+F_{302}\! \left(x , y\right)
F_{305}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{279}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{307}\! \left(x , y\right)+F_{325}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{308}\! \left(x , y\right)+F_{312}\! \left(x , y\right)+F_{323}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{308}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{309}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{132}\! \left(x \right)+F_{310}\! \left(x , y\right)
F_{310}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{308}\! \left(x , y\right)+F_{311}\! \left(x , y\right)
F_{311}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{169}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{313}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{314}\! \left(x , y\right)+F_{315}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{310}\! \left(x , y\right)
F_{315}\! \left(x , y\right) = F_{307}\! \left(x , y\right)+F_{316}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{317}\! \left(x , y\right)+F_{318}\! \left(x , y\right)+F_{322}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = 0
F_{318}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{319}\! \left(x , y\right)
F_{319}\! \left(x , y\right) = F_{320}\! \left(x , y\right)+F_{321}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{310}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{316}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{307}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{324}\! \left(x , y\right)
F_{324}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{307}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = 2 F_{51}\! \left(x \right)+F_{250}\! \left(x , y\right)+F_{326}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{326}\! \left(x , y\right) = 0
F_{327}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{329}\! \left(x , y\right)+F_{330}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = F_{202}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{325}\! \left(x , y\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_14(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_148(x) + F_4(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_44(x) + F_6(x))
Eq(F_6(x), F_25(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_14(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x) + F_23(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_1(x) + F_14(x))
Eq(F_20(x), F_16(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_14(x)*F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_14(x)*F_15(x))
Eq(F_25(x), F_12(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_14(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_14(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_29(x))
Eq(F_32(x), F_33(x) + F_42(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_14(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_14(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), x**2)
Eq(F_39(x), F_33(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_33(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_14(x)*F_32(x))
Eq(F_44(x), F_127(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_57(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_14(x)*F_48(x))
Eq(F_48(x), F_19(x) + F_49(x))
Eq(F_49(x), F_46(x) + F_50(x))
Eq(F_50(x), F_51(x) + F_52(x) + F_56(x))
Eq(F_51(x), 0)
Eq(F_52(x), F_14(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_14(x))
Eq(F_55(x), F_50(x))
Eq(F_56(x), F_14(x)*F_46(x))
Eq(F_57(x), F_51(x) + F_58(x) + F_90(x))
Eq(F_58(x), F_14(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), F_61(x) + F_8(x))
Eq(F_61(x), F_27(x))
Eq(F_62(x), F_57(x) + F_63(x))
Eq(F_63(x), 2*F_51(x) + F_64(x) + F_68(x))
Eq(F_64(x), F_14(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_61(x))
Eq(F_67(x), F_63(x))
Eq(F_68(x), F_14(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_78(x))
Eq(F_70(x), F_71(x) + F_76(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_14(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_14(x)*F_75(x))
Eq(F_75(x), F_1(x) + F_73(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_14(x)*F_70(x))
Eq(F_78(x), F_79(x) + F_88(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_14(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_71(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_71(x))
Eq(F_85(x), F_79(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_14(x)*F_79(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_14(x)*F_78(x))
Eq(F_90(x), F_14(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_97(x))
Eq(F_92(x), F_73(x) + F_93(x))
Eq(F_93(x), F_51(x) + F_94(x) + F_96(x))
Eq(F_94(x), F_14(x)*F_95(x))
Eq(F_95(x), F_12(x) + F_93(x))
Eq(F_96(x), F_14(x)*F_92(x))
Eq(F_97(x), F_117(x) + F_98(x))
Eq(F_98(x), F_104(x) + F_51(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_14(x))
Eq(F_100(x), F_101(x) + F_73(x))
Eq(F_101(x), F_102(x) + F_51(x) + F_99(x))
Eq(F_102(x), F_103(x)*F_14(x))
Eq(F_103(x), F_101(x) + F_73(x))
Eq(F_104(x), F_105(x)*F_14(x))
Eq(F_105(x), F_106(x) + F_110(x))
Eq(F_106(x), F_107(x) + F_73(x))
Eq(F_107(x), F_108(x) + F_51(x) + F_72(x))
Eq(F_108(x), F_109(x)*F_14(x))
Eq(F_109(x), F_107(x) + F_14(x))
Eq(F_110(x), F_111(x) + F_98(x))
Eq(F_111(x), F_112(x) + F_116(x) + 2*F_51(x))
Eq(F_112(x), F_113(x)*F_14(x))
Eq(F_113(x), F_114(x) + F_71(x))
Eq(F_114(x), F_112(x) + F_115(x) + 2*F_51(x))
Eq(F_115(x), F_101(x)*F_14(x))
Eq(F_116(x), F_14(x)*F_98(x))
Eq(F_117(x), F_118(x) + F_126(x) + 2*F_51(x))
Eq(F_118(x), F_119(x)*F_14(x))
Eq(F_119(x), F_120(x) + F_123(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_14(x))
Eq(F_122(x), F_120(x) + F_73(x))
Eq(F_123(x), F_118(x) + F_124(x) + 2*F_51(x))
Eq(F_124(x), F_125(x)*F_14(x))
Eq(F_125(x), F_101(x) + F_123(x))
Eq(F_126(x), F_14(x)*F_97(x))
Eq(F_127(x), F_128(x) + F_143(x))
Eq(F_128(x), F_129(x) + F_141(x) + F_51(x))
Eq(F_129(x), F_130(x)*F_14(x))
Eq(F_130(x), F_131(x) + F_134(x))
Eq(F_131(x), F_12(x) + F_132(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_12(x)*F_14(x))
Eq(F_134(x), F_128(x) + F_135(x))
Eq(F_135(x), F_136(x) + F_140(x) + 2*F_51(x))
Eq(F_136(x), F_137(x)*F_14(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_132(x))
Eq(F_139(x), F_135(x))
Eq(F_140(x), F_128(x)*F_14(x))
Eq(F_141(x), F_14(x)*F_142(x))
Eq(F_142(x), F_128(x) + F_46(x))
Eq(F_143(x), F_144(x) + 2*F_51(x) + F_68(x))
Eq(F_144(x), F_14(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_26(x))
Eq(F_147(x), F_143(x))
Eq(F_148(x), F_14(x)*F_149(x))
Eq(F_149(x), F_150(x, 1))
Eq(F_150(x, k_0), F_1(x) + F_151(x, k_0) + F_153(x, k_0) + F_155(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_152(x, k_0))
Eq(F_152(x, k_0), k_0*x)
Eq(F_153(x, k_0), F_14(x)*F_154(x, k_0))
Eq(F_154(x, k_0), (-k_0*F_150(x, k_0) + F_150(x, 1))/(1 - k_0))
Eq(F_155(x, k_0), F_14(x)*F_156(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_5(x))
Eq(F_157(x, k_0), F_158(x, k_0) + F_223(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_201(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0) + F_163(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_152(x, k_0)*F_162(x, k_0))
Eq(F_162(x, k_0), F_1(x) + F_160(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0) + F_166(x, k_0) + F_51(x))
Eq(F_164(x, k_0), F_152(x, k_0)*F_165(x, k_0))
Eq(F_165(x, k_0), F_163(x, k_0) + F_8(x))
Eq(F_166(x, k_0), F_14(x)*F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_173(x, k_0))
Eq(F_168(x, k_0), F_160(x, k_0) + F_169(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0) + F_172(x, k_0) + F_51(x))
Eq(F_170(x, k_0), F_152(x, k_0)*F_171(x, k_0))
Eq(F_171(x, k_0), F_12(x) + F_169(x, k_0))
Eq(F_172(x, k_0), F_14(x)*F_168(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_194(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0) + F_180(x, k_0) + F_51(x))
Eq(F_175(x, k_0), F_152(x, k_0)*F_176(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_73(x))
Eq(F_177(x, k_0), F_175(x, k_0) + F_178(x, k_0) + F_51(x))
Eq(F_178(x, k_0), F_14(x)*F_179(x, k_0))
Eq(F_179(x, k_0), F_160(x, k_0) + F_177(x, k_0))
Eq(F_180(x, k_0), F_14(x)*F_181(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_187(x, k_0))
Eq(F_182(x, k_0), F_160(x, k_0) + F_183(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0) + F_186(x, k_0) + F_51(x))
Eq(F_184(x, k_0), F_152(x, k_0)*F_185(x, k_0))
Eq(F_185(x, k_0), F_14(x) + F_183(x, k_0))
Eq(F_186(x, k_0), F_14(x)*F_160(x, k_0))
Eq(F_187(x, k_0), F_174(x, k_0) + F_188(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_193(x, k_0) + 2*F_51(x))
Eq(F_189(x, k_0), F_152(x, k_0)*F_190(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0) + F_71(x))
Eq(F_191(x, k_0), F_189(x, k_0) + F_192(x, k_0) + 2*F_51(x))
Eq(F_192(x, k_0), F_14(x)*F_177(x, k_0))
Eq(F_193(x, k_0), F_14(x)*F_174(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0) + F_200(x, k_0) + 2*F_51(x))
Eq(F_195(x, k_0), F_152(x, k_0)*F_196(x, k_0))
Eq(F_196(x, k_0), F_120(x) + F_197(x, k_0))
Eq(F_197(x, k_0), F_195(x, k_0) + F_198(x, k_0) + 2*F_51(x))
Eq(F_198(x, k_0), F_14(x)*F_199(x, k_0))
Eq(F_199(x, k_0), F_177(x, k_0) + F_197(x, k_0))
Eq(F_200(x, k_0), F_14(x)*F_173(x, k_0))
Eq(F_201(x, k_0), F_169(x, k_0) + F_202(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_205(x, k_0) + 2*F_51(x))
Eq(F_203(x, k_0), F_152(x, k_0)*F_204(x, k_0))
Eq(F_204(x, k_0), F_202(x, k_0) + F_26(x))
Eq(F_205(x, k_0), F_14(x)*F_206(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0) + F_211(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_209(x, k_0))
Eq(F_208(x, k_0), F_186(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_14(x)*F_207(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0) + F_221(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_14(x)*F_214(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0) + F_218(x, k_0))
Eq(F_215(x, k_0), F_208(x, k_0) + F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0))
Eq(F_217(x, k_0), F_14(x)*F_208(x, k_0))
Eq(F_218(x, k_0), F_212(x, k_0) + F_219(x, k_0))
Eq(F_219(x, k_0), F_220(x, k_0))
Eq(F_220(x, k_0), F_14(x)*F_212(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0))
Eq(F_222(x, k_0), F_14(x)*F_211(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0) + F_306(x, k_0))
Eq(F_224(x, k_0), F_225(x, k_0) + F_236(x, k_0))
Eq(F_225(x, k_0), F_184(x, k_0) + F_226(x, k_0) + F_51(x))
Eq(F_226(x, k_0), F_14(x)*F_227(x, k_0))
Eq(F_227(x, k_0), F_182(x, k_0) + F_228(x, k_0))
Eq(F_228(x, k_0), F_225(x, k_0) + F_229(x, k_0))
Eq(F_229(x, k_0), F_230(x, k_0) + F_231(x, k_0) + F_235(x, k_0) + F_51(x))
Eq(F_230(x, k_0), 0)
Eq(F_231(x, k_0), F_14(x)*F_232(x, k_0))
Eq(F_232(x, k_0), F_233(x, k_0) + F_234(x, k_0))
Eq(F_233(x, k_0), F_183(x, k_0))
Eq(F_234(x, k_0), F_229(x, k_0))
Eq(F_235(x, k_0), F_14(x)*F_225(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0) + F_240(x, k_0) + F_272(x, k_0) + F_51(x))
Eq(F_237(x, k_0), F_152(x, k_0)*F_238(x, k_0))
Eq(F_238(x, k_0), F_239(x, k_0) + F_61(x))
Eq(F_239(x, k_0), F_205(x, k_0) + F_237(x, k_0) + 2*F_51(x))
Eq(F_240(x, k_0), F_14(x)*F_241(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0) + F_243(x, k_0))
Eq(F_242(x, k_0), F_163(x, k_0) + F_239(x, k_0))
Eq(F_243(x, k_0), F_236(x, k_0) + F_244(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0) + F_246(x, k_0) + F_250(x, k_0) + 2*F_51(x))
Eq(F_245(x, k_0), 0)
Eq(F_246(x, k_0), F_14(x)*F_247(x, k_0))
Eq(F_247(x, k_0), F_248(x, k_0) + F_249(x, k_0))
Eq(F_248(x, k_0), F_239(x, k_0))
Eq(F_249(x, k_0), F_244(x, k_0))
Eq(F_250(x, k_0), F_14(x)*F_251(x, k_0))
Eq(F_251(x, k_0), F_252(x, k_0) + F_260(x, k_0))
Eq(F_252(x, k_0), F_253(x, k_0) + F_258(x, k_0))
Eq(F_253(x, k_0), F_254(x, k_0))
Eq(F_254(x, k_0), F_14(x)*F_255(x, k_0))
Eq(F_255(x, k_0), F_256(x, k_0))
Eq(F_256(x, k_0), F_14(x)*F_257(x, k_0))
Eq(F_257(x, k_0), F_160(x, k_0) + F_255(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0))
Eq(F_259(x, k_0), F_14(x)*F_252(x, k_0))
Eq(F_260(x, k_0), F_261(x, k_0) + F_270(x, k_0))
Eq(F_261(x, k_0), F_262(x, k_0))
Eq(F_262(x, k_0), F_14(x)*F_263(x, k_0))
Eq(F_263(x, k_0), F_264(x, k_0) + F_267(x, k_0))
Eq(F_264(x, k_0), F_253(x, k_0) + F_265(x, k_0))
Eq(F_265(x, k_0), F_266(x, k_0))
Eq(F_266(x, k_0), F_14(x)*F_253(x, k_0))
Eq(F_267(x, k_0), F_261(x, k_0) + F_268(x, k_0))
Eq(F_268(x, k_0), F_269(x, k_0))
Eq(F_269(x, k_0), F_14(x)*F_261(x, k_0))
Eq(F_270(x, k_0), F_271(x, k_0))
Eq(F_271(x, k_0), F_14(x)*F_260(x, k_0))
Eq(F_272(x, k_0), F_14(x)*F_273(x, k_0))
Eq(F_273(x, k_0), F_274(x, k_0) + F_279(x, k_0))
Eq(F_274(x, k_0), F_255(x, k_0) + F_275(x, k_0))
Eq(F_275(x, k_0), F_276(x, k_0) + F_278(x, k_0) + 2*F_51(x))
Eq(F_276(x, k_0), F_14(x)*F_277(x, k_0))
Eq(F_277(x, k_0), F_169(x, k_0) + F_275(x, k_0))
Eq(F_278(x, k_0), F_14(x)*F_274(x, k_0))
Eq(F_279(x, k_0), F_280(x, k_0) + F_299(x, k_0))
Eq(F_280(x, k_0), F_281(x, k_0) + F_286(x, k_0) + 2*F_51(x))
Eq(F_281(x, k_0), F_14(x)*F_282(x, k_0))
Eq(F_282(x, k_0), F_177(x, k_0) + F_283(x, k_0))
Eq(F_283(x, k_0), F_281(x, k_0) + F_284(x, k_0) + 2*F_51(x))
Eq(F_284(x, k_0), F_14(x)*F_285(x, k_0))
Eq(F_285(x, k_0), F_255(x, k_0) + F_283(x, k_0))
Eq(F_286(x, k_0), F_14(x)*F_287(x, k_0))
Eq(F_287(x, k_0), F_288(x, k_0) + F_292(x, k_0))
Eq(F_288(x, k_0), F_255(x, k_0) + F_289(x, k_0))
Eq(F_289(x, k_0), F_254(x, k_0) + F_290(x, k_0) + 2*F_51(x))
Eq(F_290(x, k_0), F_14(x)*F_291(x, k_0))
Eq(F_291(x, k_0), F_183(x, k_0) + F_289(x, k_0))
Eq(F_292(x, k_0), F_280(x, k_0) + F_293(x, k_0))
Eq(F_293(x, k_0), F_294(x, k_0) + F_298(x, k_0) + 3*F_51(x))
Eq(F_294(x, k_0), F_14(x)*F_295(x, k_0))
Eq(F_295(x, k_0), F_191(x, k_0) + F_296(x, k_0))
Eq(F_296(x, k_0), F_294(x, k_0) + F_297(x, k_0) + 3*F_51(x))
Eq(F_297(x, k_0), F_14(x)*F_283(x, k_0))
Eq(F_298(x, k_0), F_14(x)*F_280(x, k_0))
Eq(F_299(x, k_0), F_300(x, k_0) + F_305(x, k_0) + 3*F_51(x))
Eq(F_300(x, k_0), F_14(x)*F_301(x, k_0))
Eq(F_301(x, k_0), F_197(x, k_0) + F_302(x, k_0))
Eq(F_302(x, k_0), F_300(x, k_0) + F_303(x, k_0) + 3*F_51(x))
Eq(F_303(x, k_0), F_14(x)*F_304(x, k_0))
Eq(F_304(x, k_0), F_283(x, k_0) + F_302(x, k_0))
Eq(F_305(x, k_0), F_14(x)*F_279(x, k_0))
Eq(F_306(x, k_0), F_307(x, k_0) + F_325(x, k_0))
Eq(F_307(x, k_0), F_308(x, k_0) + F_312(x, k_0) + F_323(x, k_0) + F_51(x))
Eq(F_308(x, k_0), F_152(x, k_0)*F_309(x, k_0))
Eq(F_309(x, k_0), F_132(x) + F_310(x, k_0))
Eq(F_310(x, k_0), F_308(x, k_0) + F_311(x, k_0) + 2*F_51(x))
Eq(F_311(x, k_0), F_14(x)*F_169(x, k_0))
Eq(F_312(x, k_0), F_14(x)*F_313(x, k_0))
Eq(F_313(x, k_0), F_314(x, k_0) + F_315(x, k_0))
Eq(F_314(x, k_0), F_169(x, k_0) + F_310(x, k_0))
Eq(F_315(x, k_0), F_307(x, k_0) + F_316(x, k_0))
Eq(F_316(x, k_0), F_317(x, k_0) + F_318(x, k_0) + F_322(x, k_0) + 2*F_51(x))
Eq(F_317(x, k_0), 0)
Eq(F_318(x, k_0), F_14(x)*F_319(x, k_0))
Eq(F_319(x, k_0), F_320(x, k_0) + F_321(x, k_0))
Eq(F_320(x, k_0), F_310(x, k_0))
Eq(F_321(x, k_0), F_316(x, k_0))
Eq(F_322(x, k_0), F_14(x)*F_307(x, k_0))
Eq(F_323(x, k_0), F_14(x)*F_324(x, k_0))
Eq(F_324(x, k_0), F_225(x, k_0) + F_307(x, k_0))
Eq(F_325(x, k_0), F_250(x, k_0) + F_326(x, k_0) + F_327(x, k_0) + 2*F_51(x))
Eq(F_326(x, k_0), 0)
Eq(F_327(x, k_0), F_14(x)*F_328(x, k_0))
Eq(F_328(x, k_0), F_329(x, k_0) + F_330(x, k_0))
Eq(F_329(x, k_0), F_202(x, k_0))
Eq(F_330(x, k_0), F_325(x, k_0))
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": [0, 2, 1, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [[{"patt": [0], "pos": [[1, 1]]}]]}], "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": [0, 2, 1, 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": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 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": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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"}}, {"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], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "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], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 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": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": 3, "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"}}, {"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], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 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": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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": 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