0132_1023_1230
Counting sequence:
1, 1, 2, 6, 21, 74, 255, 866, 2927, 9923, 33898, 116940, 407638, 1435430, 5102259, 18290193, 66060912, 240194922, 878496202, 3229838404, 11929881124, 44247840935, 164727529486, 615321501559, 2305500595689, 8662417696363, 32630388596225, 123204241407548, 466198575408939, 1767618684939240, 6714546013276964, 25550518608518923, 97384075253254517, 371737479001347434, 1421033075965677783, 5439442850425089184, 20847465827632397819, 79996292108062775079, 307309407508646473209, 1181803368938633559297, 4549398335724521261200, 17529919062461987912481, 67608693717079306214906, 260977361198161833516830, 1008238084093737407331428, 3898224694676295029230740, 15083384195029292305316821, 58404260791147311905861476, 226303185105577198359371935, 877454544871161353147380405, 3404353277157891129807816893, 13216290215112397196311450499, 51338011104432573449670944796, 199532305933924997603839709627, 775930554260206057154183365624, 3018972758566696101118724821934, 11752059488941496116866070007952, 45769840335412087216300022060800, 178339703087167928155747161019263, 695205001226595571173211210489756, 2711235748942775524213276857934203, 10578032491562263773471528242638947, 41287607462809382358290167589603727, 161215213068947178277304116342413926, 629735768625896489568542124116221777, 2460772954621224177641759747445369408, 9619236876697038430220631836701431729, 37614982047791260976656504607733528641, 147138982660382559440746559800906650848, 575754014906412861396909251500774136592, 2253639317332234855731014349400561437619, 8824012337713607942752360668708900629617, 34560361813676118124801343972971724579320, 135399577107024126545634430251284592193000, 530615233268884358523603030690816138221153, 2079994392833981207794187532530099833393997, 8155704060301380530585384881716149718886716, 31987074560147579844317818270626197114146382, 125486903436145909516738388964315325778187451, 492413848019443503043845686450578610326424621, 1932712948743443405667683728749124251445281836, 7587646123631145718695173401388881813554831758, 29795238087681871150843889347640693983348181743, 117026520770068734774833946925155289762181126019, 459745002007845300799261502430561287855442342880, 1806519950088390894165386681729873758183675418678, 7100016244535828370476189115643232491214626422939, 27910309130822386556908471000865056839388648740981, 109737897923635704452828076806884920853115414605968, 431552209134767833468430041779830908242495052439002, 1697433880047424738570954888381183615846008897663489, 6677799332330158198301595684864506006144540161502517, 26275625312822157840904875426208891348900940966066240, 103407070217271721160930763832320001148223547949361160, 407027000795368318621243737588857094922456364722761773, 1602398047603513515134228822396356394370113482185679327, 6309431575749700212493837981405860503303102727564273116, 24847413715279992408341839600354040518569593059138365482, 97868247300143011592121780351853211000137533383579518911, 385541092089501208785107158427711000930438093430807731421, 1519030176133832423116362773126368594566488433192346923966
Generating function in Maple syntax:
1/4*(-2*(x^5+x^3-2*x+1)*(x^2-x+1/2)*(x-1)*(1-4*x)^(1/2)+6*x^8-8*x^7+7*x^6-3*x^5-x^4+5*x^3-8*x^2+5*x-1)/x/(x^2+x-1)/(x-1)^3/(x-1/2)
Generating function in latex syntax:
\frac{-2 \left(x^{5}+x^{3}-2 x +1\right) \left(x^{2}-x +\frac{1}{2}\right) \left(x -1\right) \sqrt{1-4 x}+6 x^{8}-8 x^{7}+7 x^{6}-3 x^{5}-x^{4}+5 x^{3}-8 x^{2}+5 x -1}{4 x \left(x^{2}+x -1\right) \left(x -1\right)^{3} \left(x -\frac{1}{2}\right)}
Generating function in sympy syntax:
(3*x**8/2 - 2*x**7 + 7*x**6/4 - 3*x**5/4 - x**4/4 + 5*x**3/4 - 2*x**2 + 5*x/4 + sqrt(1 - 4*x)*(x - 1)*(x**2 - x + 1/2)*(-2*x**5 - 2*x**3 + 4*x - 2)/4 - 1/4)/(x*(x - 1)**3*(x - 1/2)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x^2+x-1)^2*(x-1)^6*F(x)^2-(2*x-1)*(x^2+x-1)*(6*x^8-8*x^7+7*x^6-3*x^5-x^4+5*x^3-8*x^2+5*x-1)*(x-1)^3*F(x)+4*x^16-8*x^15+16*x^14-32*x^13+39*x^12-87*x^10+179*x^9-217*x^8+140*x^7+37*x^6-191*x^5+216*x^4-137*x^3+52*x^2-11*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(x^{2}+x -1\right) \left(6 x^{8}-8 x^{7}+7 x^{6}-3 x^{5}-x^{4}+5 x^{3}-8 x^{2}+5 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+4 x^{16}-8 x^{15}+16 x^{14}-32 x^{13}+39 x^{12}-87 x^{10}+179 x^{9}-217 x^{8}+140 x^{7}+37 x^{6}-191 x^{5}+216 x^{4}-137 x^{3}+52 x^{2}-11 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(6) = 255
a(7) = 866
a(8) = 2927
a(9) = 9923
a(10) = 33898
a(11) = 116940
a(12) = 407638
a(13) = 1435430
a(14) = 5102259
a(15) = 18290193
a(16) = 66060912
a(n+12) = -8*(2*n-3)/(n+13)*a(n)+4*(7*n-5)/(n+13)*a(n+1)-6*(n+18)/(n+13)*a(n+2)-12*(3*n-14)/(n+13)*a(n+3)+(194+113*n)/(n+13)*a(n+4)-3*(58*n+257)/(n+13)*a(n+5)+(555+89*n)/(n+13)*a(n+6)+9*(11*n+78)/(n+13)*a(n+7)-(196*n+1667)/(n+13)*a(n+8)+(1419+146*n)/(n+13)*a(n+9)-(58*n+629)/(n+13)*a(n+10)+(143+12*n)/(n+13)*a(n+11)+3/2*(n-3)*(n-6)/(n+13), n >= 17
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) = 74
a \! \left(6\right) = 255
a \! \left(7\right) = 866
a \! \left(8\right) = 2927
a \! \left(9\right) = 9923
a \! \left(10\right) = 33898
a \! \left(11\right) = 116940
a \! \left(12\right) = 407638
a \! \left(13\right) = 1435430
a \! \left(14\right) = 5102259
a \! \left(15\right) = 18290193
a \! \left(16\right) = 66060912
a \! \left(n +12\right) = -\frac{8 \left(2 n -3\right) a \! \left(n \right)}{n +13}+\frac{4 \left(7 n -5\right) a \! \left(n +1\right)}{n +13}-\frac{6 \left(n +18\right) a \! \left(n +2\right)}{n +13}-\frac{12 \left(3 n -14\right) a \! \left(n +3\right)}{n +13}+\frac{\left(194+113 n \right) a \! \left(n +4\right)}{n +13}-\frac{3 \left(58 n +257\right) a \! \left(n +5\right)}{n +13}+\frac{\left(555+89 n \right) a \! \left(n +6\right)}{n +13}+\frac{9 \left(11 n +78\right) a \! \left(n +7\right)}{n +13}-\frac{\left(196 n +1667\right) a \! \left(n +8\right)}{n +13}+\frac{\left(1419+146 n \right) a \! \left(n +9\right)}{n +13}-\frac{\left(58 n +629\right) a \! \left(n +10\right)}{n +13}+\frac{\left(143+12 n \right) a \! \left(n +11\right)}{n +13}+\frac{3 \left(n -3\right) \left(n -6\right)}{2 \left(n +13\right)}, \quad n \geq 17
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/281/
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[197,x]+F[4,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[6,x]+F[86,x]
F[6,x] = F[39,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[28,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[23,x]+F[27,x]
F[22,x] = 0
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[14,x]
F[26,x] = F[21,x]
F[27,x] = F[14,x]*F[16,x]
F[28,x] = F[22,x]+F[29,x]+F[38,x]
F[29,x] = F[14,x]*F[30,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[14,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = x^2
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[22,x]+F[27,x]+F[29,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[35,x]
F[38,x] = F[14,x]*F[15,x]
F[39,x] = F[40,x]+F[52,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[11,x]+F[43,x]
F[43,x] = F[44,x]+F[50,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[19,x]+F[47,x]
F[47,x] = F[44,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[14,x]*F[44,x]
F[50,x] = F[51,x]
F[51,x] = F[14,x]*F[43,x]
F[52,x] = F[53,x]
F[53,x] = F[14,x]*F[54,x]
F[54,x] = F[55,x]+F[61,x]
F[55,x] = F[56,x]+F[59,x]
F[56,x] = F[57,x]
F[57,x] = F[14,x]*F[58,x]
F[58,x] = F[1,x]+F[56,x]
F[59,x] = F[60,x]
F[60,x] = F[14,x]*F[55,x]
F[61,x] = F[62,x]+F[75,x]
F[62,x] = F[63,x]
F[63,x] = F[14,x]*F[64,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = F[56,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[56,x]
F[68,x] = F[62,x]+F[69,x]
F[69,x] = 2*F[22,x]+F[70,x]+F[74,x]
F[70,x] = F[14,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[66,x]
F[73,x] = F[69,x]
F[74,x] = F[14,x]*F[62,x]
F[75,x] = 2*F[22,x]+F[76,x]+F[85,x]
F[76,x] = F[14,x]*F[77,x]
F[77,x] = F[78,x]+F[81,x]
F[78,x] = F[66,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[14,x]*F[66,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = 2*F[22,x]+F[74,x]+F[76,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[82,x]
F[85,x] = F[14,x]*F[61,x]
F[86,x] = F[147,x]+F[87,x]
F[87,x] = F[88,x]+F[94,x]
F[88,x] = F[89,x]
F[89,x] = F[14,x]*F[90,x]
F[90,x] = F[58,x]+F[91,x]
F[91,x] = F[88,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[14,x]*F[91,x]
F[94,x] = F[112,x]+F[22,x]+F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[101,x]+F[97,x]
F[97,x] = F[56,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[14,x]
F[100,x] = F[56,x]+F[98,x]
F[101,x] = F[102,x]+F[108,x]
F[102,x] = F[103,x]+F[22,x]+F[95,x]
F[103,x] = F[104,x]*F[14,x]
F[104,x] = F[105,x]+F[56,x]
F[105,x] = F[103,x]+F[106,x]+F[22,x]
F[106,x] = F[107,x]*F[14,x]
F[107,x] = F[105,x]+F[56,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[14,x]
F[110,x] = F[111,x]+F[98,x]
F[111,x] = F[109,x]
F[112,x] = F[113,x]*F[14,x]
F[113,x] = F[114,x]+F[120,x]
F[114,x] = F[115,x]+F[56,x]
F[115,x] = F[116,x]+F[119,x]+F[22,x]
F[116,x] = F[117,x]*F[14,x]
F[117,x] = F[118,x]+F[14,x]
F[118,x] = F[116,x]+F[22,x]+F[67,x]
F[119,x] = F[114,x]*F[14,x]
F[120,x] = F[121,x]+F[136,x]
F[121,x] = F[106,x]+F[122,x]+F[22,x]
F[122,x] = F[123,x]*F[14,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[118,x]+F[56,x]
F[125,x] = F[121,x]+F[126,x]
F[126,x] = F[127,x]+F[131,x]+F[135,x]+F[22,x]
F[127,x] = F[128,x]*F[14,x]
F[128,x] = F[129,x]+F[66,x]
F[129,x] = 2*F[22,x]+F[127,x]+F[130,x]
F[130,x] = F[105,x]*F[14,x]
F[131,x] = F[132,x]*F[14,x]
F[132,x] = F[133,x]+F[134,x]
F[133,x] = F[118,x]
F[134,x] = F[126,x]
F[135,x] = F[121,x]*F[14,x]
F[136,x] = F[127,x]+F[137,x]+F[146,x]+F[22,x]
F[137,x] = F[138,x]*F[14,x]
F[138,x] = F[139,x]+F[142,x]
F[139,x] = F[118,x]+F[140,x]
F[140,x] = F[141,x]
F[141,x] = F[118,x]*F[14,x]
F[142,x] = F[143,x]+F[144,x]
F[143,x] = F[127,x]+F[135,x]+F[137,x]+F[22,x]
F[144,x] = F[145,x]
F[145,x] = F[14,x]*F[143,x]
F[146,x] = F[120,x]*F[14,x]
F[147,x] = F[148,x]+F[166,x]
F[148,x] = F[149,x]
F[149,x] = F[14,x]*F[150,x]
F[150,x] = F[151,x]+F[154,x]
F[151,x] = F[152,x]+F[88,x]
F[152,x] = F[153,x]
F[153,x] = F[14,x]*F[151,x]
F[154,x] = F[155,x]+F[164,x]
F[155,x] = F[156,x]
F[156,x] = F[14,x]*F[157,x]
F[157,x] = F[158,x]+F[161,x]
F[158,x] = F[159,x]+F[88,x]
F[159,x] = F[160,x]
F[160,x] = F[14,x]*F[88,x]
F[161,x] = F[155,x]+F[162,x]
F[162,x] = F[163,x]
F[163,x] = F[14,x]*F[155,x]
F[164,x] = F[165,x]
F[165,x] = F[14,x]*F[154,x]
F[166,x] = F[167,x]
F[167,x] = F[14,x]*F[168,x]
F[168,x] = F[169,x]+F[172,x]
F[169,x] = F[170,x]+F[98,x]
F[170,x] = F[171,x]
F[171,x] = F[14,x]*F[169,x]
F[172,x] = F[173,x]+F[186,x]
F[173,x] = F[174,x]
F[174,x] = F[14,x]*F[175,x]
F[175,x] = F[176,x]+F[179,x]
F[176,x] = F[177,x]+F[98,x]
F[177,x] = F[178,x]
F[178,x] = F[14,x]*F[98,x]
F[179,x] = F[173,x]+F[180,x]
F[180,x] = 3*F[22,x]+F[181,x]+F[185,x]
F[181,x] = F[14,x]*F[182,x]
F[182,x] = F[183,x]+F[184,x]
F[183,x] = F[177,x]
F[184,x] = F[180,x]
F[185,x] = F[14,x]*F[173,x]
F[186,x] = 3*F[22,x]+F[187,x]+F[196,x]
F[187,x] = F[14,x]*F[188,x]
F[188,x] = F[189,x]+F[192,x]
F[189,x] = F[177,x]+F[190,x]
F[190,x] = F[191,x]
F[191,x] = F[14,x]*F[177,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = 3*F[22,x]+F[185,x]+F[187,x]
F[194,x] = F[195,x]
F[195,x] = F[14,x]*F[193,x]
F[196,x] = F[14,x]*F[172,x]
F[197,x] = F[14,x]*F[198,x]
F[198,x] = F[199,x,1]
F[199,x,k[0]] = F[1,x]+F[200,x,k[0]]+F[202,x,k[0]]+F[204,x,k[0]]
F[200,x,k[0]] = F[199,x,k[0]]*F[201,x,k[0]]
F[201,x,k[0]] = k[0]*x
F[202,x,k[0]] = F[14,x]*F[203,x,k[0]]
F[203,x,k[0]] = (F[199,x,k[0]]*k[0]-F[199,x,1])/(-1+k[0])
F[204,x,k[0]] = F[14,x]*F[205,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]+F[5,x]
F[206,x,k[0]] = F[207,x,k[0]]+F[306,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[254,x,k[0]]
F[208,x,k[0]] = F[209,x,k[0]]+F[212,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[201,x,k[0]]*F[211,x,k[0]]
F[211,x,k[0]] = F[1,x]+F[209,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]+F[218,x,k[0]]+F[22,x]
F[213,x,k[0]] = F[201,x,k[0]]*F[214,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0]]+F[56,x]
F[215,x,k[0]] = F[213,x,k[0]]+F[216,x,k[0]]+F[22,x]
F[216,x,k[0]] = F[14,x]*F[217,x,k[0]]
F[217,x,k[0]] = F[209,x,k[0]]+F[215,x,k[0]]
F[218,x,k[0]] = F[14,x]*F[219,x,k[0]]
F[219,x,k[0]] = F[220,x,k[0]]+F[227,x,k[0]]
F[220,x,k[0]] = F[209,x,k[0]]+F[221,x,k[0]]
F[221,x,k[0]] = F[22,x]+F[222,x,k[0]]+F[226,x,k[0]]
F[222,x,k[0]] = F[201,x,k[0]]*F[223,x,k[0]]
F[223,x,k[0]] = F[14,x]+F[224,x,k[0]]
F[224,x,k[0]] = F[22,x]+F[222,x,k[0]]+F[225,x,k[0]]
F[225,x,k[0]] = F[14,x]*F[209,x,k[0]]
F[226,x,k[0]] = F[14,x]*F[220,x,k[0]]
F[227,x,k[0]] = F[228,x,k[0]]+F[243,x,k[0]]
F[228,x,k[0]] = F[213,x,k[0]]+F[22,x]+F[229,x,k[0]]
F[229,x,k[0]] = F[14,x]*F[230,x,k[0]]
F[230,x,k[0]] = F[231,x,k[0]]+F[232,x,k[0]]
F[231,x,k[0]] = F[209,x,k[0]]+F[224,x,k[0]]
F[232,x,k[0]] = F[228,x,k[0]]+F[233,x,k[0]]
F[233,x,k[0]] = F[22,x]+F[234,x,k[0]]+F[238,x,k[0]]+F[242,x,k[0]]
F[234,x,k[0]] = F[201,x,k[0]]*F[235,x,k[0]]
F[235,x,k[0]] = F[236,x,k[0]]+F[66,x]
F[236,x,k[0]] = 2*F[22,x]+F[234,x,k[0]]+F[237,x,k[0]]
F[237,x,k[0]] = F[14,x]*F[215,x,k[0]]
F[238,x,k[0]] = F[14,x]*F[239,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]+F[241,x,k[0]]
F[240,x,k[0]] = F[224,x,k[0]]
F[241,x,k[0]] = F[233,x,k[0]]
F[242,x,k[0]] = F[14,x]*F[228,x,k[0]]
F[243,x,k[0]] = F[22,x]+F[234,x,k[0]]+F[244,x,k[0]]+F[253,x,k[0]]
F[244,x,k[0]] = F[14,x]*F[245,x,k[0]]
F[245,x,k[0]] = F[246,x,k[0]]+F[249,x,k[0]]
F[246,x,k[0]] = F[224,x,k[0]]+F[247,x,k[0]]
F[247,x,k[0]] = F[248,x,k[0]]
F[248,x,k[0]] = F[14,x]*F[224,x,k[0]]
F[249,x,k[0]] = F[250,x,k[0]]+F[251,x,k[0]]
F[250,x,k[0]] = F[22,x]+F[234,x,k[0]]+F[242,x,k[0]]+F[244,x,k[0]]
F[251,x,k[0]] = F[252,x,k[0]]
F[252,x,k[0]] = F[14,x]*F[250,x,k[0]]
F[253,x,k[0]] = F[14,x]*F[227,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]+F[272,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[258,x,k[0]]+F[261,x,k[0]]
F[258,x,k[0]] = F[209,x,k[0]]+F[259,x,k[0]]
F[259,x,k[0]] = F[260,x,k[0]]
F[260,x,k[0]] = F[14,x]*F[258,x,k[0]]
F[261,x,k[0]] = F[262,x,k[0]]+F[270,x,k[0]]
F[262,x,k[0]] = F[263,x,k[0]]
F[263,x,k[0]] = F[14,x]*F[264,x,k[0]]
F[264,x,k[0]] = F[265,x,k[0]]+F[267,x,k[0]]
F[265,x,k[0]] = F[209,x,k[0]]+F[266,x,k[0]]
F[266,x,k[0]] = F[225,x,k[0]]
F[267,x,k[0]] = F[262,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[262,x,k[0]]
F[270,x,k[0]] = F[271,x,k[0]]
F[271,x,k[0]] = F[14,x]*F[261,x,k[0]]
F[272,x,k[0]] = F[273,x,k[0]]
F[273,x,k[0]] = F[14,x]*F[274,x,k[0]]
F[274,x,k[0]] = F[275,x,k[0]]+F[281,x,k[0]]
F[275,x,k[0]] = F[276,x,k[0]]+F[279,x,k[0]]
F[276,x,k[0]] = F[277,x,k[0]]
F[277,x,k[0]] = F[14,x]*F[278,x,k[0]]
F[278,x,k[0]] = F[209,x,k[0]]+F[276,x,k[0]]
F[279,x,k[0]] = F[280,x,k[0]]
F[280,x,k[0]] = F[14,x]*F[275,x,k[0]]
F[281,x,k[0]] = F[282,x,k[0]]+F[295,x,k[0]]
F[282,x,k[0]] = F[283,x,k[0]]
F[283,x,k[0]] = F[14,x]*F[284,x,k[0]]
F[284,x,k[0]] = F[285,x,k[0]]+F[288,x,k[0]]
F[285,x,k[0]] = F[276,x,k[0]]+F[286,x,k[0]]
F[286,x,k[0]] = F[287,x,k[0]]
F[287,x,k[0]] = F[14,x]*F[276,x,k[0]]
F[288,x,k[0]] = F[282,x,k[0]]+F[289,x,k[0]]
F[289,x,k[0]] = 3*F[22,x]+F[290,x,k[0]]+F[294,x,k[0]]
F[290,x,k[0]] = F[14,x]*F[291,x,k[0]]
F[291,x,k[0]] = F[292,x,k[0]]+F[293,x,k[0]]
F[292,x,k[0]] = F[286,x,k[0]]
F[293,x,k[0]] = F[289,x,k[0]]
F[294,x,k[0]] = F[14,x]*F[282,x,k[0]]
F[295,x,k[0]] = 3*F[22,x]+F[296,x,k[0]]+F[305,x,k[0]]
F[296,x,k[0]] = F[14,x]*F[297,x,k[0]]
F[297,x,k[0]] = F[298,x,k[0]]+F[301,x,k[0]]
F[298,x,k[0]] = F[286,x,k[0]]+F[299,x,k[0]]
F[299,x,k[0]] = F[300,x,k[0]]
F[300,x,k[0]] = F[14,x]*F[286,x,k[0]]
F[301,x,k[0]] = F[302,x,k[0]]+F[303,x,k[0]]
F[302,x,k[0]] = 3*F[22,x]+F[294,x,k[0]]+F[296,x,k[0]]
F[303,x,k[0]] = F[304,x,k[0]]
F[304,x,k[0]] = F[14,x]*F[302,x,k[0]]
F[305,x,k[0]] = F[14,x]*F[281,x,k[0]]
F[306,x,k[0]] = F[307,x,k[0]]+F[374,x,k[0]]
F[307,x,k[0]] = F[308,x,k[0]]+F[316,x,k[0]]
F[308,x,k[0]] = F[22,x]+F[309,x,k[0]]+F[311,x,k[0]]
F[309,x,k[0]] = F[201,x,k[0]]*F[310,x,k[0]]
F[310,x,k[0]] = F[276,x,k[0]]+F[56,x]
F[311,x,k[0]] = F[14,x]*F[312,x,k[0]]
F[312,x,k[0]] = F[278,x,k[0]]+F[313,x,k[0]]
F[313,x,k[0]] = F[308,x,k[0]]+F[314,x,k[0]]
F[314,x,k[0]] = F[315,x,k[0]]
F[315,x,k[0]] = F[14,x]*F[313,x,k[0]]
F[316,x,k[0]] = F[22,x]+F[317,x,k[0]]+F[322,x,k[0]]+F[339,x,k[0]]
F[317,x,k[0]] = F[201,x,k[0]]*F[318,x,k[0]]
F[318,x,k[0]] = F[319,x,k[0]]+F[98,x]
F[319,x,k[0]] = F[320,x,k[0]]
F[320,x,k[0]] = F[14,x]*F[321,x,k[0]]
F[321,x,k[0]] = F[276,x,k[0]]+F[319,x,k[0]]
F[322,x,k[0]] = F[14,x]*F[323,x,k[0]]
F[323,x,k[0]] = F[324,x,k[0]]+F[325,x,k[0]]
F[324,x,k[0]] = F[215,x,k[0]]+F[319,x,k[0]]
F[325,x,k[0]] = F[326,x,k[0]]+F[332,x,k[0]]
F[326,x,k[0]] = F[22,x]+F[317,x,k[0]]+F[322,x,k[0]]+F[327,x,k[0]]
F[327,x,k[0]] = F[14,x]*F[328,x,k[0]]
F[328,x,k[0]] = F[276,x,k[0]]+F[329,x,k[0]]
F[329,x,k[0]] = 2*F[22,x]+F[327,x,k[0]]+F[330,x,k[0]]
F[330,x,k[0]] = F[14,x]*F[331,x,k[0]]
F[331,x,k[0]] = F[215,x,k[0]]+F[329,x,k[0]]
F[332,x,k[0]] = F[333,x,k[0]]
F[333,x,k[0]] = F[14,x]*F[334,x,k[0]]
F[334,x,k[0]] = F[335,x,k[0]]+F[338,x,k[0]]
F[335,x,k[0]] = F[336,x,k[0]]
F[336,x,k[0]] = F[14,x]*F[337,x,k[0]]
F[337,x,k[0]] = F[276,x,k[0]]+F[335,x,k[0]]
F[338,x,k[0]] = F[333,x,k[0]]
F[339,x,k[0]] = F[14,x]*F[340,x,k[0]]
F[340,x,k[0]] = F[341,x,k[0]]+F[347,x,k[0]]
F[341,x,k[0]] = F[276,x,k[0]]+F[342,x,k[0]]
F[342,x,k[0]] = 2*F[22,x]+F[343,x,k[0]]+F[346,x,k[0]]
F[343,x,k[0]] = F[14,x]*F[344,x,k[0]]
F[344,x,k[0]] = F[224,x,k[0]]+F[345,x,k[0]]
F[345,x,k[0]] = 2*F[22,x]+F[287,x,k[0]]+F[343,x,k[0]]
F[346,x,k[0]] = F[14,x]*F[341,x,k[0]]
F[347,x,k[0]] = F[348,x,k[0]]+F[363,x,k[0]]
F[348,x,k[0]] = 2*F[22,x]+F[330,x,k[0]]+F[349,x,k[0]]
F[349,x,k[0]] = F[14,x]*F[350,x,k[0]]
F[350,x,k[0]] = F[351,x,k[0]]+F[352,x,k[0]]
F[351,x,k[0]] = F[276,x,k[0]]+F[345,x,k[0]]
F[352,x,k[0]] = F[348,x,k[0]]+F[353,x,k[0]]
F[353,x,k[0]] = 2*F[22,x]+F[354,x,k[0]]+F[358,x,k[0]]+F[362,x,k[0]]
F[354,x,k[0]] = F[14,x]*F[355,x,k[0]]
F[355,x,k[0]] = F[236,x,k[0]]+F[356,x,k[0]]
F[356,x,k[0]] = 3*F[22,x]+F[354,x,k[0]]+F[357,x,k[0]]
F[357,x,k[0]] = F[14,x]*F[329,x,k[0]]
F[358,x,k[0]] = F[14,x]*F[359,x,k[0]]
F[359,x,k[0]] = F[360,x,k[0]]+F[361,x,k[0]]
F[360,x,k[0]] = F[345,x,k[0]]
F[361,x,k[0]] = F[353,x,k[0]]
F[362,x,k[0]] = F[14,x]*F[348,x,k[0]]
F[363,x,k[0]] = 2*F[22,x]+F[354,x,k[0]]+F[364,x,k[0]]+F[373,x,k[0]]
F[364,x,k[0]] = F[14,x]*F[365,x,k[0]]
F[365,x,k[0]] = F[366,x,k[0]]+F[369,x,k[0]]
F[366,x,k[0]] = F[345,x,k[0]]+F[367,x,k[0]]
F[367,x,k[0]] = F[368,x,k[0]]
F[368,x,k[0]] = F[14,x]*F[345,x,k[0]]
F[369,x,k[0]] = F[370,x,k[0]]+F[371,x,k[0]]
F[370,x,k[0]] = 2*F[22,x]+F[354,x,k[0]]+F[362,x,k[0]]+F[364,x,k[0]]
F[371,x,k[0]] = F[372,x,k[0]]
F[372,x,k[0]] = F[14,x]*F[370,x,k[0]]
F[373,x,k[0]] = F[14,x]*F[347,x,k[0]]
F[374,x,k[0]] = F[375,x,k[0]]+F[393,x,k[0]]
F[375,x,k[0]] = F[376,x,k[0]]
F[376,x,k[0]] = F[14,x]*F[377,x,k[0]]
F[377,x,k[0]] = F[378,x,k[0]]+F[381,x,k[0]]
F[378,x,k[0]] = F[308,x,k[0]]+F[379,x,k[0]]
F[379,x,k[0]] = F[380,x,k[0]]
F[380,x,k[0]] = F[14,x]*F[378,x,k[0]]
F[381,x,k[0]] = F[382,x,k[0]]+F[391,x,k[0]]
F[382,x,k[0]] = F[383,x,k[0]]
F[383,x,k[0]] = F[14,x]*F[384,x,k[0]]
F[384,x,k[0]] = F[385,x,k[0]]+F[388,x,k[0]]
F[385,x,k[0]] = F[308,x,k[0]]+F[386,x,k[0]]
F[386,x,k[0]] = F[387,x,k[0]]
F[387,x,k[0]] = F[14,x]*F[308,x,k[0]]
F[388,x,k[0]] = F[382,x,k[0]]+F[389,x,k[0]]
F[389,x,k[0]] = F[390,x,k[0]]
F[390,x,k[0]] = F[14,x]*F[382,x,k[0]]
F[391,x,k[0]] = F[392,x,k[0]]
F[392,x,k[0]] = F[14,x]*F[381,x,k[0]]
F[393,x,k[0]] = F[394,x,k[0]]
F[394,x,k[0]] = F[14,x]*F[395,x,k[0]]
F[395,x,k[0]] = F[396,x,k[0]]+F[399,x,k[0]]
F[396,x,k[0]] = F[335,x,k[0]]+F[397,x,k[0]]
F[397,x,k[0]] = F[398,x,k[0]]
F[398,x,k[0]] = F[14,x]*F[396,x,k[0]]
F[399,x,k[0]] = F[400,x,k[0]]+F[413,x,k[0]]
F[400,x,k[0]] = F[401,x,k[0]]
F[401,x,k[0]] = F[14,x]*F[402,x,k[0]]
F[402,x,k[0]] = F[403,x,k[0]]+F[406,x,k[0]]
F[403,x,k[0]] = F[335,x,k[0]]+F[404,x,k[0]]
F[404,x,k[0]] = F[405,x,k[0]]
F[405,x,k[0]] = F[14,x]*F[335,x,k[0]]
F[406,x,k[0]] = F[400,x,k[0]]+F[407,x,k[0]]
F[407,x,k[0]] = 4*F[22,x]+F[408,x,k[0]]+F[412,x,k[0]]
F[408,x,k[0]] = F[14,x]*F[409,x,k[0]]
F[409,x,k[0]] = F[410,x,k[0]]+F[411,x,k[0]]
F[410,x,k[0]] = F[404,x,k[0]]
F[411,x,k[0]] = F[407,x,k[0]]
F[412,x,k[0]] = F[14,x]*F[400,x,k[0]]
F[413,x,k[0]] = 4*F[22,x]+F[414,x,k[0]]+F[423,x,k[0]]
F[414,x,k[0]] = F[14,x]*F[415,x,k[0]]
F[415,x,k[0]] = F[416,x,k[0]]+F[419,x,k[0]]
F[416,x,k[0]] = F[404,x,k[0]]+F[417,x,k[0]]
F[417,x,k[0]] = F[418,x,k[0]]
F[418,x,k[0]] = F[14,x]*F[404,x,k[0]]
F[419,x,k[0]] = F[420,x,k[0]]+F[421,x,k[0]]
F[420,x,k[0]] = 4*F[22,x]+F[412,x,k[0]]+F[414,x,k[0]]
F[421,x,k[0]] = F[422,x,k[0]]
F[422,x,k[0]] = F[14,x]*F[420,x,k[0]]
F[423,x,k[0]] = F[14,x]*F[399,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_{197}\! \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_{6}\! \left(x \right)+F_{86}\! \left(x \right)
F_{6}\! \left(x \right) = F_{39}\! \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_{28}\! \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_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right)
F_{27}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{28}\! \left(x \right) = F_{22}\! \left(x \right)+F_{29}\! \left(x \right)+F_{38}\! \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_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = x^{2}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{52}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{50}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{43}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right) F_{55}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{75}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{56}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{68}\! \left(x \right) = F_{62}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{70}\! \left(x \right)+F_{74}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{66}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{76}\! \left(x \right)+F_{85}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{78}\! \left(x \right) = F_{66}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right) F_{66}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{14}\! \left(x \right) F_{61}\! \left(x \right)
F_{86}\! \left(x \right) = F_{147}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{94}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{14}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{58}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{14}\! \left(x \right) F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{112}\! \left(x \right)+F_{22}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{101}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{56}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \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_{56}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{108}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{22}\! \left(x \right)+F_{95}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{14}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{56}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{106}\! \left(x \right)+F_{22}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{14}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{56}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \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) = F_{109}\! \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_{120}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{56}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{119}\! \left(x \right)+F_{22}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{14}\! \left(x \right)
F_{118}\! \left(x \right) = F_{116}\! \left(x \right)+F_{22}\! \left(x \right)+F_{67}\! \left(x \right)
F_{119}\! \left(x \right) = F_{114}\! \left(x \right) F_{14}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{136}\! \left(x \right)
F_{121}\! \left(x \right) = F_{106}\! \left(x \right)+F_{122}\! \left(x \right)+F_{22}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{14}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)+F_{56}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{131}\! \left(x \right)+F_{135}\! \left(x \right)+F_{22}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{14}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{66}\! \left(x \right)
F_{129}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{127}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{105}\! \left(x \right) F_{14}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{14}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{118}\! \left(x \right)
F_{134}\! \left(x \right) = F_{126}\! \left(x \right)
F_{135}\! \left(x \right) = F_{121}\! \left(x \right) F_{14}\! \left(x \right)
F_{136}\! \left(x \right) = F_{127}\! \left(x \right)+F_{137}\! \left(x \right)+F_{146}\! \left(x \right)+F_{22}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{14}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{142}\! \left(x \right)
F_{139}\! \left(x \right) = F_{118}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{118}\! \left(x \right) F_{14}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{143}\! \left(x \right) = F_{127}\! \left(x \right)+F_{135}\! \left(x \right)+F_{137}\! \left(x \right)+F_{22}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{14}\! \left(x \right) F_{143}\! \left(x \right)
F_{146}\! \left(x \right) = F_{120}\! \left(x \right) F_{14}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{166}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{14}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{154}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{88}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{14}\! \left(x \right) F_{151}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{164}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{14}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{161}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{88}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{14}\! \left(x \right) F_{88}\! \left(x \right)
F_{161}\! \left(x \right) = F_{155}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{14}\! \left(x \right) F_{155}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{14}\! \left(x \right) F_{154}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{14}\! \left(x \right) F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{172}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{98}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{14}\! \left(x \right) F_{169}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{186}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{14}\! \left(x \right) F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{179}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{98}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{179}\! \left(x \right) = F_{173}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{181}\! \left(x \right)+F_{185}\! \left(x \right)
F_{181}\! \left(x \right) = F_{14}\! \left(x \right) F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{184}\! \left(x \right)
F_{183}\! \left(x \right) = F_{177}\! \left(x \right)
F_{184}\! \left(x \right) = F_{180}\! \left(x \right)
F_{185}\! \left(x \right) = F_{14}\! \left(x \right) F_{173}\! \left(x \right)
F_{186}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{187}\! \left(x \right)+F_{196}\! \left(x \right)
F_{187}\! \left(x \right) = F_{14}\! \left(x \right) F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{192}\! \left(x \right)
F_{189}\! \left(x \right) = F_{177}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{14}\! \left(x \right) F_{177}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{185}\! \left(x \right)+F_{187}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{14}\! \left(x \right) F_{193}\! \left(x \right)
F_{196}\! \left(x \right) = F_{14}\! \left(x \right) F_{172}\! \left(x \right)
F_{197}\! \left(x \right) = F_{14}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x , 1\right)
F_{199}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{200}\! \left(x , y\right)+F_{202}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{199}\! \left(x , y\right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = y x
F_{202}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = -\frac{-y F_{199}\! \left(x , y\right)+F_{199}\! \left(x , 1\right)}{-1+y}
F_{204}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{306}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{254}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{209}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{218}\! \left(x , y\right)+F_{22}\! \left(x \right)
F_{213}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{216}\! \left(x , y\right)+F_{22}\! \left(x \right)
F_{216}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)+F_{227}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{222}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{222}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{209}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{220}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{22}\! \left(x \right)+F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{230}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{231}\! \left(x , y\right)+F_{232}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{224}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{234}\! \left(x , y\right)+F_{238}\! \left(x , y\right)+F_{242}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{236}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{236}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{234}\! \left(x , y\right)+F_{237}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{215}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right)+F_{241}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{233}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{228}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{234}\! \left(x , y\right)+F_{244}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{245}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{247}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{224}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{250}\! \left(x , y\right)+F_{251}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{234}\! \left(x , y\right)+F_{242}\! \left(x , y\right)+F_{244}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{250}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{227}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{272}\! \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_{258}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{259}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{258}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right)+F_{270}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{263}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{264}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{265}\! \left(x , y\right)+F_{267}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{266}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = F_{225}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{262}\! \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_{262}\! \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_{261}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{274}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{275}\! \left(x , y\right)+F_{281}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{279}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{277}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{278}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{276}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{280}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{275}\! \left(x , y\right)
F_{281}\! \left(x , y\right) = F_{282}\! \left(x , y\right)+F_{295}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = F_{283}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{284}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{285}\! \left(x , y\right)+F_{288}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{286}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{287}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{276}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{282}\! \left(x , y\right)+F_{289}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = 3 F_{22}\! \left(x \right)+F_{290}\! \left(x , y\right)+F_{294}\! \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_{292}\! \left(x , y\right)+F_{293}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{286}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = F_{289}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{282}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = 3 F_{22}\! \left(x \right)+F_{296}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{297}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{298}\! \left(x , y\right)+F_{301}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{286}\! \left(x , y\right)+F_{299}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{300}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{286}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{302}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = 3 F_{22}\! \left(x \right)+F_{294}\! \left(x , y\right)+F_{296}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{302}\! \left(x , y\right)
F_{305}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{281}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{307}\! \left(x , y\right)+F_{374}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{308}\! \left(x , y\right)+F_{316}\! \left(x , y\right)
F_{308}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{309}\! \left(x , y\right)+F_{311}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{310}\! \left(x , y\right)
F_{310}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{311}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{312}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{278}\! \left(x , y\right)+F_{313}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{308}\! \left(x , y\right)+F_{314}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = F_{315}\! \left(x , y\right)
F_{315}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{313}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{317}\! \left(x , y\right)+F_{322}\! \left(x , y\right)+F_{339}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{318}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{319}\! \left(x , y\right)+F_{98}\! \left(x \right)
F_{319}\! \left(x , y\right) = F_{320}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{321}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{319}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{323}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{324}\! \left(x , y\right)+F_{325}\! \left(x , y\right)
F_{324}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{319}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{326}\! \left(x , y\right)+F_{332}\! \left(x , y\right)
F_{326}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{317}\! \left(x , y\right)+F_{322}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{327}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{329}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{327}\! \left(x , y\right)+F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{331}\! \left(x , y\right)
F_{331}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{334}\! \left(x , y\right)
F_{334}\! \left(x , y\right) = F_{335}\! \left(x , y\right)+F_{338}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{336}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{337}\! \left(x , y\right)
F_{337}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{335}\! \left(x , y\right)
F_{338}\! \left(x , y\right) = F_{333}\! \left(x , y\right)
F_{339}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{340}\! \left(x , y\right)
F_{340}\! \left(x , y\right) = F_{341}\! \left(x , y\right)+F_{347}\! \left(x , y\right)
F_{341}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{342}\! \left(x , y\right)
F_{342}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{343}\! \left(x , y\right)+F_{346}\! \left(x , y\right)
F_{343}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{344}\! \left(x , y\right)
F_{344}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{345}\! \left(x , y\right)
F_{345}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{287}\! \left(x , y\right)+F_{343}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{341}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{348}\! \left(x , y\right)+F_{363}\! \left(x , y\right)
F_{348}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{330}\! \left(x , y\right)+F_{349}\! \left(x , y\right)
F_{349}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{350}\! \left(x , y\right)
F_{350}\! \left(x , y\right) = F_{351}\! \left(x , y\right)+F_{352}\! \left(x , y\right)
F_{351}\! \left(x , y\right) = F_{276}\! \left(x , y\right)+F_{345}\! \left(x , y\right)
F_{352}\! \left(x , y\right) = F_{348}\! \left(x , y\right)+F_{353}\! \left(x , y\right)
F_{353}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{354}\! \left(x , y\right)+F_{358}\! \left(x , y\right)+F_{362}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{355}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{236}\! \left(x , y\right)+F_{356}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = 3 F_{22}\! \left(x \right)+F_{354}\! \left(x , y\right)+F_{357}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{329}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{359}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = F_{360}\! \left(x , y\right)+F_{361}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{345}\! \left(x , y\right)
F_{361}\! \left(x , y\right) = F_{353}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{348}\! \left(x , y\right)
F_{363}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{354}\! \left(x , y\right)+F_{364}\! \left(x , y\right)+F_{373}\! \left(x , y\right)
F_{364}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{365}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = F_{366}\! \left(x , y\right)+F_{369}\! \left(x , y\right)
F_{366}\! \left(x , y\right) = F_{345}\! \left(x , y\right)+F_{367}\! \left(x , y\right)
F_{367}\! \left(x , y\right) = F_{368}\! \left(x , y\right)
F_{368}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{345}\! \left(x , y\right)
F_{369}\! \left(x , y\right) = F_{370}\! \left(x , y\right)+F_{371}\! \left(x , y\right)
F_{370}\! \left(x , y\right) = 2 F_{22}\! \left(x \right)+F_{354}\! \left(x , y\right)+F_{362}\! \left(x , y\right)+F_{364}\! \left(x , y\right)
F_{371}\! \left(x , y\right) = F_{372}\! \left(x , y\right)
F_{372}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{370}\! \left(x , y\right)
F_{373}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{347}\! \left(x , y\right)
F_{374}\! \left(x , y\right) = F_{375}\! \left(x , y\right)+F_{393}\! \left(x , y\right)
F_{375}\! \left(x , y\right) = F_{376}\! \left(x , y\right)
F_{376}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{377}\! \left(x , y\right)
F_{377}\! \left(x , y\right) = F_{378}\! \left(x , y\right)+F_{381}\! \left(x , y\right)
F_{378}\! \left(x , y\right) = F_{308}\! \left(x , y\right)+F_{379}\! \left(x , y\right)
F_{379}\! \left(x , y\right) = F_{380}\! \left(x , y\right)
F_{380}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{378}\! \left(x , y\right)
F_{381}\! \left(x , y\right) = F_{382}\! \left(x , y\right)+F_{391}\! \left(x , y\right)
F_{382}\! \left(x , y\right) = F_{383}\! \left(x , y\right)
F_{383}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{384}\! \left(x , y\right)
F_{384}\! \left(x , y\right) = F_{385}\! \left(x , y\right)+F_{388}\! \left(x , y\right)
F_{385}\! \left(x , y\right) = F_{308}\! \left(x , y\right)+F_{386}\! \left(x , y\right)
F_{386}\! \left(x , y\right) = F_{387}\! \left(x , y\right)
F_{387}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{308}\! \left(x , y\right)
F_{388}\! \left(x , y\right) = F_{382}\! \left(x , y\right)+F_{389}\! \left(x , y\right)
F_{389}\! \left(x , y\right) = F_{390}\! \left(x , y\right)
F_{390}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{382}\! \left(x , y\right)
F_{391}\! \left(x , y\right) = F_{392}\! \left(x , y\right)
F_{392}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{381}\! \left(x , y\right)
F_{393}\! \left(x , y\right) = F_{394}\! \left(x , y\right)
F_{394}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{395}\! \left(x , y\right)
F_{395}\! \left(x , y\right) = F_{396}\! \left(x , y\right)+F_{399}\! \left(x , y\right)
F_{396}\! \left(x , y\right) = F_{335}\! \left(x , y\right)+F_{397}\! \left(x , y\right)
F_{397}\! \left(x , y\right) = F_{398}\! \left(x , y\right)
F_{398}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{396}\! \left(x , y\right)
F_{399}\! \left(x , y\right) = F_{400}\! \left(x , y\right)+F_{413}\! \left(x , y\right)
F_{400}\! \left(x , y\right) = F_{401}\! \left(x , y\right)
F_{401}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{402}\! \left(x , y\right)
F_{402}\! \left(x , y\right) = F_{403}\! \left(x , y\right)+F_{406}\! \left(x , y\right)
F_{403}\! \left(x , y\right) = F_{335}\! \left(x , y\right)+F_{404}\! \left(x , y\right)
F_{404}\! \left(x , y\right) = F_{405}\! \left(x , y\right)
F_{405}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{335}\! \left(x , y\right)
F_{406}\! \left(x , y\right) = F_{400}\! \left(x , y\right)+F_{407}\! \left(x , y\right)
F_{407}\! \left(x , y\right) = 4 F_{22}\! \left(x \right)+F_{408}\! \left(x , y\right)+F_{412}\! \left(x , y\right)
F_{408}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{409}\! \left(x , y\right)
F_{409}\! \left(x , y\right) = F_{410}\! \left(x , y\right)+F_{411}\! \left(x , y\right)
F_{410}\! \left(x , y\right) = F_{404}\! \left(x , y\right)
F_{411}\! \left(x , y\right) = F_{407}\! \left(x , y\right)
F_{412}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{400}\! \left(x , y\right)
F_{413}\! \left(x , y\right) = 4 F_{22}\! \left(x \right)+F_{414}\! \left(x , y\right)+F_{423}\! \left(x , y\right)
F_{414}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{415}\! \left(x , y\right)
F_{415}\! \left(x , y\right) = F_{416}\! \left(x , y\right)+F_{419}\! \left(x , y\right)
F_{416}\! \left(x , y\right) = F_{404}\! \left(x , y\right)+F_{417}\! \left(x , y\right)
F_{417}\! \left(x , y\right) = F_{418}\! \left(x , y\right)
F_{418}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{404}\! \left(x , y\right)
F_{419}\! \left(x , y\right) = F_{420}\! \left(x , y\right)+F_{421}\! \left(x , y\right)
F_{420}\! \left(x , y\right) = 4 F_{22}\! \left(x \right)+F_{412}\! \left(x , y\right)+F_{414}\! \left(x , y\right)
F_{421}\! \left(x , y\right) = F_{422}\! \left(x , y\right)
F_{422}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{420}\! \left(x , y\right)
F_{423}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{399}\! \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_197(x) + F_4(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_6(x) + F_86(x))
Eq(F_6(x), F_39(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_28(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) + F_23(x) + F_27(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_14(x))
Eq(F_26(x), F_21(x))
Eq(F_27(x), F_14(x)*F_16(x))
Eq(F_28(x), F_22(x) + F_29(x) + F_38(x))
Eq(F_29(x), F_14(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_14(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), x**2)
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_22(x) + F_27(x) + F_29(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_35(x))
Eq(F_38(x), F_14(x)*F_15(x))
Eq(F_39(x), F_40(x) + F_52(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_11(x) + F_43(x))
Eq(F_43(x), F_44(x) + F_50(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_19(x) + F_47(x))
Eq(F_47(x), F_44(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_14(x)*F_44(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_14(x)*F_43(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_14(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_61(x))
Eq(F_55(x), F_56(x) + F_59(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_14(x)*F_58(x))
Eq(F_58(x), F_1(x) + F_56(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_14(x)*F_55(x))
Eq(F_61(x), F_62(x) + F_75(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_14(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), F_56(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_56(x))
Eq(F_68(x), F_62(x) + F_69(x))
Eq(F_69(x), 2*F_22(x) + F_70(x) + F_74(x))
Eq(F_70(x), F_14(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_66(x))
Eq(F_73(x), F_69(x))
Eq(F_74(x), F_14(x)*F_62(x))
Eq(F_75(x), 2*F_22(x) + F_76(x) + F_85(x))
Eq(F_76(x), F_14(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_81(x))
Eq(F_78(x), F_66(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_14(x)*F_66(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), 2*F_22(x) + F_74(x) + F_76(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_82(x))
Eq(F_85(x), F_14(x)*F_61(x))
Eq(F_86(x), F_147(x) + F_87(x))
Eq(F_87(x), F_88(x) + F_94(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_14(x)*F_90(x))
Eq(F_90(x), F_58(x) + F_91(x))
Eq(F_91(x), F_88(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_14(x)*F_91(x))
Eq(F_94(x), F_112(x) + F_22(x) + F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_101(x) + F_97(x))
Eq(F_97(x), F_56(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_14(x))
Eq(F_100(x), F_56(x) + F_98(x))
Eq(F_101(x), F_102(x) + F_108(x))
Eq(F_102(x), F_103(x) + F_22(x) + F_95(x))
Eq(F_103(x), F_104(x)*F_14(x))
Eq(F_104(x), F_105(x) + F_56(x))
Eq(F_105(x), F_103(x) + F_106(x) + F_22(x))
Eq(F_106(x), F_107(x)*F_14(x))
Eq(F_107(x), F_105(x) + F_56(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_14(x))
Eq(F_110(x), F_111(x) + F_98(x))
Eq(F_111(x), F_109(x))
Eq(F_112(x), F_113(x)*F_14(x))
Eq(F_113(x), F_114(x) + F_120(x))
Eq(F_114(x), F_115(x) + F_56(x))
Eq(F_115(x), F_116(x) + F_119(x) + F_22(x))
Eq(F_116(x), F_117(x)*F_14(x))
Eq(F_117(x), F_118(x) + F_14(x))
Eq(F_118(x), F_116(x) + F_22(x) + F_67(x))
Eq(F_119(x), F_114(x)*F_14(x))
Eq(F_120(x), F_121(x) + F_136(x))
Eq(F_121(x), F_106(x) + F_122(x) + F_22(x))
Eq(F_122(x), F_123(x)*F_14(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_118(x) + F_56(x))
Eq(F_125(x), F_121(x) + F_126(x))
Eq(F_126(x), F_127(x) + F_131(x) + F_135(x) + F_22(x))
Eq(F_127(x), F_128(x)*F_14(x))
Eq(F_128(x), F_129(x) + F_66(x))
Eq(F_129(x), F_127(x) + F_130(x) + 2*F_22(x))
Eq(F_130(x), F_105(x)*F_14(x))
Eq(F_131(x), F_132(x)*F_14(x))
Eq(F_132(x), F_133(x) + F_134(x))
Eq(F_133(x), F_118(x))
Eq(F_134(x), F_126(x))
Eq(F_135(x), F_121(x)*F_14(x))
Eq(F_136(x), F_127(x) + F_137(x) + F_146(x) + F_22(x))
Eq(F_137(x), F_138(x)*F_14(x))
Eq(F_138(x), F_139(x) + F_142(x))
Eq(F_139(x), F_118(x) + F_140(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_118(x)*F_14(x))
Eq(F_142(x), F_143(x) + F_144(x))
Eq(F_143(x), F_127(x) + F_135(x) + F_137(x) + F_22(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_14(x)*F_143(x))
Eq(F_146(x), F_120(x)*F_14(x))
Eq(F_147(x), F_148(x) + F_166(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_14(x)*F_150(x))
Eq(F_150(x), F_151(x) + F_154(x))
Eq(F_151(x), F_152(x) + F_88(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_14(x)*F_151(x))
Eq(F_154(x), F_155(x) + F_164(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_14(x)*F_157(x))
Eq(F_157(x), F_158(x) + F_161(x))
Eq(F_158(x), F_159(x) + F_88(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_14(x)*F_88(x))
Eq(F_161(x), F_155(x) + F_162(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_14(x)*F_155(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_14(x)*F_154(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_14(x)*F_168(x))
Eq(F_168(x), F_169(x) + F_172(x))
Eq(F_169(x), F_170(x) + F_98(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_14(x)*F_169(x))
Eq(F_172(x), F_173(x) + F_186(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_14(x)*F_175(x))
Eq(F_175(x), F_176(x) + F_179(x))
Eq(F_176(x), F_177(x) + F_98(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_14(x)*F_98(x))
Eq(F_179(x), F_173(x) + F_180(x))
Eq(F_180(x), F_181(x) + F_185(x) + 3*F_22(x))
Eq(F_181(x), F_14(x)*F_182(x))
Eq(F_182(x), F_183(x) + F_184(x))
Eq(F_183(x), F_177(x))
Eq(F_184(x), F_180(x))
Eq(F_185(x), F_14(x)*F_173(x))
Eq(F_186(x), F_187(x) + F_196(x) + 3*F_22(x))
Eq(F_187(x), F_14(x)*F_188(x))
Eq(F_188(x), F_189(x) + F_192(x))
Eq(F_189(x), F_177(x) + F_190(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_14(x)*F_177(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_185(x) + F_187(x) + 3*F_22(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_14(x)*F_193(x))
Eq(F_196(x), F_14(x)*F_172(x))
Eq(F_197(x), F_14(x)*F_198(x))
Eq(F_198(x), F_199(x, 1))
Eq(F_199(x, k_0), F_1(x) + F_200(x, k_0) + F_202(x, k_0) + F_204(x, k_0))
Eq(F_200(x, k_0), F_199(x, k_0)*F_201(x, k_0))
Eq(F_201(x, k_0), k_0*x)
Eq(F_202(x, k_0), F_14(x)*F_203(x, k_0))
Eq(F_203(x, k_0), (-k_0*F_199(x, k_0) + F_199(x, 1))/(1 - k_0))
Eq(F_204(x, k_0), F_14(x)*F_205(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0) + F_5(x))
Eq(F_206(x, k_0), F_207(x, k_0) + F_306(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_254(x, k_0))
Eq(F_208(x, k_0), F_209(x, k_0) + F_212(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_201(x, k_0)*F_211(x, k_0))
Eq(F_211(x, k_0), F_1(x) + F_209(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0) + F_218(x, k_0) + F_22(x))
Eq(F_213(x, k_0), F_201(x, k_0)*F_214(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0) + F_56(x))
Eq(F_215(x, k_0), F_213(x, k_0) + F_216(x, k_0) + F_22(x))
Eq(F_216(x, k_0), F_14(x)*F_217(x, k_0))
Eq(F_217(x, k_0), F_209(x, k_0) + F_215(x, k_0))
Eq(F_218(x, k_0), F_14(x)*F_219(x, k_0))
Eq(F_219(x, k_0), F_220(x, k_0) + F_227(x, k_0))
Eq(F_220(x, k_0), F_209(x, k_0) + F_221(x, k_0))
Eq(F_221(x, k_0), F_22(x) + F_222(x, k_0) + F_226(x, k_0))
Eq(F_222(x, k_0), F_201(x, k_0)*F_223(x, k_0))
Eq(F_223(x, k_0), F_14(x) + F_224(x, k_0))
Eq(F_224(x, k_0), F_22(x) + F_222(x, k_0) + F_225(x, k_0))
Eq(F_225(x, k_0), F_14(x)*F_209(x, k_0))
Eq(F_226(x, k_0), F_14(x)*F_220(x, k_0))
Eq(F_227(x, k_0), F_228(x, k_0) + F_243(x, k_0))
Eq(F_228(x, k_0), F_213(x, k_0) + F_22(x) + F_229(x, k_0))
Eq(F_229(x, k_0), F_14(x)*F_230(x, k_0))
Eq(F_230(x, k_0), F_231(x, k_0) + F_232(x, k_0))
Eq(F_231(x, k_0), F_209(x, k_0) + F_224(x, k_0))
Eq(F_232(x, k_0), F_228(x, k_0) + F_233(x, k_0))
Eq(F_233(x, k_0), F_22(x) + F_234(x, k_0) + F_238(x, k_0) + F_242(x, k_0))
Eq(F_234(x, k_0), F_201(x, k_0)*F_235(x, k_0))
Eq(F_235(x, k_0), F_236(x, k_0) + F_66(x))
Eq(F_236(x, k_0), 2*F_22(x) + F_234(x, k_0) + F_237(x, k_0))
Eq(F_237(x, k_0), F_14(x)*F_215(x, k_0))
Eq(F_238(x, k_0), F_14(x)*F_239(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0) + F_241(x, k_0))
Eq(F_240(x, k_0), F_224(x, k_0))
Eq(F_241(x, k_0), F_233(x, k_0))
Eq(F_242(x, k_0), F_14(x)*F_228(x, k_0))
Eq(F_243(x, k_0), F_22(x) + F_234(x, k_0) + F_244(x, k_0) + F_253(x, k_0))
Eq(F_244(x, k_0), F_14(x)*F_245(x, k_0))
Eq(F_245(x, k_0), F_246(x, k_0) + F_249(x, k_0))
Eq(F_246(x, k_0), F_224(x, k_0) + F_247(x, k_0))
Eq(F_247(x, k_0), F_248(x, k_0))
Eq(F_248(x, k_0), F_14(x)*F_224(x, k_0))
Eq(F_249(x, k_0), F_250(x, k_0) + F_251(x, k_0))
Eq(F_250(x, k_0), F_22(x) + F_234(x, k_0) + F_242(x, k_0) + F_244(x, k_0))
Eq(F_251(x, k_0), F_252(x, k_0))
Eq(F_252(x, k_0), F_14(x)*F_250(x, k_0))
Eq(F_253(x, k_0), F_14(x)*F_227(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0) + F_272(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_258(x, k_0) + F_261(x, k_0))
Eq(F_258(x, k_0), F_209(x, k_0) + F_259(x, k_0))
Eq(F_259(x, k_0), F_260(x, k_0))
Eq(F_260(x, k_0), F_14(x)*F_258(x, k_0))
Eq(F_261(x, k_0), F_262(x, k_0) + F_270(x, k_0))
Eq(F_262(x, k_0), F_263(x, k_0))
Eq(F_263(x, k_0), F_14(x)*F_264(x, k_0))
Eq(F_264(x, k_0), F_265(x, k_0) + F_267(x, k_0))
Eq(F_265(x, k_0), F_209(x, k_0) + F_266(x, k_0))
Eq(F_266(x, k_0), F_225(x, k_0))
Eq(F_267(x, k_0), F_262(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_262(x, k_0))
Eq(F_270(x, k_0), F_271(x, k_0))
Eq(F_271(x, k_0), F_14(x)*F_261(x, k_0))
Eq(F_272(x, k_0), F_273(x, k_0))
Eq(F_273(x, k_0), F_14(x)*F_274(x, k_0))
Eq(F_274(x, k_0), F_275(x, k_0) + F_281(x, k_0))
Eq(F_275(x, k_0), F_276(x, k_0) + F_279(x, k_0))
Eq(F_276(x, k_0), F_277(x, k_0))
Eq(F_277(x, k_0), F_14(x)*F_278(x, k_0))
Eq(F_278(x, k_0), F_209(x, k_0) + F_276(x, k_0))
Eq(F_279(x, k_0), F_280(x, k_0))
Eq(F_280(x, k_0), F_14(x)*F_275(x, k_0))
Eq(F_281(x, k_0), F_282(x, k_0) + F_295(x, k_0))
Eq(F_282(x, k_0), F_283(x, k_0))
Eq(F_283(x, k_0), F_14(x)*F_284(x, k_0))
Eq(F_284(x, k_0), F_285(x, k_0) + F_288(x, k_0))
Eq(F_285(x, k_0), F_276(x, k_0) + F_286(x, k_0))
Eq(F_286(x, k_0), F_287(x, k_0))
Eq(F_287(x, k_0), F_14(x)*F_276(x, k_0))
Eq(F_288(x, k_0), F_282(x, k_0) + F_289(x, k_0))
Eq(F_289(x, k_0), 3*F_22(x) + F_290(x, k_0) + F_294(x, k_0))
Eq(F_290(x, k_0), F_14(x)*F_291(x, k_0))
Eq(F_291(x, k_0), F_292(x, k_0) + F_293(x, k_0))
Eq(F_292(x, k_0), F_286(x, k_0))
Eq(F_293(x, k_0), F_289(x, k_0))
Eq(F_294(x, k_0), F_14(x)*F_282(x, k_0))
Eq(F_295(x, k_0), 3*F_22(x) + F_296(x, k_0) + F_305(x, k_0))
Eq(F_296(x, k_0), F_14(x)*F_297(x, k_0))
Eq(F_297(x, k_0), F_298(x, k_0) + F_301(x, k_0))
Eq(F_298(x, k_0), F_286(x, k_0) + F_299(x, k_0))
Eq(F_299(x, k_0), F_300(x, k_0))
Eq(F_300(x, k_0), F_14(x)*F_286(x, k_0))
Eq(F_301(x, k_0), F_302(x, k_0) + F_303(x, k_0))
Eq(F_302(x, k_0), 3*F_22(x) + F_294(x, k_0) + F_296(x, k_0))
Eq(F_303(x, k_0), F_304(x, k_0))
Eq(F_304(x, k_0), F_14(x)*F_302(x, k_0))
Eq(F_305(x, k_0), F_14(x)*F_281(x, k_0))
Eq(F_306(x, k_0), F_307(x, k_0) + F_374(x, k_0))
Eq(F_307(x, k_0), F_308(x, k_0) + F_316(x, k_0))
Eq(F_308(x, k_0), F_22(x) + F_309(x, k_0) + F_311(x, k_0))
Eq(F_309(x, k_0), F_201(x, k_0)*F_310(x, k_0))
Eq(F_310(x, k_0), F_276(x, k_0) + F_56(x))
Eq(F_311(x, k_0), F_14(x)*F_312(x, k_0))
Eq(F_312(x, k_0), F_278(x, k_0) + F_313(x, k_0))
Eq(F_313(x, k_0), F_308(x, k_0) + F_314(x, k_0))
Eq(F_314(x, k_0), F_315(x, k_0))
Eq(F_315(x, k_0), F_14(x)*F_313(x, k_0))
Eq(F_316(x, k_0), F_22(x) + F_317(x, k_0) + F_322(x, k_0) + F_339(x, k_0))
Eq(F_317(x, k_0), F_201(x, k_0)*F_318(x, k_0))
Eq(F_318(x, k_0), F_319(x, k_0) + F_98(x))
Eq(F_319(x, k_0), F_320(x, k_0))
Eq(F_320(x, k_0), F_14(x)*F_321(x, k_0))
Eq(F_321(x, k_0), F_276(x, k_0) + F_319(x, k_0))
Eq(F_322(x, k_0), F_14(x)*F_323(x, k_0))
Eq(F_323(x, k_0), F_324(x, k_0) + F_325(x, k_0))
Eq(F_324(x, k_0), F_215(x, k_0) + F_319(x, k_0))
Eq(F_325(x, k_0), F_326(x, k_0) + F_332(x, k_0))
Eq(F_326(x, k_0), F_22(x) + F_317(x, k_0) + F_322(x, k_0) + F_327(x, k_0))
Eq(F_327(x, k_0), F_14(x)*F_328(x, k_0))
Eq(F_328(x, k_0), F_276(x, k_0) + F_329(x, k_0))
Eq(F_329(x, k_0), 2*F_22(x) + F_327(x, k_0) + F_330(x, k_0))
Eq(F_330(x, k_0), F_14(x)*F_331(x, k_0))
Eq(F_331(x, k_0), F_215(x, k_0) + F_329(x, k_0))
Eq(F_332(x, k_0), F_333(x, k_0))
Eq(F_333(x, k_0), F_14(x)*F_334(x, k_0))
Eq(F_334(x, k_0), F_335(x, k_0) + F_338(x, k_0))
Eq(F_335(x, k_0), F_336(x, k_0))
Eq(F_336(x, k_0), F_14(x)*F_337(x, k_0))
Eq(F_337(x, k_0), F_276(x, k_0) + F_335(x, k_0))
Eq(F_338(x, k_0), F_333(x, k_0))
Eq(F_339(x, k_0), F_14(x)*F_340(x, k_0))
Eq(F_340(x, k_0), F_341(x, k_0) + F_347(x, k_0))
Eq(F_341(x, k_0), F_276(x, k_0) + F_342(x, k_0))
Eq(F_342(x, k_0), 2*F_22(x) + F_343(x, k_0) + F_346(x, k_0))
Eq(F_343(x, k_0), F_14(x)*F_344(x, k_0))
Eq(F_344(x, k_0), F_224(x, k_0) + F_345(x, k_0))
Eq(F_345(x, k_0), 2*F_22(x) + F_287(x, k_0) + F_343(x, k_0))
Eq(F_346(x, k_0), F_14(x)*F_341(x, k_0))
Eq(F_347(x, k_0), F_348(x, k_0) + F_363(x, k_0))
Eq(F_348(x, k_0), 2*F_22(x) + F_330(x, k_0) + F_349(x, k_0))
Eq(F_349(x, k_0), F_14(x)*F_350(x, k_0))
Eq(F_350(x, k_0), F_351(x, k_0) + F_352(x, k_0))
Eq(F_351(x, k_0), F_276(x, k_0) + F_345(x, k_0))
Eq(F_352(x, k_0), F_348(x, k_0) + F_353(x, k_0))
Eq(F_353(x, k_0), 2*F_22(x) + F_354(x, k_0) + F_358(x, k_0) + F_362(x, k_0))
Eq(F_354(x, k_0), F_14(x)*F_355(x, k_0))
Eq(F_355(x, k_0), F_236(x, k_0) + F_356(x, k_0))
Eq(F_356(x, k_0), 3*F_22(x) + F_354(x, k_0) + F_357(x, k_0))
Eq(F_357(x, k_0), F_14(x)*F_329(x, k_0))
Eq(F_358(x, k_0), F_14(x)*F_359(x, k_0))
Eq(F_359(x, k_0), F_360(x, k_0) + F_361(x, k_0))
Eq(F_360(x, k_0), F_345(x, k_0))
Eq(F_361(x, k_0), F_353(x, k_0))
Eq(F_362(x, k_0), F_14(x)*F_348(x, k_0))
Eq(F_363(x, k_0), 2*F_22(x) + F_354(x, k_0) + F_364(x, k_0) + F_373(x, k_0))
Eq(F_364(x, k_0), F_14(x)*F_365(x, k_0))
Eq(F_365(x, k_0), F_366(x, k_0) + F_369(x, k_0))
Eq(F_366(x, k_0), F_345(x, k_0) + F_367(x, k_0))
Eq(F_367(x, k_0), F_368(x, k_0))
Eq(F_368(x, k_0), F_14(x)*F_345(x, k_0))
Eq(F_369(x, k_0), F_370(x, k_0) + F_371(x, k_0))
Eq(F_370(x, k_0), 2*F_22(x) + F_354(x, k_0) + F_362(x, k_0) + F_364(x, k_0))
Eq(F_371(x, k_0), F_372(x, k_0))
Eq(F_372(x, k_0), F_14(x)*F_370(x, k_0))
Eq(F_373(x, k_0), F_14(x)*F_347(x, k_0))
Eq(F_374(x, k_0), F_375(x, k_0) + F_393(x, k_0))
Eq(F_375(x, k_0), F_376(x, k_0))
Eq(F_376(x, k_0), F_14(x)*F_377(x, k_0))
Eq(F_377(x, k_0), F_378(x, k_0) + F_381(x, k_0))
Eq(F_378(x, k_0), F_308(x, k_0) + F_379(x, k_0))
Eq(F_379(x, k_0), F_380(x, k_0))
Eq(F_380(x, k_0), F_14(x)*F_378(x, k_0))
Eq(F_381(x, k_0), F_382(x, k_0) + F_391(x, k_0))
Eq(F_382(x, k_0), F_383(x, k_0))
Eq(F_383(x, k_0), F_14(x)*F_384(x, k_0))
Eq(F_384(x, k_0), F_385(x, k_0) + F_388(x, k_0))
Eq(F_385(x, k_0), F_308(x, k_0) + F_386(x, k_0))
Eq(F_386(x, k_0), F_387(x, k_0))
Eq(F_387(x, k_0), F_14(x)*F_308(x, k_0))
Eq(F_388(x, k_0), F_382(x, k_0) + F_389(x, k_0))
Eq(F_389(x, k_0), F_390(x, k_0))
Eq(F_390(x, k_0), F_14(x)*F_382(x, k_0))
Eq(F_391(x, k_0), F_392(x, k_0))
Eq(F_392(x, k_0), F_14(x)*F_381(x, k_0))
Eq(F_393(x, k_0), F_394(x, k_0))
Eq(F_394(x, k_0), F_14(x)*F_395(x, k_0))
Eq(F_395(x, k_0), F_396(x, k_0) + F_399(x, k_0))
Eq(F_396(x, k_0), F_335(x, k_0) + F_397(x, k_0))
Eq(F_397(x, k_0), F_398(x, k_0))
Eq(F_398(x, k_0), F_14(x)*F_396(x, k_0))
Eq(F_399(x, k_0), F_400(x, k_0) + F_413(x, k_0))
Eq(F_400(x, k_0), F_401(x, k_0))
Eq(F_401(x, k_0), F_14(x)*F_402(x, k_0))
Eq(F_402(x, k_0), F_403(x, k_0) + F_406(x, k_0))
Eq(F_403(x, k_0), F_335(x, k_0) + F_404(x, k_0))
Eq(F_404(x, k_0), F_405(x, k_0))
Eq(F_405(x, k_0), F_14(x)*F_335(x, k_0))
Eq(F_406(x, k_0), F_400(x, k_0) + F_407(x, k_0))
Eq(F_407(x, k_0), 4*F_22(x) + F_408(x, k_0) + F_412(x, k_0))
Eq(F_408(x, k_0), F_14(x)*F_409(x, k_0))
Eq(F_409(x, k_0), F_410(x, k_0) + F_411(x, k_0))
Eq(F_410(x, k_0), F_404(x, k_0))
Eq(F_411(x, k_0), F_407(x, k_0))
Eq(F_412(x, k_0), F_14(x)*F_400(x, k_0))
Eq(F_413(x, k_0), 4*F_22(x) + F_414(x, k_0) + F_423(x, k_0))
Eq(F_414(x, k_0), F_14(x)*F_415(x, k_0))
Eq(F_415(x, k_0), F_416(x, k_0) + F_419(x, k_0))
Eq(F_416(x, k_0), F_404(x, k_0) + F_417(x, k_0))
Eq(F_417(x, k_0), F_418(x, k_0))
Eq(F_418(x, k_0), F_14(x)*F_404(x, k_0))
Eq(F_419(x, k_0), F_420(x, k_0) + F_421(x, k_0))
Eq(F_420(x, k_0), 4*F_22(x) + F_412(x, k_0) + F_414(x, k_0))
Eq(F_421(x, k_0), F_422(x, k_0))
Eq(F_422(x, k_0), F_14(x)*F_420(x, k_0))
Eq(F_423(x, k_0), F_14(x)*F_399(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": [1, 0, 2, 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": [1, 0, 2], "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], [0, 0], [0, 0], [0, 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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 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": [1, 0, 2, 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"}}, {"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], [1, 0]]}, {"patt": [1, 0, 2], "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], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 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": [1, 0, 2], "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], [0, 0], [0, 0], [0, 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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 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}}, {"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": [[0, 1], [2, 1]]}, {"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": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 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": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "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": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[3, 1], [3, 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": [[1, 1], [1, 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": [1, 0, 2], "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], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 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"}}, {"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": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 0], [2, 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": [[1, 0], [1, 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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