01243_01342_01432_02143_10243_10342_10432_20341_20431

Counting sequence:
1, 1, 2, 6, 24, 111, 548, 2795, 14545, 76817, 410543, 2216053, 12064062, 66161284, 365184731, 2027187595, 11310410206, 63392797171, 356768868109, 2015371414617, 11423574707928, 64953637778309, 370382245342619, 2117606892150249, 12136765159719034, 69718176192623873, 401333526794064567, 2314829099767051124, 13376120138730563324, 77426213413028983461, 448896292931877354335, 2606524114782439044677, 15156412808383719849960, 88249958730392188428974, 514497604718373983904751, 3003121586201847391991221, 17549125293140334760076598, 102660985648311774644304918, 601172464223953106438395712, 3523825960660868526942271639, 20674315096904733612283395023, 121403200020765122713498009656, 713499660253411740053984483642, 4196676898374619518197750882395, 24703017248972358792183230363538, 145516667746434087757519053464526, 857788521623983960866814260946223, 5059874951272663042552167537027262, 29866166696032094062018820866144064, 176395753465188007350089653771369901, 1042449809684920769538298865544556815, 6164113451675844815359082943210025335, 36469108405001489453016356691532233708, 215878729846391741331194821603867202430, 1278546014977597128031650901424874085291, 7575943632727575584754498569546784919480, 44912108969189426509493541581449890169313, 266372491977559675156718640889110543008555, 1580548179151262491185281940939593955567465, 9382360432696621295922841604696615156554486, 55718110493362656156028546600215065875230916, 331020371457061931757600020777558035653215363, 1967349842117409641870577410492105912008249650, 11696925321800700733805306083799034906437045572, 69569687174201298435552520854470092339546636917, 413925122165057152171812972238003003297377612943, 2463612102937544912467739250897295804920569860129, 14667878028406135568726713723049769654285978261139, 87357957024555171706800233756800822639648431646851, 520443809279828575855887077544907692527575716569350, 3101541343967223015300846158504016750627699966624698, 18488852763839660459110904265958380119022482011594002, 110247177079404945158687210613787636501345869792298233, 657577165746103759027984300081080650532910855810974521, 3923236102473968094037140846015082184409669280225840343, 23413024141017542571577668862727596377892847514382448190, 139760009610398216759061746467657503120062749694917907518, 834483553286029006277533961745713679670067570775183196672, 4983785156661230686094086174647821934156497875675778174198, 29771782539866301967311493750143534295646948625141634062285, 177890101517502479806964308120278590423495807862768944988689, 1063157641244526495191153445430994950121385463066710238827631, 6355359063231674375181122003225183104379510659874873101105802, 37999401687333975729130411296208193288308086096222010987066365, 227250809708337621834530057280464829575156675343879217798000752, 1359327138793813601960435910106970083460199304972847516440473001, 8132617203377456449582343722768462014701528791836884270082397255, 48665643141930485410175828404692950528453399840418557727345316487, 291271815291103523700329751390380927391250735599357389676749629512, 1743638489526764465572932924317787644102113471723377224910117623765, 10439858529522457444650606750012480966077571908325749265056806889864, 62518883429819989653635327886732170551286658121594532896571721199547, 374459241657993317250399454697026832998859657650321870797698930806299, 2243225828951399332167836758418519753879848032226953414229810060181241, 13440485516470961631584815929645495550979960208006012578044211599134106, 80543203306804899746093516338022871901121129954092840886117851319540650, 482740049551932708698719341379646834081042320346803153132742254776295100, 2893788670326978956828036557769242568648725469648028973239128787271834763, 17349539128457660007635755600065892224808525364055908952739416154708906532, 104034016479839810725743893345263945109462301982703558720787958700050692743, 623918358050578728657118155626762284851875554960336379839455608389070094552

Implicit equation for the generating function in Maple syntax:
x^11*F(x)^12+x^8*(4+x)*F(x)^11+x^5*(3*x^5-9*x^4-2*x^3-4*x^2+x-1)*F(x)^10+x^4*(5*x^5+12*x^3-20*x^2+15*x-3)*F(x)^9+x^3*(3*x^6-18*x^5+19*x^4+11*x^3-15*x^2-4*x+8)*F(x)^8+x^2*(10*x^6-31*x^5+22*x^4-32*x^3+66*x^2-62*x+10)*F(x)^7+x*(x^7-x^6+11*x^5+14*x^4-94*x^3+120*x^2-22*x-7)*F(x)^6+(5*x^7-30*x^6+45*x^5+19*x^4-81*x^3+x^2+29*x+1)*F(x)^5+(8*x^6-31*x^5+23*x^4+12*x^3+28*x^2-46*x-5)*F(x)^4+(4*x^5-6*x^4-20*x^2+34*x+10)*F(x)^3+(-x^4+4*x^3+2*x^2-11*x-10)*F(x)^2+(-x^3+x^2+x+5)*F(x)-1 = 0

Implicit equation for the generating function in latex syntax:
x^{11} F \! \left(x \right)^{12}+x^{8} \left(4+x \right) F \! \left(x \right)^{11}+x^{5} \left(3 x^{5}-9 x^{4}-2 x^{3}-4 x^{2}+x -1\right) F \! \left(x \right)^{10}+x^{4} \left(5 x^{5}+12 x^{3}-20 x^{2}+15 x -3\right) F \! \left(x \right)^{9}+x^{3} \left(3 x^{6}-18 x^{5}+19 x^{4}+11 x^{3}-15 x^{2}-4 x +8\right) F \! \left(x \right)^{8}+x^{2} \left(10 x^{6}-31 x^{5}+22 x^{4}-32 x^{3}+66 x^{2}-62 x +10\right) F \! \left(x \right)^{7}+x \left(x^{7}-x^{6}+11 x^{5}+14 x^{4}-94 x^{3}+120 x^{2}-22 x -7\right) F \! \left(x \right)^{6}+\left(5 x^{7}-30 x^{6}+45 x^{5}+19 x^{4}-81 x^{3}+x^{2}+29 x +1\right) F \! \left(x \right)^{5}+\left(8 x^{6}-31 x^{5}+23 x^{4}+12 x^{3}+28 x^{2}-46 x -5\right) F \! \left(x \right)^{4}+\left(4 x^{5}-6 x^{4}-20 x^{2}+34 x +10\right) F \! \left(x \right)^{3}+\left(-x^{4}+4 x^{3}+2 x^{2}-11 x -10\right) F \! \left(x \right)^{2}+\left(-x^{3}+x^{2}+x +5\right) F \! \left(x \right)-1 = 0

Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24433/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[41,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[41,x]*F[7,x]
F[7,x] = F[60,x]+F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = x*(1+F[11,x])^2*(x*F[11,x]+1)
F[12,x] = x^2
F[13,x] = F[14,x]+F[16,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = -F[2,x]+F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[41,x]
F[18,x] = F[19,x]+F[52,x]
F[19,x] = F[20,x]+F[51,x]
F[20,x] = F[21,x]+F[23,x]
F[21,x] = F[2,x]*F[22,x]
F[22,x] = 1+x^2*F[22,x]^3+(-x^2+x)*F[22,x]^2
F[23,x] = F[24,x]
F[24,x] = F[19,x]*F[25,x]*F[41,x]
F[25,x] = 1/F[41,x]/F[46,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]*F[41,x]
F[29,x] = 1/F[41,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = -F[22,x]+F[32,x]
F[32,x] = 1/F[0,x]*F[33,x]
F[33,x] = -F[42,x]+F[34,x]
F[34,x] = 1/F[41,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[11,x]+F[37,x]
F[37,x] = -F[2,x]+F[38,x]
F[38,x] = -F[22,x]+F[39,x]
F[39,x] = 1/F[41,x]*F[40,x]
F[40,x] = F[2,x]
F[41,x] = x
F[42,x] = -F[45,x]+F[43,x]
F[43,x] = 1/F[41,x]*F[44,x]
F[44,x] = F[37,x]
F[45,x] = F[2,x]*F[32,x]
F[46,x] = F[47,x]+F[51,x]
F[47,x] = F[20,x]+F[48,x]
F[48,x] = F[22,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[25,x]*F[41,x]*F[48,x]
F[51,x] = F[22,x]*F[5,x]
F[52,x] = F[53,x]+F[56,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[55,x]
F[55,x] = F[11,x]+F[21,x]
F[56,x] = F[57,x]
F[57,x] = F[41,x]*F[58,x]
F[58,x] = F[27,x]+F[59,x]
F[59,x] = F[14,x]*F[22,x]
F[60,x] = F[61,x]
F[61,x] = F[41,x]*F[62,x]
F[62,x] = F[339,x]+F[63,x]
F[63,x] = F[178,x]+F[64,x]
F[64,x] = F[169,x]+F[65,x]
F[65,x] = F[0,x]*F[66,x]
F[66,x] = F[4,x]+F[67,x]
F[67,x] = F[14,x]+F[68,x]
F[68,x] = -F[14,x]+F[69,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[41,x]*F[71,x]
F[71,x] = F[15,x]
F[72,x] = F[73,x]+F[80,x]
F[73,x] = F[74,x]
F[74,x] = F[10,x]+F[75,x]
F[75,x] = F[41,x]*F[76,x]*F[79,x]
F[76,x] = F[77,x]
F[77,x] = F[41,x]*F[78,x]*F[79,x]
F[78,x] = F[1,x]+F[76,x]
F[79,x] = F[1,x]+F[41,x]
F[80,x] = F[16,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[41,x]*F[83,x]
F[83,x] = F[160,x]+F[84,x]
F[84,x] = F[155,x]+F[85,x]
F[85,x] = F[150,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[41,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[41,x]*F[78,x]*F[79,x]*F[90,x]
F[90,x] = F[148,x]+F[91,x]
F[91,x] = F[22,x]*F[92,x]
F[92,x] = F[140,x]+F[93,x]
F[93,x] = F[131,x]+F[94,x]
F[94,x] = F[0,x]+F[95,x]
F[95,x] = F[2,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[41,x]*F[98,x]
F[98,x] = F[129,x]+F[99,x]
F[99,x] = F[100,x]+F[127,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[41,x]
F[102,x] = 1/F[41,x]/F[48,x]*F[103,x]
F[103,x] = F[104,x]
F[104,x] = -F[107,x]+F[105,x]
F[105,x] = 1/F[41,x]*F[106,x]
F[106,x] = F[15,x]
F[107,x] = F[108,x]+F[125,x]
F[108,x] = F[109,x]*F[2,x]
F[109,x] = F[0,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[41,x]
F[112,x] = F[113,x]+F[122,x]
F[113,x] = F[109,x]+F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[41,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[109,x]*F[94,x]
F[118,x] = F[119,x]
F[119,x] = F[109,x]*F[120,x]*F[22,x]*F[41,x]
F[120,x] = 1/F[22,x]/F[41,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = -F[114,x]+F[123,x]
F[123,x] = 1/F[41,x]*F[124,x]
F[124,x] = F[96,x]
F[125,x] = F[126,x]
F[126,x] = F[102,x]*F[19,x]*F[41,x]
F[127,x] = F[128,x]
F[128,x] = F[104,x]*F[41,x]
F[129,x] = -F[130,x]+F[92,x]
F[130,x] = F[4,x]+F[99,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[0,x]*F[2,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[41,x]
F[135,x] = F[136,x]+F[138,x]
F[136,x] = F[109,x]*F[137,x]
F[137,x] = F[2,x]+F[96,x]
F[138,x] = F[139,x]
F[139,x] = F[102,x]*F[41,x]*F[90,x]
F[140,x] = F[141,x]+F[144,x]
F[141,x] = F[100,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[102,x]*F[41,x]*F[55,x]
F[144,x] = F[145,x]
F[145,x] = F[0,x]*F[146,x]*F[41,x]
F[146,x] = F[147,x]
F[147,x] = F[102,x]*F[29,x]*F[41,x]
F[148,x] = F[149,x]
F[149,x] = F[25,x]*F[41,x]*F[90,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]*F[41,x]
F[153,x] = F[154,x]
F[154,x] = F[0,x]*F[29,x]*F[41,x]*F[78,x]*F[79,x]
F[155,x] = F[156,x]+F[158,x]
F[156,x] = F[157,x]
F[157,x] = F[41,x]*F[86,x]
F[158,x] = F[159,x]
F[159,x] = F[151,x]*F[41,x]
F[160,x] = F[161,x]
F[161,x] = F[162,x]*F[41,x]
F[162,x] = F[163,x]+F[165,x]
F[163,x] = F[164,x]
F[164,x] = F[79,x]^2*F[22,x]*F[41,x]*F[78,x]*F[94,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[79,x]
F[167,x] = F[168,x]
F[168,x] = F[32,x]*F[41,x]*F[78,x]*F[79,x]
F[169,x] = F[170,x]
F[170,x] = F[171,x]*F[177,x]*F[41,x]
F[171,x] = F[172,x]+F[175,x]
F[172,x] = F[173,x]+F[46,x]
F[173,x] = F[174,x]
F[174,x] = F[171,x]*F[41,x]
F[175,x] = F[176,x]
F[176,x] = F[172,x]*F[41,x]
F[177,x] = F[0,x]+F[100,x]
F[178,x] = F[179,x]
F[179,x] = F[180,x]*F[41,x]
F[180,x] = F[181,x]+F[195,x]
F[181,x] = F[102,x]*F[182,x]
F[182,x] = F[183,x]+F[188,x]
F[183,x] = F[184,x]+F[46,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[22,x]*F[67,x]
F[186,x] = F[187,x]
F[187,x] = F[173,x]*F[25,x]*F[41,x]
F[188,x] = F[189,x]
F[189,x] = F[190,x]*F[41,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[182,x]*F[25,x]
F[192,x] = F[193,x]*F[22,x]
F[193,x] = F[194,x]
F[194,x] = F[172,x]*F[41,x]
F[195,x] = 1/F[41,x]*F[196,x]
F[196,x] = F[197,x]
F[197,x] = F[198,x]*F[41,x]
F[198,x] = F[199,x]
F[199,x] = -F[338,x]+F[200,x]
F[200,x] = 1/F[41,x]*F[201,x]
F[201,x] = F[202,x]
F[202,x] = F[203,x]
F[203,x] = F[204,x]*F[41,x]
F[204,x] = F[205,x]+F[323,x]
F[205,x] = F[206,x]*F[210,x]
F[206,x] = F[207,x]+F[46,x]
F[207,x] = F[208,x]+F[56,x]
F[208,x] = F[209,x]
F[209,x] = F[0,x]*F[22,x]*F[41,x]
F[210,x] = F[211,x]+F[212,x]
F[211,x] = F[0,x]*F[78,x]
F[212,x] = -F[321,x]+F[213,x]
F[213,x] = F[214,x]
F[214,x] = F[215,x]*F[41,x]*F[78,x]
F[215,x] = 1/F[172,x]/F[41,x]*F[216,x]
F[216,x] = F[217,x]
F[217,x] = -F[227,x]+F[218,x]
F[218,x] = F[219,x]+F[224,x]
F[219,x] = F[202,x]+F[220,x]
F[220,x] = F[221,x]+F[222,x]
F[221,x] = F[0,x]*F[4,x]
F[222,x] = F[223,x]
F[223,x] = F[102,x]*F[41,x]*F[46,x]
F[224,x] = -F[202,x]+F[225,x]
F[225,x] = 1/F[41,x]*F[226,x]
F[226,x] = F[68,x]
F[227,x] = F[228,x]+F[230,x]
F[228,x] = F[0,x]*F[229,x]
F[229,x] = F[173,x]+F[4,x]
F[230,x] = -F[231,x]+F[224,x]
F[231,x] = F[232,x]
F[232,x] = F[172,x]*F[233,x]*F[41,x]
F[233,x] = F[104,x]+F[234,x]
F[234,x] = -F[320,x]+F[235,x]
F[235,x] = F[236,x]
F[236,x] = F[237,x]*F[41,x]
F[237,x] = 1/F[243,x]/F[41,x]*F[238,x]
F[238,x] = F[239,x]
F[239,x] = -F[318,x]+F[240,x]
F[240,x] = F[241,x]+F[274,x]
F[241,x] = F[242,x]
F[242,x] = F[243,x]*F[273,x]*F[41,x]
F[243,x] = F[244,x]
F[244,x] = F[245,x]*F[41,x]
F[245,x] = F[246,x]+F[249,x]
F[246,x] = F[0,x]*F[22,x]*F[247,x]
F[247,x] = F[1,x]+F[248,x]
F[248,x] = F[247,x]*F[41,x]
F[249,x] = F[250,x]
F[250,x] = F[0,x]*F[22,x]*F[251,x]*F[259,x]*F[41,x]
F[251,x] = F[247,x]+F[252,x]
F[252,x] = F[253,x]+F[41,x]
F[253,x] = F[254,x]+F[255,x]+F[258,x]
F[254,x] = 0
F[255,x] = F[256,x]*F[41,x]
F[256,x] = F[257,x]
F[257,x] = F[247,x]*F[41,x]
F[258,x] = F[252,x]*F[41,x]
F[259,x] = F[247,x]+F[260,x]
F[260,x] = F[261,x]+F[76,x]
F[261,x] = F[254,x]+F[262,x]+F[272,x]
F[262,x] = F[263,x]*F[41,x]
F[263,x] = F[264,x]+F[265,x]
F[264,x] = F[253,x]+F[256,x]
F[265,x] = F[261,x]+F[266,x]
F[266,x] = 2*F[254,x]+F[267,x]+F[268,x]
F[267,x] = F[261,x]*F[41,x]
F[268,x] = F[269,x]*F[41,x]
F[269,x] = F[266,x]+F[270,x]
F[270,x] = F[271,x]
F[271,x] = F[41,x]*F[76,x]
F[272,x] = F[260,x]*F[41,x]
F[273,x] = F[104,x]+F[109,x]
F[274,x] = F[275,x]
F[275,x] = F[276,x]*F[279,x]*F[41,x]
F[276,x] = F[243,x]+F[277,x]
F[277,x] = F[278,x]
F[278,x] = F[0,x]*F[22,x]
F[279,x] = 1/F[41,x]*F[280,x]
F[280,x] = F[281,x]
F[281,x] = -F[296,x]+F[282,x]
F[282,x] = F[283,x]
F[283,x] = -F[289,x]+F[284,x]
F[284,x] = 1/F[41,x]*F[285,x]
F[285,x] = F[286,x]
F[286,x] = -F[287,x]+F[129,x]
F[287,x] = F[142,x]+F[288,x]
F[288,x] = F[0,x]*F[2,x]
F[289,x] = F[290,x]+F[294,x]
F[290,x] = 1/F[41,x]*F[291,x]
F[291,x] = F[292,x]
F[292,x] = -F[288,x]+F[293,x]
F[293,x] = -F[140,x]+F[98,x]
F[294,x] = F[295,x]
F[295,x] = F[109,x]*F[146,x]*F[41,x]
F[296,x] = F[297,x]
F[297,x] = F[298,x]*F[302,x]*F[41,x]
F[298,x] = F[299,x]
F[299,x] = F[300,x]*F[41,x]
F[300,x] = 1/F[22,x]/F[41,x]*F[301,x]
F[301,x] = F[146,x]
F[302,x] = F[303,x]+F[306,x]
F[303,x] = F[1,x]+F[304,x]
F[304,x] = F[305,x]
F[305,x] = F[251,x]*F[41,x]
F[306,x] = 1/F[41,x]*F[307,x]
F[307,x] = -F[316,x]+F[308,x]
F[308,x] = -F[311,x]+F[309,x]
F[309,x] = 1/F[41,x]*F[310,x]
F[310,x] = F[15,x]
F[311,x] = F[312,x]
F[312,x] = F[313,x]*F[41,x]
F[313,x] = 1/F[41,x]*F[314,x]
F[314,x] = F[315,x]
F[315,x] = F[69,x]+F[80,x]
F[316,x] = F[317,x]+F[76,x]
F[317,x] = F[304,x]*F[41,x]
F[318,x] = F[319,x]
F[319,x] = F[0,x]*F[22,x]*F[279,x]*F[41,x]
F[320,x] = F[109,x]*F[41,x]
F[321,x] = F[322,x]
F[322,x] = F[233,x]*F[41,x]*F[78,x]
F[323,x] = F[324,x]
F[324,x] = -F[337,x]+F[325,x]
F[325,x] = 1/F[41,x]*F[326,x]
F[326,x] = F[327,x]
F[327,x] = -F[330,x]+F[328,x]
F[328,x] = 1/F[41,x]*F[329,x]
F[329,x] = F[15,x]
F[330,x] = F[288,x]+F[331,x]
F[331,x] = F[332,x]
F[332,x] = F[333,x]*F[41,x]
F[333,x] = F[334,x]+F[335,x]
F[334,x] = F[4,x]*F[95,x]
F[335,x] = F[336,x]
F[336,x] = F[120,x]*F[41,x]*F[46,x]
F[337,x] = F[177,x]*F[46,x]
F[338,x] = F[171,x]*F[177,x]
F[339,x] = F[340,x]
F[340,x] = F[171,x]*F[41,x]*F[79,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{60}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{3}+2 x^{2} F_{11} \left(x \right)^{2}+x^{2} F_{11}\! \left(x \right)+x F_{11} \left(x \right)^{2}+2 x F_{11}\! \left(x \right)+x
F_{12}\! \left(x \right) = x^{2}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{16}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{41}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{52}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{51}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x^{2} F_{22} \left(x \right)^{3}-x^{2} F_{22} \left(x \right)^{2}+x F_{22} \left(x \right)^{2}+1
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right) F_{25}\! \left(x \right) F_{41}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{41}\! \left(x \right) F_{46}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{33}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = x
F_{42}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right) F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{22}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{25}\! \left(x \right) F_{41}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{5}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{41}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{27}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{41}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{339}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{178}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{169}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{0}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{15}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{80}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{10}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{41}\! \left(x \right) F_{76}\! \left(x \right) F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{80}\! \left(x \right) = F_{16}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{41}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{160}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{155}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{150}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{41}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{148}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{22}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{140}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{131}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{0}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{2}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{41}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{129}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{127}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{41}\! \left(x \right) F_{48}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{15}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{125}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{2}\! \left(x \right)
F_{109}\! \left(x \right) = F_{0}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{41}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{122}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{41}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{109}\! \left(x \right) F_{94}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{109}\! \left(x \right) F_{120}\! \left(x \right) F_{22}\! \left(x \right) F_{41}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{22}\! \left(x \right) F_{41}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = \frac{F_{124}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{124}\! \left(x \right) = F_{96}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{102}\! \left(x \right) F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{104}\! \left(x \right) F_{41}\! \left(x \right)
F_{129}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{92}\! \left(x \right)
F_{130}\! \left(x \right) = F_{4}\! \left(x \right)+F_{99}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{41}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{138}\! \left(x \right)
F_{136}\! \left(x \right) = F_{109}\! \left(x \right) F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{2}\! \left(x \right)+F_{96}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right) F_{90}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{144}\! \left(x \right)
F_{141}\! \left(x \right) = F_{100}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right) F_{55}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{0}\! \left(x \right) F_{146}\! \left(x \right) F_{41}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{102}\! \left(x \right) F_{29}\! \left(x \right) F_{41}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{25}\! \left(x \right) F_{41}\! \left(x \right) F_{90}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{41}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{0}\! \left(x \right) F_{29}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{158}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{41}\! \left(x \right) F_{86}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{151}\! \left(x \right) F_{41}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{41}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{165}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{79} \left(x \right)^{2} F_{22}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{94}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{79}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{32}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{177}\! \left(x \right) F_{41}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{175}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{46}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{171}\! \left(x \right) F_{41}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{172}\! \left(x \right) F_{41}\! \left(x \right)
F_{177}\! \left(x \right) = F_{0}\! \left(x \right)+F_{100}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{41}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{195}\! \left(x \right)
F_{181}\! \left(x \right) = F_{102}\! \left(x \right) F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{188}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{46}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{22}\! \left(x \right) F_{67}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{173}\! \left(x \right) F_{25}\! \left(x \right) F_{41}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{41}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{182}\! \left(x \right) F_{25}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{22}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{172}\! \left(x \right) F_{41}\! \left(x \right)
F_{195}\! \left(x \right) = \frac{F_{196}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right) F_{41}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = -F_{338}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right) F_{41}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{323}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right) F_{210}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{46}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{56}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{41}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{212}\! \left(x \right)
F_{211}\! \left(x \right) = F_{0}\! \left(x \right) F_{78}\! \left(x \right)
F_{212}\! \left(x \right) = -F_{321}\! \left(x \right)+F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right)
F_{215}\! \left(x \right) = \frac{F_{216}\! \left(x \right)}{F_{172}\! \left(x \right) F_{41}\! \left(x \right)}
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)
F_{217}\! \left(x \right) = -F_{227}\! \left(x \right)+F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)+F_{224}\! \left(x \right)
F_{219}\! \left(x \right) = F_{202}\! \left(x \right)+F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)+F_{222}\! \left(x \right)
F_{221}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right) F_{46}\! \left(x \right)
F_{224}\! \left(x \right) = -F_{202}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = \frac{F_{226}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{226}\! \left(x \right) = F_{68}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)+F_{230}\! \left(x \right)
F_{228}\! \left(x \right) = F_{0}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{173}\! \left(x \right)+F_{4}\! \left(x \right)
F_{230}\! \left(x \right) = -F_{231}\! \left(x \right)+F_{224}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{172}\! \left(x \right) F_{233}\! \left(x \right) F_{41}\! \left(x \right)
F_{233}\! \left(x \right) = F_{104}\! \left(x \right)+F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = -F_{320}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right) F_{41}\! \left(x \right)
F_{237}\! \left(x \right) = \frac{F_{238}\! \left(x \right)}{F_{243}\! \left(x \right) F_{41}\! \left(x \right)}
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = -F_{318}\! \left(x \right)+F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{274}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right) F_{273}\! \left(x \right) F_{41}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right) F_{41}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)+F_{249}\! \left(x \right)
F_{246}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{1}\! \left(x \right)+F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{247}\! \left(x \right) F_{41}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{251}\! \left(x \right) F_{259}\! \left(x \right) F_{41}\! \left(x \right)
F_{251}\! \left(x \right) = F_{247}\! \left(x \right)+F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{41}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)+F_{255}\! \left(x \right)+F_{258}\! \left(x \right)
F_{254}\! \left(x \right) = 0
F_{255}\! \left(x \right) = F_{256}\! \left(x \right) F_{41}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{247}\! \left(x \right) F_{41}\! \left(x \right)
F_{258}\! \left(x \right) = F_{252}\! \left(x \right) F_{41}\! \left(x \right)
F_{259}\! \left(x \right) = F_{247}\! \left(x \right)+F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)+F_{76}\! \left(x \right)
F_{261}\! \left(x \right) = F_{254}\! \left(x \right)+F_{262}\! \left(x \right)+F_{272}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{41}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)+F_{265}\! \left(x \right)
F_{264}\! \left(x \right) = F_{253}\! \left(x \right)+F_{256}\! \left(x \right)
F_{265}\! \left(x \right) = F_{261}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = 2 F_{254}\! \left(x \right)+F_{267}\! \left(x \right)+F_{268}\! \left(x \right)
F_{267}\! \left(x \right) = F_{261}\! \left(x \right) F_{41}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right) F_{41}\! \left(x \right)
F_{269}\! \left(x \right) = F_{266}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{41}\! \left(x \right) F_{76}\! \left(x \right)
F_{272}\! \left(x \right) = F_{260}\! \left(x \right) F_{41}\! \left(x \right)
F_{273}\! \left(x \right) = F_{104}\! \left(x \right)+F_{109}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right) F_{279}\! \left(x \right) F_{41}\! \left(x \right)
F_{276}\! \left(x \right) = F_{243}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right)
F_{279}\! \left(x \right) = \frac{F_{280}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = -F_{296}\! \left(x \right)+F_{282}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = -F_{289}\! \left(x \right)+F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = \frac{F_{285}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{129}\! \left(x \right)
F_{287}\! \left(x \right) = F_{142}\! \left(x \right)+F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)+F_{294}\! \left(x \right)
F_{290}\! \left(x \right) = \frac{F_{291}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)
F_{292}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{98}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{109}\! \left(x \right) F_{146}\! \left(x \right) F_{41}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right) F_{302}\! \left(x \right) F_{41}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right) F_{41}\! \left(x \right)
F_{300}\! \left(x \right) = \frac{F_{301}\! \left(x \right)}{F_{22}\! \left(x \right) F_{41}\! \left(x \right)}
F_{301}\! \left(x \right) = F_{146}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)+F_{306}\! \left(x \right)
F_{303}\! \left(x \right) = F_{1}\! \left(x \right)+F_{304}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)
F_{305}\! \left(x \right) = F_{251}\! \left(x \right) F_{41}\! \left(x \right)
F_{306}\! \left(x \right) = \frac{F_{307}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{307}\! \left(x \right) = -F_{316}\! \left(x \right)+F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = -F_{311}\! \left(x \right)+F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = \frac{F_{310}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{310}\! \left(x \right) = F_{15}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right) F_{41}\! \left(x \right)
F_{313}\! \left(x \right) = \frac{F_{314}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{69}\! \left(x \right)+F_{80}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right)+F_{76}\! \left(x \right)
F_{317}\! \left(x \right) = F_{304}\! \left(x \right) F_{41}\! \left(x \right)
F_{318}\! \left(x \right) = F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{279}\! \left(x \right) F_{41}\! \left(x \right)
F_{320}\! \left(x \right) = F_{109}\! \left(x \right) F_{41}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = F_{233}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = -F_{337}\! \left(x \right)+F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = \frac{F_{326}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = -F_{330}\! \left(x \right)+F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = \frac{F_{329}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{329}\! \left(x \right) = F_{15}\! \left(x \right)
F_{330}\! \left(x \right) = F_{288}\! \left(x \right)+F_{331}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right) F_{41}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right)+F_{335}\! \left(x \right)
F_{334}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{335}\! \left(x \right) = F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{120}\! \left(x \right) F_{41}\! \left(x \right) F_{46}\! \left(x \right)
F_{337}\! \left(x \right) = F_{177}\! \left(x \right) F_{46}\! \left(x \right)
F_{338}\! \left(x \right) = F_{171}\! \left(x \right) F_{177}\! \left(x \right)
F_{339}\! \left(x \right) = F_{340}\! \left(x \right)
F_{340}\! \left(x \right) = F_{171}\! \left(x \right) F_{41}\! \left(x \right) F_{79}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_41(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_41(x)*F_7(x))
Eq(F_7(x), F_60(x) + F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x**2*(F_11(x) + 1)**3 - x*(x - 1)*(F_11(x) + 1)**2)
Eq(F_12(x), x**2)
Eq(F_13(x), F_14(x) + F_16(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), -F_2(x) + F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_41(x))
Eq(F_18(x), F_19(x) + F_52(x))
Eq(F_19(x), F_20(x) + F_51(x))
Eq(F_20(x), F_21(x) + F_23(x))
Eq(F_21(x), F_2(x)*F_22(x))
Eq(F_22(x), x**2*F_22(x)**3 - x*(x - 1)*F_22(x)**2 + 1)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_19(x)*F_25(x)*F_41(x))
Eq(F_25(x), F_26(x)/(F_41(x)*F_46(x)))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x)*F_41(x))
Eq(F_29(x), F_30(x)/F_41(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), -F_22(x) + F_32(x))
Eq(F_32(x), F_33(x)/F_0(x))
Eq(F_33(x), F_34(x) - F_42(x))
Eq(F_34(x), F_35(x)/F_41(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x) + F_37(x))
Eq(F_37(x), -F_2(x) + F_38(x))
Eq(F_38(x), -F_22(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_41(x))
Eq(F_40(x), F_2(x))
Eq(F_41(x), x)
Eq(F_42(x), F_43(x) - F_45(x))
Eq(F_43(x), F_44(x)/F_41(x))
Eq(F_44(x), F_37(x))
Eq(F_45(x), F_2(x)*F_32(x))
Eq(F_46(x), F_47(x) + F_51(x))
Eq(F_47(x), F_20(x) + F_48(x))
Eq(F_48(x), F_22(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_25(x)*F_41(x)*F_48(x))
Eq(F_51(x), F_22(x)*F_5(x))
Eq(F_52(x), F_53(x) + F_56(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_55(x))
Eq(F_55(x), F_11(x) + F_21(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_41(x)*F_58(x))
Eq(F_58(x), F_27(x) + F_59(x))
Eq(F_59(x), F_14(x)*F_22(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_41(x)*F_62(x))
Eq(F_62(x), F_339(x) + F_63(x))
Eq(F_63(x), F_178(x) + F_64(x))
Eq(F_64(x), F_169(x) + F_65(x))
Eq(F_65(x), F_0(x)*F_66(x))
Eq(F_66(x), F_4(x) + F_67(x))
Eq(F_67(x), F_14(x) + F_68(x))
Eq(F_68(x), -F_14(x) + F_69(x))
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_41(x))
Eq(F_71(x), F_15(x))
Eq(F_72(x), F_73(x) + F_80(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_10(x) + F_75(x))
Eq(F_75(x), F_41(x)*F_76(x)*F_79(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_41(x)*F_78(x)*F_79(x))
Eq(F_78(x), F_1(x) + F_76(x))
Eq(F_79(x), F_1(x) + F_41(x))
Eq(F_80(x), F_16(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_41(x)*F_83(x))
Eq(F_83(x), F_160(x) + F_84(x))
Eq(F_84(x), F_155(x) + F_85(x))
Eq(F_85(x), F_150(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_41(x)*F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_41(x)*F_78(x)*F_79(x)*F_90(x))
Eq(F_90(x), F_148(x) + F_91(x))
Eq(F_91(x), F_22(x)*F_92(x))
Eq(F_92(x), F_140(x) + F_93(x))
Eq(F_93(x), F_131(x) + F_94(x))
Eq(F_94(x), F_0(x) + F_95(x))
Eq(F_95(x), F_2(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_41(x)*F_98(x))
Eq(F_98(x), F_129(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_127(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_41(x))
Eq(F_102(x), F_103(x)/(F_41(x)*F_48(x)))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x) - F_107(x))
Eq(F_105(x), F_106(x)/F_41(x))
Eq(F_106(x), F_15(x))
Eq(F_107(x), F_108(x) + F_125(x))
Eq(F_108(x), F_109(x)*F_2(x))
Eq(F_109(x), F_0(x) + F_110(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_41(x))
Eq(F_112(x), F_113(x) + F_122(x))
Eq(F_113(x), F_109(x) + F_114(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_41(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_109(x)*F_94(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_109(x)*F_120(x)*F_22(x)*F_41(x))
Eq(F_120(x), F_121(x)/(F_22(x)*F_41(x)))
Eq(F_121(x), F_122(x))
Eq(F_122(x), -F_114(x) + F_123(x))
Eq(F_123(x), F_124(x)/F_41(x))
Eq(F_124(x), F_96(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_102(x)*F_19(x)*F_41(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_104(x)*F_41(x))
Eq(F_129(x), -F_130(x) + F_92(x))
Eq(F_130(x), F_4(x) + F_99(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_0(x)*F_2(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_41(x))
Eq(F_135(x), F_136(x) + F_138(x))
Eq(F_136(x), F_109(x)*F_137(x))
Eq(F_137(x), F_2(x) + F_96(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_102(x)*F_41(x)*F_90(x))
Eq(F_140(x), F_141(x) + F_144(x))
Eq(F_141(x), F_100(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_102(x)*F_41(x)*F_55(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_0(x)*F_146(x)*F_41(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_102(x)*F_29(x)*F_41(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_25(x)*F_41(x)*F_90(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x)*F_41(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_0(x)*F_29(x)*F_41(x)*F_78(x)*F_79(x))
Eq(F_155(x), F_156(x) + F_158(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_41(x)*F_86(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_151(x)*F_41(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_162(x)*F_41(x))
Eq(F_162(x), F_163(x) + F_165(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_22(x)*F_41(x)*F_78(x)*F_79(x)**2*F_94(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_79(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_32(x)*F_41(x)*F_78(x)*F_79(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_171(x)*F_177(x)*F_41(x))
Eq(F_171(x), F_172(x) + F_175(x))
Eq(F_172(x), F_173(x) + F_46(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_171(x)*F_41(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_172(x)*F_41(x))
Eq(F_177(x), F_0(x) + F_100(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_180(x)*F_41(x))
Eq(F_180(x), F_181(x) + F_195(x))
Eq(F_181(x), F_102(x)*F_182(x))
Eq(F_182(x), F_183(x) + F_188(x))
Eq(F_183(x), F_184(x) + F_46(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_22(x)*F_67(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_173(x)*F_25(x)*F_41(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_190(x)*F_41(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_182(x)*F_25(x))
Eq(F_192(x), F_193(x)*F_22(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_172(x)*F_41(x))
Eq(F_195(x), F_196(x)/F_41(x))
Eq(F_196(x), F_197(x))
Eq(F_197(x), F_198(x)*F_41(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x) - F_338(x))
Eq(F_200(x), F_201(x)/F_41(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_204(x)*F_41(x))
Eq(F_204(x), F_205(x) + F_323(x))
Eq(F_205(x), F_206(x)*F_210(x))
Eq(F_206(x), F_207(x) + F_46(x))
Eq(F_207(x), F_208(x) + F_56(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_0(x)*F_22(x)*F_41(x))
Eq(F_210(x), F_211(x) + F_212(x))
Eq(F_211(x), F_0(x)*F_78(x))
Eq(F_212(x), F_213(x) - F_321(x))
Eq(F_213(x), F_214(x))
Eq(F_214(x), F_215(x)*F_41(x)*F_78(x))
Eq(F_215(x), F_216(x)/(F_172(x)*F_41(x)))
Eq(F_216(x), F_217(x))
Eq(F_217(x), F_218(x) - F_227(x))
Eq(F_218(x), F_219(x) + F_224(x))
Eq(F_219(x), F_202(x) + F_220(x))
Eq(F_220(x), F_221(x) + F_222(x))
Eq(F_221(x), F_0(x)*F_4(x))
Eq(F_222(x), F_223(x))
Eq(F_223(x), F_102(x)*F_41(x)*F_46(x))
Eq(F_224(x), -F_202(x) + F_225(x))
Eq(F_225(x), F_226(x)/F_41(x))
Eq(F_226(x), F_68(x))
Eq(F_227(x), F_228(x) + F_230(x))
Eq(F_228(x), F_0(x)*F_229(x))
Eq(F_229(x), F_173(x) + F_4(x))
Eq(F_230(x), F_224(x) - F_231(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_172(x)*F_233(x)*F_41(x))
Eq(F_233(x), F_104(x) + F_234(x))
Eq(F_234(x), F_235(x) - F_320(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_237(x)*F_41(x))
Eq(F_237(x), F_238(x)/(F_243(x)*F_41(x)))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_240(x) - F_318(x))
Eq(F_240(x), F_241(x) + F_274(x))
Eq(F_241(x), F_242(x))
Eq(F_242(x), F_243(x)*F_273(x)*F_41(x))
Eq(F_243(x), F_244(x))
Eq(F_244(x), F_245(x)*F_41(x))
Eq(F_245(x), F_246(x) + F_249(x))
Eq(F_246(x), F_0(x)*F_22(x)*F_247(x))
Eq(F_247(x), F_1(x) + F_248(x))
Eq(F_248(x), F_247(x)*F_41(x))
Eq(F_249(x), F_250(x))
Eq(F_250(x), F_0(x)*F_22(x)*F_251(x)*F_259(x)*F_41(x))
Eq(F_251(x), F_247(x) + F_252(x))
Eq(F_252(x), F_253(x) + F_41(x))
Eq(F_253(x), F_254(x) + F_255(x) + F_258(x))
Eq(F_254(x), 0)
Eq(F_255(x), F_256(x)*F_41(x))
Eq(F_256(x), F_257(x))
Eq(F_257(x), F_247(x)*F_41(x))
Eq(F_258(x), F_252(x)*F_41(x))
Eq(F_259(x), F_247(x) + F_260(x))
Eq(F_260(x), F_261(x) + F_76(x))
Eq(F_261(x), F_254(x) + F_262(x) + F_272(x))
Eq(F_262(x), F_263(x)*F_41(x))
Eq(F_263(x), F_264(x) + F_265(x))
Eq(F_264(x), F_253(x) + F_256(x))
Eq(F_265(x), F_261(x) + F_266(x))
Eq(F_266(x), 2*F_254(x) + F_267(x) + F_268(x))
Eq(F_267(x), F_261(x)*F_41(x))
Eq(F_268(x), F_269(x)*F_41(x))
Eq(F_269(x), F_266(x) + F_270(x))
Eq(F_270(x), F_271(x))
Eq(F_271(x), F_41(x)*F_76(x))
Eq(F_272(x), F_260(x)*F_41(x))
Eq(F_273(x), F_104(x) + F_109(x))
Eq(F_274(x), F_275(x))
Eq(F_275(x), F_276(x)*F_279(x)*F_41(x))
Eq(F_276(x), F_243(x) + F_277(x))
Eq(F_277(x), F_278(x))
Eq(F_278(x), F_0(x)*F_22(x))
Eq(F_279(x), F_280(x)/F_41(x))
Eq(F_280(x), F_281(x))
Eq(F_281(x), F_282(x) - F_296(x))
Eq(F_282(x), F_283(x))
Eq(F_283(x), F_284(x) - F_289(x))
Eq(F_284(x), F_285(x)/F_41(x))
Eq(F_285(x), F_286(x))
Eq(F_286(x), F_129(x) - F_287(x))
Eq(F_287(x), F_142(x) + F_288(x))
Eq(F_288(x), F_0(x)*F_2(x))
Eq(F_289(x), F_290(x) + F_294(x))
Eq(F_290(x), F_291(x)/F_41(x))
Eq(F_291(x), F_292(x))
Eq(F_292(x), -F_288(x) + F_293(x))
Eq(F_293(x), -F_140(x) + F_98(x))
Eq(F_294(x), F_295(x))
Eq(F_295(x), F_109(x)*F_146(x)*F_41(x))
Eq(F_296(x), F_297(x))
Eq(F_297(x), F_298(x)*F_302(x)*F_41(x))
Eq(F_298(x), F_299(x))
Eq(F_299(x), F_300(x)*F_41(x))
Eq(F_300(x), F_301(x)/(F_22(x)*F_41(x)))
Eq(F_301(x), F_146(x))
Eq(F_302(x), F_303(x) + F_306(x))
Eq(F_303(x), F_1(x) + F_304(x))
Eq(F_304(x), F_305(x))
Eq(F_305(x), F_251(x)*F_41(x))
Eq(F_306(x), F_307(x)/F_41(x))
Eq(F_307(x), F_308(x) - F_316(x))
Eq(F_308(x), F_309(x) - F_311(x))
Eq(F_309(x), F_310(x)/F_41(x))
Eq(F_310(x), F_15(x))
Eq(F_311(x), F_312(x))
Eq(F_312(x), F_313(x)*F_41(x))
Eq(F_313(x), F_314(x)/F_41(x))
Eq(F_314(x), F_315(x))
Eq(F_315(x), F_69(x) + F_80(x))
Eq(F_316(x), F_317(x) + F_76(x))
Eq(F_317(x), F_304(x)*F_41(x))
Eq(F_318(x), F_319(x))
Eq(F_319(x), F_0(x)*F_22(x)*F_279(x)*F_41(x))
Eq(F_320(x), F_109(x)*F_41(x))
Eq(F_321(x), F_322(x))
Eq(F_322(x), F_233(x)*F_41(x)*F_78(x))
Eq(F_323(x), F_324(x))
Eq(F_324(x), F_325(x) - F_337(x))
Eq(F_325(x), F_326(x)/F_41(x))
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_328(x) - F_330(x))
Eq(F_328(x), F_329(x)/F_41(x))
Eq(F_329(x), F_15(x))
Eq(F_330(x), F_288(x) + F_331(x))
Eq(F_331(x), F_332(x))
Eq(F_332(x), F_333(x)*F_41(x))
Eq(F_333(x), F_334(x) + F_335(x))
Eq(F_334(x), F_4(x)*F_95(x))
Eq(F_335(x), F_336(x))
Eq(F_336(x), F_120(x)*F_41(x)*F_46(x))
Eq(F_337(x), F_177(x)*F_46(x))
Eq(F_338(x), F_171(x)*F_177(x))
Eq(F_339(x), F_340(x))
Eq(F_340(x), F_171(x)*F_41(x)*F_79(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, 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0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "indices": [0, 0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 2
Strategy pack name: point_and_row_placements_req_corrob
Tree: http://www.permpal.com/tree/24439/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[14,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[88,x]
F[5,x] = F[14,x]*F[6,x]
F[6,x] = F[4,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[83,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = F[4,x]^2
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[15,x]*F[16,x]*F[4,x]
F[14,x] = x
F[15,x] = 1+x^2*F[15,x]^3+(-x^2+x)*F[15,x]^2
F[16,x] = 1/F[14,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]+F[68,x]
F[19,x] = F[20,x]+F[21,x]+F[67,x]
F[20,x] = 0
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[0,x]+F[19,x]
F[24,x] = 2*F[20,x]+F[25,x]+F[26,x]
F[25,x] = F[14,x]*F[23,x]
F[26,x] = F[14,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[52,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = -F[1,x]-F[34,x]-F[46,x]-F[64,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[18,x]+F[4,x]
F[33,x] = F[18,x]
F[34,x] = F[14,x]*F[35,x]
F[35,x] = F[23,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[32,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[9,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[19,x]*F[4,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[15,x]*F[16,x]*F[19,x]
F[46,x] = F[14,x]*F[47,x]
F[47,x] = F[48,x]+F[63,x]
F[48,x] = F[49,x]+F[6,x]
F[49,x] = 1/F[14,x]*F[50,x]
F[50,x] = -F[20,x]-F[51,x]-F[62,x]+F[18,x]
F[51,x] = F[14,x]*F[52,x]
F[52,x] = F[22,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[14,x]*F[55,x]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[22,x]*F[4,x]
F[58,x] = F[59,x]
F[59,x] = F[14,x]*F[15,x]*F[16,x]*F[22,x]
F[60,x] = F[61,x]
F[61,x] = F[14,x]*F[15,x]*F[16,x]
F[62,x] = F[14,x]*F[33,x]
F[63,x] = F[49,x]
F[64,x] = F[14,x]*F[65,x]
F[65,x] = F[31,x]+F[66,x]
F[66,x] = F[33,x]
F[67,x] = F[14,x]*F[18,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[70,x]
F[70,x] = F[42,x]+F[71,x]
F[71,x] = F[33,x]+F[72,x]+F[73,x]
F[72,x] = F[14,x]*F[60,x]
F[73,x] = F[74,x]
F[74,x] = F[14,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[14,x]*F[16,x]*F[77,x]
F[77,x] = F[78,x]+F[81,x]
F[78,x] = F[1,x]+F[79,x]+F[80,x]
F[79,x] = F[14,x]*F[15,x]
F[80,x] = F[14,x]*F[77,x]
F[81,x] = F[82,x]
F[82,x] = F[14,x]*F[77,x]*F[78,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[16,x]*F[85,x]
F[85,x] = F[15,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[14,x]*F[15,x]*F[77,x]
F[88,x] = F[14,x]*F[32,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{88}\! \left(x \right)
F_{5}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{4}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{83}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = F_{4} \left(x \right)^{2}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = x^{2} F_{15} \left(x \right)^{3}-x^{2} F_{15} \left(x \right)^{2}+x F_{15} \left(x \right)^{2}+1
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{68}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{67}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{34}\! \left(x \right)-F_{46}\! \left(x \right)-F_{64}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \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_{9}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{46}\! \left(x \right) = F_{14}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{63}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{6}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{50}\! \left(x \right) = -F_{20}\! \left(x \right)-F_{51}\! \left(x \right)-F_{62}\! \left(x \right)+F_{18}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{22}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{62}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{63}\! \left(x \right) = F_{49}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{31}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{33}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{42}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{33}\! \left(x \right)+F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right) F_{60}\! \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_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \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_{1}\! \left(x \right)+F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right) F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{15}\! \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_{15}\! \left(x \right) F_{77}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right) F_{32}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_14(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_88(x))
Eq(F_5(x), F_14(x)*F_6(x))
Eq(F_6(x), F_4(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_83(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), F_4(x)**2)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_15(x)*F_16(x)*F_4(x))
Eq(F_14(x), x)
Eq(F_15(x), x**2*F_15(x)**3 - x*(x - 1)*F_15(x)**2 + 1)
Eq(F_16(x), F_17(x)/F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) + F_68(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_67(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_0(x) + F_19(x))
Eq(F_24(x), 2*F_20(x) + F_25(x) + F_26(x))
Eq(F_25(x), F_14(x)*F_23(x))
Eq(F_26(x), F_14(x)*F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x) - F_52(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), -F_1(x) + F_31(x) - F_34(x) - F_46(x) - F_64(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_18(x) + F_4(x))
Eq(F_33(x), F_18(x))
Eq(F_34(x), F_14(x)*F_35(x))
Eq(F_35(x), F_23(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_32(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_9(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_19(x)*F_4(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_15(x)*F_16(x)*F_19(x))
Eq(F_46(x), F_14(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_63(x))
Eq(F_48(x), F_49(x) + F_6(x))
Eq(F_49(x), F_50(x)/F_14(x))
Eq(F_50(x), F_18(x) - F_20(x) - F_51(x) - F_62(x))
Eq(F_51(x), F_14(x)*F_52(x))
Eq(F_52(x), F_22(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_14(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_22(x)*F_4(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_14(x)*F_15(x)*F_16(x)*F_22(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_14(x)*F_15(x)*F_16(x))
Eq(F_62(x), F_14(x)*F_33(x))
Eq(F_63(x), F_49(x))
Eq(F_64(x), F_14(x)*F_65(x))
Eq(F_65(x), F_31(x) + F_66(x))
Eq(F_66(x), F_33(x))
Eq(F_67(x), F_14(x)*F_18(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_70(x))
Eq(F_70(x), F_42(x) + F_71(x))
Eq(F_71(x), F_33(x) + F_72(x) + F_73(x))
Eq(F_72(x), F_14(x)*F_60(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_14(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_14(x)*F_16(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_81(x))
Eq(F_78(x), F_1(x) + F_79(x) + F_80(x))
Eq(F_79(x), F_14(x)*F_15(x))
Eq(F_80(x), F_14(x)*F_77(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_14(x)*F_77(x)*F_78(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_16(x)*F_85(x))
Eq(F_85(x), F_15(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_14(x)*F_15(x)*F_77(x))
Eq(F_88(x), F_14(x)*F_32(x))
Pack JSON:
{"name": "point_and_row_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 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], [1, 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": [[1, 0], [1, 0], [1, 0], [2, 0]]}, 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[2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[1, 0]]}]}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24970/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[40,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[40,x]*F[7,x]
F[7,x] = F[288,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[40,x]
F[11,x] = F[12,x]+F[183,x]
F[12,x] = F[13,x]+F[14,x]
F[13,x] = F[0,x]*F[8,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[40,x]*F[88,x]
F[16,x] = F[17,x]+F[53,x]
F[17,x] = F[18,x]+F[51,x]
F[18,x] = F[19,x]+F[50,x]
F[19,x] = F[20,x]+F[45,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = 1+x^2*F[21,x]^3+(-x^2+x)*F[21,x]^2
F[22,x] = F[23,x]
F[23,x] = F[20,x]*F[24,x]*F[40,x]
F[24,x] = 1/F[18,x]/F[40,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]*F[40,x]
F[27,x] = 1/F[40,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = -F[21,x]+F[30,x]
F[30,x] = 1/F[0,x]*F[31,x]
F[31,x] = -F[41,x]+F[32,x]
F[32,x] = 1/F[40,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = x*(1+F[35,x])^2*(x*F[35,x]+1)
F[36,x] = -F[2,x]+F[37,x]
F[37,x] = -F[21,x]+F[38,x]
F[38,x] = 1/F[40,x]*F[39,x]
F[39,x] = F[2,x]
F[40,x] = x
F[41,x] = -F[44,x]+F[42,x]
F[42,x] = 1/F[40,x]*F[43,x]
F[43,x] = F[36,x]
F[44,x] = F[2,x]*F[30,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[2,x]*F[21,x]
F[47,x] = F[48,x]
F[48,x] = F[24,x]*F[40,x]*F[49,x]
F[49,x] = F[45,x]+F[50,x]
F[50,x] = F[21,x]*F[5,x]
F[51,x] = F[52,x]
F[52,x] = F[16,x]*F[40,x]
F[53,x] = F[54,x]+F[67,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[56,x]
F[56,x] = F[0,x]*F[21,x]*F[40,x]
F[57,x] = F[58,x]
F[58,x] = F[40,x]^2*F[0,x]*F[21,x]*F[59,x]*F[60,x]
F[59,x] = F[1,x]+F[40,x]
F[60,x] = F[1,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[40,x]*F[63,x]
F[63,x] = F[59,x]+F[64,x]
F[64,x] = F[61,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[40,x]*F[61,x]
F[67,x] = F[68,x,1]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[40,x]*F[70,x,k[0]]
F[70,x,k[0]] = F[22,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x]+F[76,x,k[0]]
F[72,x] = F[47,x]+F[73,x]
F[73,x] = F[21,x]*F[74,x]
F[74,x] = F[2,x]+F[75,x]
F[75,x] = -F[2,x]+F[5,x]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[78,x]*F[79,x,k[0]]*F[80,x,k[0]]*F[81,x,k[0]]
F[78,x] = F[22,x]+F[72,x]
F[79,x,k[0]] = k[0]*x
F[80,x,k[0]] = F[1,x]+F[79,x,k[0]]
F[81,x,k[0]] = F[1,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[79,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[80,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[82,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[79,x,k[0]]*F[82,x,k[0]]
F[88,x] = F[0,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[40,x]*F[91,x]
F[91,x] = 1/F[20,x]/F[40,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[95,x]
F[95,x] = F[20,x]*F[40,x]*F[88,x]
F[96,x] = F[97,x]
F[97,x] = F[40,x]*F[98,x]
F[98,x] = F[151,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[20,x]*F[40,x]
F[101,x] = 1/F[21,x]/F[40,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = -F[129,x]+F[104,x]
F[104,x] = 1/F[40,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[40,x]
F[108,x] = F[109,x]+F[112,x]
F[109,x] = F[110,x]+F[89,x]
F[110,x] = F[111,x]
F[111,x] = F[40,x]*F[93,x]
F[112,x] = -F[150,x]+F[113,x]
F[113,x] = F[114,x]+F[141,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[0,x]+F[116,x]
F[116,x] = F[106,x]+F[2,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[0,x]*F[2,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[40,x]
F[121,x] = F[122,x]+F[135,x]
F[122,x] = F[123,x]*F[124,x]
F[123,x] = F[106,x]+F[2,x]
F[124,x] = F[0,x]+F[125,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[40,x]
F[127,x] = F[103,x]+F[128,x]
F[128,x] = F[124,x]+F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]*F[40,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[115,x]*F[124,x]
F[133,x] = F[134,x]
F[134,x] = F[101,x]*F[124,x]*F[21,x]*F[40,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[40,x]*F[91,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[113,x]*F[21,x]
F[139,x] = F[140,x]
F[140,x] = F[137,x]*F[24,x]*F[40,x]
F[141,x] = F[142,x]+F[146,x]
F[142,x] = F[143,x]+F[89,x]
F[143,x] = F[144,x]
F[144,x] = F[145,x]*F[40,x]*F[91,x]
F[145,x] = F[35,x]+F[46,x]
F[146,x] = F[147,x]
F[147,x] = F[0,x]*F[148,x]*F[40,x]
F[148,x] = F[149,x]
F[149,x] = F[27,x]*F[40,x]*F[91,x]
F[150,x] = F[109,x]+F[4,x]
F[151,x] = F[152,x]+F[177,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[40,x]
F[154,x] = 1/F[40,x]*F[155,x]
F[155,x] = F[156,x]
F[156,x] = -F[182,x]+F[157,x]
F[157,x] = 1/F[40,x]*F[158,x]
F[158,x] = F[159,x]
F[159,x] = -F[162,x]+F[160,x]
F[160,x] = 1/F[40,x]*F[161,x]
F[161,x] = F[75,x]
F[162,x] = F[163,x]+F[167,x]
F[163,x] = F[164,x]+F[165,x]
F[164,x] = F[0,x]*F[2,x]
F[165,x] = F[166,x]
F[166,x] = F[40,x]*F[49,x]*F[88,x]
F[167,x] = F[168,x]+F[174,x]
F[168,x] = F[169,x]
F[169,x] = F[170,x]*F[40,x]
F[170,x] = F[171,x]+F[172,x]
F[171,x] = F[116,x]*F[4,x]
F[172,x] = F[173,x]
F[173,x] = F[101,x]*F[18,x]*F[40,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x]*F[40,x]
F[176,x] = F[177,x]+F[180,x]
F[177,x] = F[178,x]
F[178,x] = F[154,x]*F[179,x]*F[40,x]
F[179,x] = F[22,x]+F[35,x]
F[180,x] = F[181,x]
F[181,x] = F[154,x]*F[40,x]*F[49,x]
F[182,x] = F[20,x]*F[88,x]
F[183,x] = F[184,x]
F[184,x] = F[185,x]*F[40,x]
F[185,x] = F[186,x]+F[200,x]
F[186,x] = F[187,x]*F[91,x]
F[187,x] = F[188,x]+F[193,x]
F[188,x] = F[18,x]+F[189,x]
F[189,x] = F[190,x]+F[191,x]
F[190,x] = F[21,x]*F[9,x]
F[191,x] = F[192,x]
F[192,x] = F[24,x]*F[40,x]*F[51,x]
F[193,x] = F[194,x]
F[194,x] = F[195,x]*F[40,x]
F[195,x] = F[196,x]+F[197,x]
F[196,x] = F[187,x]*F[24,x]
F[197,x] = F[198,x]*F[21,x]
F[198,x] = F[199,x]
F[199,x] = F[17,x]*F[40,x]
F[200,x] = 1/F[40,x]*F[201,x]
F[201,x] = F[202,x]
F[202,x] = F[203,x]*F[40,x]
F[203,x] = F[204,x]
F[205,x,k[0]] = F[204,x]+F[343,x,k[0]]
F[206,x,k[0]] = F[205,x,k[0]]*F[40,x]
F[206,x,k[0]] = F[207,x,k[0]]
F[207,x,k[0]] = F[208,x]+F[335,x,k[0]]
F[208,x] = F[209,x]
F[209,x] = F[210,x]*F[40,x]
F[210,x] = F[211,x]+F[333,x]
F[211,x] = F[212,x]*F[215,x]
F[212,x] = F[18,x]+F[213,x]
F[213,x] = F[214,x]
F[214,x] = F[18,x]*F[40,x]
F[215,x] = F[216,x]+F[217,x]
F[216,x] = F[0,x]*F[60,x]
F[217,x] = -F[312,x]+F[218,x]
F[218,x] = -F[222,x]+F[219,x]
F[219,x] = 1/F[40,x]*F[220,x]
F[220,x] = F[221,x]
F[221,x] = -F[61,x]+F[89,x]
F[222,x] = F[223,x]
F[223,x] = F[224,x]*F[40,x]
F[224,x] = -F[311,x]+F[225,x]
F[225,x] = -F[229,x]+F[226,x]
F[226,x] = 1/F[40,x]*F[227,x]
F[227,x] = F[228,x]
F[228,x] = -F[109,x]+F[219,x]
F[229,x] = F[230,x]+F[232,x]
F[230,x] = F[156,x]+F[231,x]
F[231,x] = F[110,x]
F[232,x] = -F[265,x]+F[233,x]
F[233,x] = F[234,x]
F[234,x] = -F[239,x]+F[235,x]
F[235,x] = 1/F[40,x]*F[236,x]
F[236,x] = F[237,x]
F[237,x] = -F[238,x]+F[112,x]
F[238,x] = F[143,x]+F[164,x]
F[239,x] = F[240,x]+F[263,x]
F[240,x] = F[241,x]+F[257,x]
F[241,x] = F[242,x]
F[242,x] = F[243,x]*F[40,x]*F[88,x]
F[243,x] = 1/F[40,x]*F[244,x]
F[244,x] = F[245,x]
F[245,x] = F[246,x]+F[29,x]
F[246,x] = F[247,x]
F[247,x] = F[21,x]*F[248,x]*F[40,x]*F[61,x]
F[248,x] = F[249,x]+F[252,x]
F[249,x] = F[1,x]+F[250,x]
F[250,x] = F[251,x]
F[251,x] = F[249,x]*F[40,x]
F[252,x] = F[253,x]+F[40,x]
F[253,x] = F[254,x]+F[255,x]+F[256,x]
F[254,x] = 0
F[255,x] = F[250,x]*F[40,x]
F[256,x] = F[252,x]*F[40,x]
F[257,x] = -F[261,x]+F[258,x]
F[258,x] = 1/F[40,x]*F[259,x]
F[259,x] = F[260,x]
F[260,x] = -F[141,x]+F[108,x]
F[261,x] = F[241,x]+F[262,x]
F[262,x] = F[0,x]*F[124,x]
F[263,x] = F[264,x]
F[264,x] = F[124,x]*F[148,x]*F[40,x]
F[265,x] = F[266,x]
F[266,x] = F[267,x]*F[271,x]*F[40,x]
F[267,x] = F[268,x]
F[268,x] = F[269,x]*F[40,x]
F[269,x] = 1/F[21,x]/F[40,x]*F[270,x]
F[270,x] = F[148,x]
F[271,x] = F[272,x]+F[275,x]
F[272,x] = F[1,x]+F[273,x]
F[273,x] = F[274,x]
F[274,x] = F[248,x]*F[40,x]
F[275,x] = 1/F[40,x]*F[276,x]
F[276,x] = -F[309,x]+F[277,x]
F[277,x] = -F[280,x]+F[278,x]
F[278,x] = 1/F[40,x]*F[279,x]
F[279,x] = F[75,x]
F[280,x] = F[281,x]
F[281,x] = F[282,x]*F[40,x]
F[282,x] = 1/F[40,x]*F[283,x]
F[283,x] = F[284,x]
F[284,x] = F[285,x]+F[294,x]
F[285,x] = -F[288,x]+F[286,x]
F[286,x] = 1/F[40,x]*F[287,x]
F[287,x] = F[75,x]
F[288,x] = F[289,x]+F[294,x]
F[289,x] = F[290,x]
F[290,x] = F[291,x]+F[293,x]
F[291,x] = F[292,x]+F[35,x]
F[292,x] = x^2
F[293,x] = F[40,x]*F[59,x]*F[61,x]
F[294,x] = F[295,x]
F[295,x] = F[296,x]*F[40,x]
F[296,x] = F[297,x]+F[303,x]
F[297,x] = F[298,x]+F[302,x]
F[298,x] = F[299,x,1]
F[299,x,k[0]] = F[300,x,k[0]]+F[46,x]
F[300,x,k[0]] = F[301,x,k[0]]
F[301,x,k[0]] = F[145,x]*F[79,x,k[0]]*F[80,x,k[0]]*F[81,x,k[0]]
F[302,x] = F[71,x,1]
F[303,x] = F[304,x]+F[67,x]
F[304,x] = F[305,x]+F[307,x]
F[305,x] = F[306,x]
F[306,x] = F[145,x]*F[40,x]
F[307,x] = F[308,x]
F[308,x] = F[40,x]^2*F[145,x]*F[59,x]*F[60,x]
F[309,x] = F[310,x]+F[61,x]
F[310,x] = F[273,x]*F[40,x]
F[311,x] = F[218,x]*F[59,x]
F[312,x] = F[313,x]
F[313,x] = F[314,x]*F[40,x]*F[60,x]
F[314,x] = 1/F[17,x]/F[40,x]*F[315,x]
F[315,x] = F[316,x]
F[316,x] = -F[331,x]+F[317,x]
F[317,x] = F[318,x]+F[320,x]
F[318,x] = F[319,x]
F[319,x] = F[18,x]*F[40,x]*F[93,x]
F[320,x] = -F[328,x]+F[321,x]
F[321,x] = -F[324,x]+F[322,x]
F[322,x] = 1/F[40,x]*F[323,x]
F[323,x] = F[285,x]
F[324,x] = F[325,x]+F[326,x]
F[325,x] = F[4,x]^2
F[326,x] = F[327,x]
F[327,x] = F[18,x]*F[224,x]*F[40,x]
F[328,x] = F[318,x]+F[329,x]
F[329,x] = F[330,x]
F[330,x] = F[18,x]*F[40,x]*F[91,x]
F[331,x] = -F[332,x]+F[208,x]
F[332,x] = F[0,x]*F[51,x]
F[333,x] = F[334,x]
F[334,x] = F[154,x]*F[18,x]*F[40,x]
F[335,x,k[0]] = F[336,x,k[0]]
F[336,x,k[0]] = F[337,x,k[0]]*F[59,x]
F[337,x,k[0]] = k[0]*F[338,x]
F[338,x] = F[339,x]
F[339,x] = F[340,x]*F[40,x]
F[340,x] = F[213,x]+F[341,x]
F[341,x] = F[342,x]
F[342,x] = F[213,x]*F[40,x]
F[343,x,k[0]] = F[344,x]+F[345,x,k[0]]
F[344,x] = F[16,x]*F[88,x]
F[345,x,k[0]] = F[346,x,k[0]]*F[59,x]
F[346,x,k[0]] = k[0]*F[347,x]
F[347,x] = 1/F[40,x]*F[348,x]
F[348,x] = F[338,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{40}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{288}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{183}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right) F_{88}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{53}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{51}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{50}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{45}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = x^{2} F_{21} \left(x \right)^{3}-x^{2} F_{21} \left(x \right)^{2}+x F_{21} \left(x \right)^{2}+1
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right) F_{24}\! \left(x \right) F_{40}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{18}\! \left(x \right) F_{40}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{21}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{31}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = x^{2} F_{35} \left(x \right)^{3}+2 x^{2} F_{35} \left(x \right)^{2}+x^{2} F_{35}\! \left(x \right)+x F_{35} \left(x \right)^{2}+2 x F_{35}\! \left(x \right)+x
F_{36}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{21}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = x
F_{41}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{36}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right) F_{30}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right) F_{21}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{24}\! \left(x \right) F_{40}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{67}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{0}\! \left(x \right) F_{21}\! \left(x \right) F_{40}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{40} \left(x \right)^{2} F_{0}\! \left(x \right) F_{21}\! \left(x \right) F_{59}\! \left(x \right) F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)
F_{60}\! \left(x \right) = F_{1}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{40}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{59}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{40}\! \left(x \right) F_{61}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x , 1\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x \right)+F_{76}\! \left(x , y\right)
F_{72}\! \left(x \right) = F_{47}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{21}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x \right) F_{79}\! \left(x , y\right) F_{80}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{78}\! \left(x \right) = F_{22}\! \left(x \right)+F_{72}\! \left(x \right)
F_{79}\! \left(x , y\right) = y x
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{79}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{79}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{79}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{88}\! \left(x \right) = F_{0}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{40}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{20}\! \left(x \right) F_{40}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{20}\! \left(x \right) F_{40}\! \left(x \right) F_{88}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{40}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{151}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{20}\! \left(x \right) F_{40}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{21}\! \left(x \right) F_{40}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{129}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{40}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{112}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{89}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{40}\! \left(x \right) F_{93}\! \left(x \right)
F_{112}\! \left(x \right) = -F_{150}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{141}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{0}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{106}\! \left(x \right)+F_{2}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{40}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{135}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{106}\! \left(x \right)+F_{2}\! \left(x \right)
F_{124}\! \left(x \right) = F_{0}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{40}\! \left(x \right)
F_{127}\! \left(x \right) = F_{103}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{124}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{40}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{115}\! \left(x \right) F_{124}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{101}\! \left(x \right) F_{124}\! \left(x \right) F_{21}\! \left(x \right) F_{40}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{40}\! \left(x \right) F_{91}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{113}\! \left(x \right) F_{21}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{137}\! \left(x \right) F_{24}\! \left(x \right) F_{40}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{89}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{40}\! \left(x \right) F_{91}\! \left(x \right)
F_{145}\! \left(x \right) = F_{35}\! \left(x \right)+F_{46}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{0}\! \left(x \right) F_{148}\! \left(x \right) F_{40}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{27}\! \left(x \right) F_{40}\! \left(x \right) F_{91}\! \left(x \right)
F_{150}\! \left(x \right) = F_{109}\! \left(x \right)+F_{4}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{177}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{40}\! \left(x \right)
F_{154}\! \left(x \right) = \frac{F_{155}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = -F_{182}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = \frac{F_{158}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = -F_{162}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = \frac{F_{161}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{161}\! \left(x \right) = F_{75}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{167}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{40}\! \left(x \right) F_{49}\! \left(x \right) F_{88}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{174}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{40}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{172}\! \left(x \right)
F_{171}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{101}\! \left(x \right) F_{18}\! \left(x \right) F_{40}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{40}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{180}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{154}\! \left(x \right) F_{179}\! \left(x \right) F_{40}\! \left(x \right)
F_{179}\! \left(x \right) = F_{22}\! \left(x \right)+F_{35}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{154}\! \left(x \right) F_{40}\! \left(x \right) F_{49}\! \left(x \right)
F_{182}\! \left(x \right) = F_{20}\! \left(x \right) F_{88}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{40}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{200}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{91}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{193}\! \left(x \right)
F_{188}\! \left(x \right) = F_{18}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{191}\! \left(x \right)
F_{190}\! \left(x \right) = F_{21}\! \left(x \right) F_{9}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{24}\! \left(x \right) F_{40}\! \left(x \right) F_{51}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right) F_{40}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{196}\! \left(x \right) = F_{187}\! \left(x \right) F_{24}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right) F_{21}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{17}\! \left(x \right) F_{40}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{40}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{205}\! \left(x , y\right) = F_{204}\! \left(x \right)+F_{343}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{205}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x \right)+F_{335}\! \left(x , y\right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right) F_{40}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{333}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right) F_{215}\! \left(x \right)
F_{212}\! \left(x \right) = F_{18}\! \left(x \right)+F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{18}\! \left(x \right) F_{40}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)+F_{217}\! \left(x \right)
F_{216}\! \left(x \right) = F_{0}\! \left(x \right) F_{60}\! \left(x \right)
F_{217}\! \left(x \right) = -F_{312}\! \left(x \right)+F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = -F_{222}\! \left(x \right)+F_{219}\! \left(x \right)
F_{219}\! \left(x \right) = \frac{F_{220}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{89}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right) F_{40}\! \left(x \right)
F_{224}\! \left(x \right) = -F_{311}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = -F_{229}\! \left(x \right)+F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = \frac{F_{227}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{219}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{232}\! \left(x \right)
F_{230}\! \left(x \right) = F_{156}\! \left(x \right)+F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{110}\! \left(x \right)
F_{232}\! \left(x \right) = -F_{265}\! \left(x \right)+F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = -F_{239}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = \frac{F_{236}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = -F_{238}\! \left(x \right)+F_{112}\! \left(x \right)
F_{238}\! \left(x \right) = F_{143}\! \left(x \right)+F_{164}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)+F_{263}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{257}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right) F_{40}\! \left(x \right) F_{88}\! \left(x \right)
F_{243}\! \left(x \right) = \frac{F_{244}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)+F_{29}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{21}\! \left(x \right) F_{248}\! \left(x \right) F_{40}\! \left(x \right) F_{61}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right)+F_{252}\! \left(x \right)
F_{249}\! \left(x \right) = F_{1}\! \left(x \right)+F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{249}\! \left(x \right) F_{40}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{40}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)+F_{255}\! \left(x \right)+F_{256}\! \left(x \right)
F_{254}\! \left(x \right) = 0
F_{255}\! \left(x \right) = F_{250}\! \left(x \right) F_{40}\! \left(x \right)
F_{256}\! \left(x \right) = F_{252}\! \left(x \right) F_{40}\! \left(x \right)
F_{257}\! \left(x \right) = -F_{261}\! \left(x \right)+F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = \frac{F_{259}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = -F_{141}\! \left(x \right)+F_{108}\! \left(x \right)
F_{261}\! \left(x \right) = F_{241}\! \left(x \right)+F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{0}\! \left(x \right) F_{124}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{124}\! \left(x \right) F_{148}\! \left(x \right) F_{40}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right) F_{271}\! \left(x \right) F_{40}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right) F_{40}\! \left(x \right)
F_{269}\! \left(x \right) = \frac{F_{270}\! \left(x \right)}{F_{21}\! \left(x \right) F_{40}\! \left(x \right)}
F_{270}\! \left(x \right) = F_{148}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)+F_{275}\! \left(x \right)
F_{272}\! \left(x \right) = F_{1}\! \left(x \right)+F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{248}\! \left(x \right) F_{40}\! \left(x \right)
F_{275}\! \left(x \right) = \frac{F_{276}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{276}\! \left(x \right) = -F_{309}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = -F_{280}\! \left(x \right)+F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = \frac{F_{279}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{279}\! \left(x \right) = F_{75}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right) F_{40}\! \left(x \right)
F_{282}\! \left(x \right) = \frac{F_{283}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right)+F_{294}\! \left(x \right)
F_{285}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = \frac{F_{287}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{287}\! \left(x \right) = F_{75}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right)+F_{294}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right)+F_{293}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{35}\! \left(x \right)
F_{292}\! \left(x \right) = x^{2}
F_{293}\! \left(x \right) = F_{40}\! \left(x \right) F_{59}\! \left(x \right) F_{61}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right) F_{40}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)+F_{303}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)+F_{302}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x , 1\right)
F_{299}\! \left(x , y\right) = F_{300}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{300}\! \left(x , y\right) = F_{301}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{145}\! \left(x \right) F_{79}\! \left(x , y\right) F_{80}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{302}\! \left(x \right) = F_{71}\! \left(x , 1\right)
F_{303}\! \left(x \right) = F_{304}\! \left(x \right)+F_{67}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{307}\! \left(x \right)
F_{305}\! \left(x \right) = F_{306}\! \left(x \right)
F_{306}\! \left(x \right) = F_{145}\! \left(x \right) F_{40}\! \left(x \right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{40} \left(x \right)^{2} F_{145}\! \left(x \right) F_{59}\! \left(x \right) F_{60}\! \left(x \right)
F_{309}\! \left(x \right) = F_{310}\! \left(x \right)+F_{61}\! \left(x \right)
F_{310}\! \left(x \right) = F_{273}\! \left(x \right) F_{40}\! \left(x \right)
F_{311}\! \left(x \right) = F_{218}\! \left(x \right) F_{59}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right) F_{40}\! \left(x \right) F_{60}\! \left(x \right)
F_{314}\! \left(x \right) = \frac{F_{315}\! \left(x \right)}{F_{17}\! \left(x \right) F_{40}\! \left(x \right)}
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = -F_{331}\! \left(x \right)+F_{317}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)+F_{320}\! \left(x \right)
F_{318}\! \left(x \right) = F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = F_{18}\! \left(x \right) F_{40}\! \left(x \right) F_{93}\! \left(x \right)
F_{320}\! \left(x \right) = -F_{328}\! \left(x \right)+F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = -F_{324}\! \left(x \right)+F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = \frac{F_{323}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{323}\! \left(x \right) = F_{285}\! \left(x \right)
F_{324}\! \left(x \right) = F_{325}\! \left(x \right)+F_{326}\! \left(x \right)
F_{325}\! \left(x \right) = F_{4} \left(x \right)^{2}
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{18}\! \left(x \right) F_{224}\! \left(x \right) F_{40}\! \left(x \right)
F_{328}\! \left(x \right) = F_{318}\! \left(x \right)+F_{329}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)
F_{330}\! \left(x \right) = F_{18}\! \left(x \right) F_{40}\! \left(x \right) F_{91}\! \left(x \right)
F_{331}\! \left(x \right) = -F_{332}\! \left(x \right)+F_{208}\! \left(x \right)
F_{332}\! \left(x \right) = F_{0}\! \left(x \right) F_{51}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right)
F_{334}\! \left(x \right) = F_{154}\! \left(x \right) F_{18}\! \left(x \right) F_{40}\! \left(x \right)
F_{335}\! \left(x , y\right) = F_{336}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = F_{337}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{337}\! \left(x , y\right) = y F_{338}\! \left(x \right)
F_{338}\! \left(x \right) = F_{339}\! \left(x \right)
F_{339}\! \left(x \right) = F_{340}\! \left(x \right) F_{40}\! \left(x \right)
F_{340}\! \left(x \right) = F_{213}\! \left(x \right)+F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = F_{342}\! \left(x \right)
F_{342}\! \left(x \right) = F_{213}\! \left(x \right) F_{40}\! \left(x \right)
F_{343}\! \left(x , y\right) = F_{344}\! \left(x \right)+F_{345}\! \left(x , y\right)
F_{344}\! \left(x \right) = F_{16}\! \left(x \right) F_{88}\! \left(x \right)
F_{345}\! \left(x , y\right) = F_{346}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{346}\! \left(x , y\right) = y F_{347}\! \left(x \right)
F_{347}\! \left(x \right) = \frac{F_{348}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{348}\! \left(x \right) = F_{338}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_40(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_40(x)*F_7(x))
Eq(F_7(x), F_288(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_40(x))
Eq(F_11(x), F_12(x) + F_183(x))
Eq(F_12(x), F_13(x) + F_14(x))
Eq(F_13(x), F_0(x)*F_8(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_40(x)*F_88(x))
Eq(F_16(x), F_17(x) + F_53(x))
Eq(F_17(x), F_18(x) + F_51(x))
Eq(F_18(x), F_19(x) + F_50(x))
Eq(F_19(x), F_20(x) + F_45(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), x**2*F_21(x)**3 - x*(x - 1)*F_21(x)**2 + 1)
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_20(x)*F_24(x)*F_40(x))
Eq(F_24(x), F_25(x)/(F_18(x)*F_40(x)))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x)*F_40(x))
Eq(F_27(x), F_28(x)/F_40(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), -F_21(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_0(x))
Eq(F_31(x), F_32(x) - F_41(x))
Eq(F_32(x), F_33(x)/F_40(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), x**2*(F_35(x) + 1)**3 - x*(x - 1)*(F_35(x) + 1)**2)
Eq(F_36(x), -F_2(x) + F_37(x))
Eq(F_37(x), -F_21(x) + F_38(x))
Eq(F_38(x), F_39(x)/F_40(x))
Eq(F_39(x), F_2(x))
Eq(F_40(x), x)
Eq(F_41(x), F_42(x) - F_44(x))
Eq(F_42(x), F_43(x)/F_40(x))
Eq(F_43(x), F_36(x))
Eq(F_44(x), F_2(x)*F_30(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_2(x)*F_21(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_24(x)*F_40(x)*F_49(x))
Eq(F_49(x), F_45(x) + F_50(x))
Eq(F_50(x), F_21(x)*F_5(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_16(x)*F_40(x))
Eq(F_53(x), F_54(x) + F_67(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_0(x)*F_21(x)*F_40(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_0(x)*F_21(x)*F_40(x)**2*F_59(x)*F_60(x))
Eq(F_59(x), F_1(x) + F_40(x))
Eq(F_60(x), F_1(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_40(x)*F_63(x))
Eq(F_63(x), F_59(x) + F_64(x))
Eq(F_64(x), F_61(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_40(x)*F_61(x))
Eq(F_67(x), F_68(x, 1))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_40(x)*F_70(x, k_0))
Eq(F_70(x, k_0), F_22(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x) + F_76(x, k_0))
Eq(F_72(x), F_47(x) + F_73(x))
Eq(F_73(x), F_21(x)*F_74(x))
Eq(F_74(x), F_2(x) + F_75(x))
Eq(F_75(x), -F_2(x) + F_5(x))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x)*F_79(x, k_0)*F_80(x, k_0)*F_81(x, k_0))
Eq(F_78(x), F_22(x) + F_72(x))
Eq(F_79(x, k_0), k_0*x)
Eq(F_80(x, k_0), F_1(x) + F_79(x, k_0))
Eq(F_81(x, k_0), F_1(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_79(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_80(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_82(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_79(x, k_0)*F_82(x, k_0))
Eq(F_88(x), F_0(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_40(x)*F_91(x))
Eq(F_91(x), F_92(x)/(F_20(x)*F_40(x)))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_20(x)*F_40(x)*F_88(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_40(x)*F_98(x))
Eq(F_98(x), F_151(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_20(x)*F_40(x))
Eq(F_101(x), F_102(x)/(F_21(x)*F_40(x)))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x) - F_129(x))
Eq(F_104(x), F_105(x)/F_40(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_40(x))
Eq(F_108(x), F_109(x) + F_112(x))
Eq(F_109(x), F_110(x) + F_89(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_40(x)*F_93(x))
Eq(F_112(x), F_113(x) - F_150(x))
Eq(F_113(x), F_114(x) + F_141(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_0(x) + F_116(x))
Eq(F_116(x), F_106(x) + F_2(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_0(x)*F_2(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_40(x))
Eq(F_121(x), F_122(x) + F_135(x))
Eq(F_122(x), F_123(x)*F_124(x))
Eq(F_123(x), F_106(x) + F_2(x))
Eq(F_124(x), F_0(x) + F_125(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_40(x))
Eq(F_127(x), F_103(x) + F_128(x))
Eq(F_128(x), F_124(x) + F_129(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x)*F_40(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_115(x)*F_124(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_101(x)*F_124(x)*F_21(x)*F_40(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_40(x)*F_91(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_113(x)*F_21(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_137(x)*F_24(x)*F_40(x))
Eq(F_141(x), F_142(x) + F_146(x))
Eq(F_142(x), F_143(x) + F_89(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_145(x)*F_40(x)*F_91(x))
Eq(F_145(x), F_35(x) + F_46(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_0(x)*F_148(x)*F_40(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_27(x)*F_40(x)*F_91(x))
Eq(F_150(x), F_109(x) + F_4(x))
Eq(F_151(x), F_152(x) + F_177(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_40(x))
Eq(F_154(x), F_155(x)/F_40(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x) - F_182(x))
Eq(F_157(x), F_158(x)/F_40(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x) - F_162(x))
Eq(F_160(x), F_161(x)/F_40(x))
Eq(F_161(x), F_75(x))
Eq(F_162(x), F_163(x) + F_167(x))
Eq(F_163(x), F_164(x) + F_165(x))
Eq(F_164(x), F_0(x)*F_2(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_40(x)*F_49(x)*F_88(x))
Eq(F_167(x), F_168(x) + F_174(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_170(x)*F_40(x))
Eq(F_170(x), F_171(x) + F_172(x))
Eq(F_171(x), F_116(x)*F_4(x))
Eq(F_172(x), F_173(x))
Eq(F_173(x), F_101(x)*F_18(x)*F_40(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x)*F_40(x))
Eq(F_176(x), F_177(x) + F_180(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_154(x)*F_179(x)*F_40(x))
Eq(F_179(x), F_22(x) + F_35(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_154(x)*F_40(x)*F_49(x))
Eq(F_182(x), F_20(x)*F_88(x))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_185(x)*F_40(x))
Eq(F_185(x), F_186(x) + F_200(x))
Eq(F_186(x), F_187(x)*F_91(x))
Eq(F_187(x), F_188(x) + F_193(x))
Eq(F_188(x), F_18(x) + F_189(x))
Eq(F_189(x), F_190(x) + F_191(x))
Eq(F_190(x), F_21(x)*F_9(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_24(x)*F_40(x)*F_51(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_195(x)*F_40(x))
Eq(F_195(x), F_196(x) + F_197(x))
Eq(F_196(x), F_187(x)*F_24(x))
Eq(F_197(x), F_198(x)*F_21(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_17(x)*F_40(x))
Eq(F_200(x), F_201(x)/F_40(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_203(x)*F_40(x))
Eq(F_203(x), F_204(x))
Eq(F_205(x, k_0), F_204(x) + F_343(x, k_0))
Eq(F_206(x, k_0), F_205(x, k_0)*F_40(x))
Eq(F_206(x, k_0), F_207(x, k_0))
Eq(F_207(x, k_0), F_208(x) + F_335(x, k_0))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_210(x)*F_40(x))
Eq(F_210(x), F_211(x) + F_333(x))
Eq(F_211(x), F_212(x)*F_215(x))
Eq(F_212(x), F_18(x) + F_213(x))
Eq(F_213(x), F_214(x))
Eq(F_214(x), F_18(x)*F_40(x))
Eq(F_215(x), F_216(x) + F_217(x))
Eq(F_216(x), F_0(x)*F_60(x))
Eq(F_217(x), F_218(x) - F_312(x))
Eq(F_218(x), F_219(x) - F_222(x))
Eq(F_219(x), F_220(x)/F_40(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), -F_61(x) + F_89(x))
Eq(F_222(x), F_223(x))
Eq(F_223(x), F_224(x)*F_40(x))
Eq(F_224(x), F_225(x) - F_311(x))
Eq(F_225(x), F_226(x) - F_229(x))
Eq(F_226(x), F_227(x)/F_40(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), -F_109(x) + F_219(x))
Eq(F_229(x), F_230(x) + F_232(x))
Eq(F_230(x), F_156(x) + F_231(x))
Eq(F_231(x), F_110(x))
Eq(F_232(x), F_233(x) - F_265(x))
Eq(F_233(x), F_234(x))
Eq(F_234(x), F_235(x) - F_239(x))
Eq(F_235(x), F_236(x)/F_40(x))
Eq(F_236(x), F_237(x))
Eq(F_237(x), F_112(x) - F_238(x))
Eq(F_238(x), F_143(x) + F_164(x))
Eq(F_239(x), F_240(x) + F_263(x))
Eq(F_240(x), F_241(x) + F_257(x))
Eq(F_241(x), F_242(x))
Eq(F_242(x), F_243(x)*F_40(x)*F_88(x))
Eq(F_243(x), F_244(x)/F_40(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_246(x) + F_29(x))
Eq(F_246(x), F_247(x))
Eq(F_247(x), F_21(x)*F_248(x)*F_40(x)*F_61(x))
Eq(F_248(x), F_249(x) + F_252(x))
Eq(F_249(x), F_1(x) + F_250(x))
Eq(F_250(x), F_251(x))
Eq(F_251(x), F_249(x)*F_40(x))
Eq(F_252(x), F_253(x) + F_40(x))
Eq(F_253(x), F_254(x) + F_255(x) + F_256(x))
Eq(F_254(x), 0)
Eq(F_255(x), F_250(x)*F_40(x))
Eq(F_256(x), F_252(x)*F_40(x))
Eq(F_257(x), F_258(x) - F_261(x))
Eq(F_258(x), F_259(x)/F_40(x))
Eq(F_259(x), F_260(x))
Eq(F_260(x), F_108(x) - F_141(x))
Eq(F_261(x), F_241(x) + F_262(x))
Eq(F_262(x), F_0(x)*F_124(x))
Eq(F_263(x), F_264(x))
Eq(F_264(x), F_124(x)*F_148(x)*F_40(x))
Eq(F_265(x), F_266(x))
Eq(F_266(x), F_267(x)*F_271(x)*F_40(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_269(x)*F_40(x))
Eq(F_269(x), F_270(x)/(F_21(x)*F_40(x)))
Eq(F_270(x), F_148(x))
Eq(F_271(x), F_272(x) + F_275(x))
Eq(F_272(x), F_1(x) + F_273(x))
Eq(F_273(x), F_274(x))
Eq(F_274(x), F_248(x)*F_40(x))
Eq(F_275(x), F_276(x)/F_40(x))
Eq(F_276(x), F_277(x) - F_309(x))
Eq(F_277(x), F_278(x) - F_280(x))
Eq(F_278(x), F_279(x)/F_40(x))
Eq(F_279(x), F_75(x))
Eq(F_280(x), F_281(x))
Eq(F_281(x), F_282(x)*F_40(x))
Eq(F_282(x), F_283(x)/F_40(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), F_285(x) + F_294(x))
Eq(F_285(x), F_286(x) - F_288(x))
Eq(F_286(x), F_287(x)/F_40(x))
Eq(F_287(x), F_75(x))
Eq(F_288(x), F_289(x) + F_294(x))
Eq(F_289(x), F_290(x))
Eq(F_290(x), F_291(x) + F_293(x))
Eq(F_291(x), F_292(x) + F_35(x))
Eq(F_292(x), x**2)
Eq(F_293(x), F_40(x)*F_59(x)*F_61(x))
Eq(F_294(x), F_295(x))
Eq(F_295(x), F_296(x)*F_40(x))
Eq(F_296(x), F_297(x) + F_303(x))
Eq(F_297(x), F_298(x) + F_302(x))
Eq(F_298(x), F_299(x, 1))
Eq(F_299(x, k_0), F_300(x, k_0) + F_46(x))
Eq(F_300(x, k_0), F_301(x, k_0))
Eq(F_301(x, k_0), F_145(x)*F_79(x, k_0)*F_80(x, k_0)*F_81(x, k_0))
Eq(F_302(x), F_71(x, 1))
Eq(F_303(x), F_304(x) + F_67(x))
Eq(F_304(x), F_305(x) + F_307(x))
Eq(F_305(x), F_306(x))
Eq(F_306(x), F_145(x)*F_40(x))
Eq(F_307(x), F_308(x))
Eq(F_308(x), F_145(x)*F_40(x)**2*F_59(x)*F_60(x))
Eq(F_309(x), F_310(x) + F_61(x))
Eq(F_310(x), F_273(x)*F_40(x))
Eq(F_311(x), F_218(x)*F_59(x))
Eq(F_312(x), F_313(x))
Eq(F_313(x), F_314(x)*F_40(x)*F_60(x))
Eq(F_314(x), F_315(x)/(F_17(x)*F_40(x)))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_317(x) - F_331(x))
Eq(F_317(x), F_318(x) + F_320(x))
Eq(F_318(x), F_319(x))
Eq(F_319(x), F_18(x)*F_40(x)*F_93(x))
Eq(F_320(x), F_321(x) - F_328(x))
Eq(F_321(x), F_322(x) - F_324(x))
Eq(F_322(x), F_323(x)/F_40(x))
Eq(F_323(x), F_285(x))
Eq(F_324(x), F_325(x) + F_326(x))
Eq(F_325(x), F_4(x)**2)
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_18(x)*F_224(x)*F_40(x))
Eq(F_328(x), F_318(x) + F_329(x))
Eq(F_329(x), F_330(x))
Eq(F_330(x), F_18(x)*F_40(x)*F_91(x))
Eq(F_331(x), F_208(x) - F_332(x))
Eq(F_332(x), F_0(x)*F_51(x))
Eq(F_333(x), F_334(x))
Eq(F_334(x), F_154(x)*F_18(x)*F_40(x))
Eq(F_335(x, k_0), F_336(x, k_0))
Eq(F_336(x, k_0), F_337(x, k_0)*F_59(x))
Eq(F_337(x, k_0), k_0*F_338(x))
Eq(F_338(x), F_339(x))
Eq(F_339(x), F_340(x)*F_40(x))
Eq(F_340(x), F_213(x) + F_341(x))
Eq(F_341(x), F_342(x))
Eq(F_342(x), F_213(x)*F_40(x))
Eq(F_343(x, k_0), F_344(x) + F_345(x, k_0))
Eq(F_344(x), F_16(x)*F_88(x))
Eq(F_345(x, k_0), F_346(x, k_0)*F_59(x))
Eq(F_346(x, k_0), k_0*F_347(x))
Eq(F_347(x), F_348(x)/F_40(x))
Eq(F_348(x), F_338(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", 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true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25155/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[41,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[41,x]*F[7,x]
F[7,x] = F[60,x]+F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = x*(1+F[11,x])^2*(x*F[11,x]+1)
F[12,x] = x^2
F[13,x] = F[14,x]+F[16,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = -F[2,x]+F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[41,x]
F[18,x] = F[19,x]+F[52,x]
F[19,x] = F[20,x]+F[51,x]
F[20,x] = F[21,x]+F[23,x]
F[21,x] = F[2,x]*F[22,x]
F[22,x] = 1+x^2*F[22,x]^3+(-x^2+x)*F[22,x]^2
F[23,x] = F[24,x]
F[24,x] = F[19,x]*F[25,x]*F[41,x]
F[25,x] = 1/F[41,x]/F[46,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]*F[41,x]
F[29,x] = 1/F[41,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = -F[22,x]+F[32,x]
F[32,x] = 1/F[0,x]*F[33,x]
F[33,x] = -F[42,x]+F[34,x]
F[34,x] = 1/F[41,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[11,x]+F[37,x]
F[37,x] = -F[2,x]+F[38,x]
F[38,x] = -F[22,x]+F[39,x]
F[39,x] = 1/F[41,x]*F[40,x]
F[40,x] = F[2,x]
F[41,x] = x
F[42,x] = -F[45,x]+F[43,x]
F[43,x] = 1/F[41,x]*F[44,x]
F[44,x] = F[37,x]
F[45,x] = F[2,x]*F[32,x]
F[46,x] = F[47,x]+F[51,x]
F[47,x] = F[20,x]+F[48,x]
F[48,x] = F[22,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[25,x]*F[41,x]*F[48,x]
F[51,x] = F[22,x]*F[5,x]
F[52,x] = F[53,x]+F[56,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[55,x]
F[55,x] = F[11,x]+F[21,x]
F[56,x] = F[57,x]
F[57,x] = F[41,x]*F[58,x]
F[58,x] = F[27,x]+F[59,x]
F[59,x] = F[14,x]*F[22,x]
F[60,x] = F[61,x]
F[61,x] = F[41,x]*F[62,x]
F[62,x] = F[339,x]+F[63,x]
F[63,x] = F[178,x]+F[64,x]
F[64,x] = F[169,x]+F[65,x]
F[65,x] = F[0,x]*F[66,x]
F[66,x] = F[4,x]+F[67,x]
F[67,x] = F[14,x]+F[68,x]
F[68,x] = -F[14,x]+F[69,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[41,x]*F[71,x]
F[71,x] = F[15,x]
F[72,x] = F[73,x]+F[80,x]
F[73,x] = F[74,x]
F[74,x] = F[10,x]+F[75,x]
F[75,x] = F[41,x]*F[76,x]*F[79,x]
F[76,x] = F[77,x]
F[77,x] = F[41,x]*F[78,x]*F[79,x]
F[78,x] = F[1,x]+F[76,x]
F[79,x] = F[1,x]+F[41,x]
F[80,x] = F[16,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[41,x]*F[83,x]
F[83,x] = F[160,x]+F[84,x]
F[84,x] = F[155,x]+F[85,x]
F[85,x] = F[150,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[41,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[41,x]*F[78,x]*F[79,x]*F[90,x]
F[90,x] = F[148,x]+F[91,x]
F[91,x] = F[22,x]*F[92,x]
F[92,x] = F[140,x]+F[93,x]
F[93,x] = F[131,x]+F[94,x]
F[94,x] = F[0,x]+F[95,x]
F[95,x] = F[2,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[41,x]*F[98,x]
F[98,x] = F[129,x]+F[99,x]
F[99,x] = F[100,x]+F[127,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[41,x]
F[102,x] = 1/F[41,x]/F[48,x]*F[103,x]
F[103,x] = F[104,x]
F[104,x] = -F[107,x]+F[105,x]
F[105,x] = 1/F[41,x]*F[106,x]
F[106,x] = F[15,x]
F[107,x] = F[108,x]+F[125,x]
F[108,x] = F[109,x]*F[2,x]
F[109,x] = F[0,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[41,x]
F[112,x] = F[113,x]+F[122,x]
F[113,x] = F[109,x]+F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[41,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[109,x]*F[94,x]
F[118,x] = F[119,x]
F[119,x] = F[109,x]*F[120,x]*F[22,x]*F[41,x]
F[120,x] = 1/F[22,x]/F[41,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = -F[114,x]+F[123,x]
F[123,x] = 1/F[41,x]*F[124,x]
F[124,x] = F[96,x]
F[125,x] = F[126,x]
F[126,x] = F[102,x]*F[19,x]*F[41,x]
F[127,x] = F[128,x]
F[128,x] = F[104,x]*F[41,x]
F[129,x] = -F[130,x]+F[92,x]
F[130,x] = F[4,x]+F[99,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[0,x]*F[2,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[41,x]
F[135,x] = F[136,x]+F[138,x]
F[136,x] = F[109,x]*F[137,x]
F[137,x] = F[2,x]+F[96,x]
F[138,x] = F[139,x]
F[139,x] = F[102,x]*F[41,x]*F[90,x]
F[140,x] = F[141,x]+F[144,x]
F[141,x] = F[100,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[102,x]*F[41,x]*F[55,x]
F[144,x] = F[145,x]
F[145,x] = F[0,x]*F[146,x]*F[41,x]
F[146,x] = F[147,x]
F[147,x] = F[102,x]*F[29,x]*F[41,x]
F[148,x] = F[149,x]
F[149,x] = F[25,x]*F[41,x]*F[90,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]*F[41,x]
F[153,x] = F[154,x]
F[154,x] = F[0,x]*F[29,x]*F[41,x]*F[78,x]*F[79,x]
F[155,x] = F[156,x]+F[158,x]
F[156,x] = F[157,x]
F[157,x] = F[41,x]*F[86,x]
F[158,x] = F[159,x]
F[159,x] = F[151,x]*F[41,x]
F[160,x] = F[161,x]
F[161,x] = F[162,x]*F[41,x]
F[162,x] = F[163,x]+F[165,x]
F[163,x] = F[164,x]
F[164,x] = F[79,x]^2*F[22,x]*F[41,x]*F[78,x]*F[94,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[79,x]
F[167,x] = F[168,x]
F[168,x] = F[32,x]*F[41,x]*F[78,x]*F[79,x]
F[169,x] = F[170,x]
F[170,x] = F[171,x]*F[177,x]*F[41,x]
F[171,x] = F[172,x]+F[175,x]
F[172,x] = F[173,x]+F[46,x]
F[173,x] = F[174,x]
F[174,x] = F[171,x]*F[41,x]
F[175,x] = F[176,x]
F[176,x] = F[172,x]*F[41,x]
F[177,x] = F[0,x]+F[100,x]
F[178,x] = F[179,x]
F[179,x] = F[180,x]*F[41,x]
F[180,x] = F[181,x]+F[195,x]
F[181,x] = F[102,x]*F[182,x]
F[182,x] = F[183,x]+F[188,x]
F[183,x] = F[184,x]+F[46,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[22,x]*F[67,x]
F[186,x] = F[187,x]
F[187,x] = F[173,x]*F[25,x]*F[41,x]
F[188,x] = F[189,x]
F[189,x] = F[190,x]*F[41,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[182,x]*F[25,x]
F[192,x] = F[193,x]*F[22,x]
F[193,x] = F[194,x]
F[194,x] = F[172,x]*F[41,x]
F[195,x] = 1/F[41,x]*F[196,x]
F[196,x] = F[197,x]
F[197,x] = F[198,x]*F[41,x]
F[198,x] = F[199,x]
F[199,x] = -F[338,x]+F[200,x]
F[200,x] = 1/F[41,x]*F[201,x]
F[201,x] = F[202,x]
F[202,x] = F[203,x]
F[203,x] = F[204,x]*F[41,x]
F[204,x] = F[205,x]+F[323,x]
F[205,x] = F[206,x]*F[210,x]
F[206,x] = F[207,x]+F[46,x]
F[207,x] = F[208,x]+F[56,x]
F[208,x] = F[209,x]
F[209,x] = F[0,x]*F[22,x]*F[41,x]
F[210,x] = F[211,x]+F[212,x]
F[211,x] = F[0,x]*F[78,x]
F[212,x] = -F[321,x]+F[213,x]
F[213,x] = F[214,x]
F[214,x] = F[215,x]*F[41,x]*F[78,x]
F[215,x] = 1/F[172,x]/F[41,x]*F[216,x]
F[216,x] = F[217,x]
F[217,x] = -F[227,x]+F[218,x]
F[218,x] = F[219,x]+F[224,x]
F[219,x] = F[202,x]+F[220,x]
F[220,x] = F[221,x]+F[222,x]
F[221,x] = F[0,x]*F[4,x]
F[222,x] = F[223,x]
F[223,x] = F[102,x]*F[41,x]*F[46,x]
F[224,x] = -F[202,x]+F[225,x]
F[225,x] = 1/F[41,x]*F[226,x]
F[226,x] = F[68,x]
F[227,x] = F[228,x]+F[230,x]
F[228,x] = F[0,x]*F[229,x]
F[229,x] = F[173,x]+F[4,x]
F[230,x] = -F[231,x]+F[224,x]
F[231,x] = F[232,x]
F[232,x] = F[172,x]*F[233,x]*F[41,x]
F[233,x] = F[104,x]+F[234,x]
F[234,x] = -F[320,x]+F[235,x]
F[235,x] = F[236,x]
F[236,x] = F[237,x]*F[41,x]
F[237,x] = 1/F[243,x]/F[41,x]*F[238,x]
F[238,x] = F[239,x]
F[239,x] = -F[318,x]+F[240,x]
F[240,x] = F[241,x]+F[274,x]
F[241,x] = F[242,x]
F[242,x] = F[243,x]*F[273,x]*F[41,x]
F[243,x] = F[244,x]
F[244,x] = F[245,x]*F[41,x]
F[245,x] = F[246,x]+F[249,x]
F[246,x] = F[0,x]*F[22,x]*F[247,x]
F[247,x] = F[1,x]+F[248,x]
F[248,x] = F[247,x]*F[41,x]
F[249,x] = F[250,x]
F[250,x] = F[0,x]*F[22,x]*F[251,x]*F[259,x]*F[41,x]
F[251,x] = F[247,x]+F[252,x]
F[252,x] = F[253,x]+F[41,x]
F[253,x] = F[254,x]+F[255,x]+F[258,x]
F[254,x] = 0
F[255,x] = F[256,x]*F[41,x]
F[256,x] = F[257,x]
F[257,x] = F[247,x]*F[41,x]
F[258,x] = F[252,x]*F[41,x]
F[259,x] = F[247,x]+F[260,x]
F[260,x] = F[261,x]+F[76,x]
F[261,x] = F[254,x]+F[262,x]+F[272,x]
F[262,x] = F[263,x]*F[41,x]
F[263,x] = F[264,x]+F[265,x]
F[264,x] = F[253,x]+F[256,x]
F[265,x] = F[261,x]+F[266,x]
F[266,x] = 2*F[254,x]+F[267,x]+F[268,x]
F[267,x] = F[261,x]*F[41,x]
F[268,x] = F[269,x]*F[41,x]
F[269,x] = F[266,x]+F[270,x]
F[270,x] = F[271,x]
F[271,x] = F[41,x]*F[76,x]
F[272,x] = F[260,x]*F[41,x]
F[273,x] = F[104,x]+F[109,x]
F[274,x] = F[275,x]
F[275,x] = F[276,x]*F[279,x]*F[41,x]
F[276,x] = F[243,x]+F[277,x]
F[277,x] = F[278,x]
F[278,x] = F[0,x]*F[22,x]
F[279,x] = 1/F[41,x]*F[280,x]
F[280,x] = F[281,x]
F[281,x] = -F[296,x]+F[282,x]
F[282,x] = F[283,x]
F[283,x] = -F[289,x]+F[284,x]
F[284,x] = 1/F[41,x]*F[285,x]
F[285,x] = F[286,x]
F[286,x] = -F[287,x]+F[129,x]
F[287,x] = F[142,x]+F[288,x]
F[288,x] = F[0,x]*F[2,x]
F[289,x] = F[290,x]+F[294,x]
F[290,x] = 1/F[41,x]*F[291,x]
F[291,x] = F[292,x]
F[292,x] = -F[288,x]+F[293,x]
F[293,x] = -F[140,x]+F[98,x]
F[294,x] = F[295,x]
F[295,x] = F[109,x]*F[146,x]*F[41,x]
F[296,x] = F[297,x]
F[297,x] = F[298,x]*F[302,x]*F[41,x]
F[298,x] = F[299,x]
F[299,x] = F[300,x]*F[41,x]
F[300,x] = 1/F[22,x]/F[41,x]*F[301,x]
F[301,x] = F[146,x]
F[302,x] = F[303,x]+F[306,x]
F[303,x] = F[1,x]+F[304,x]
F[304,x] = F[305,x]
F[305,x] = F[251,x]*F[41,x]
F[306,x] = 1/F[41,x]*F[307,x]
F[307,x] = -F[316,x]+F[308,x]
F[308,x] = -F[311,x]+F[309,x]
F[309,x] = 1/F[41,x]*F[310,x]
F[310,x] = F[15,x]
F[311,x] = F[312,x]
F[312,x] = F[313,x]*F[41,x]
F[313,x] = 1/F[41,x]*F[314,x]
F[314,x] = F[315,x]
F[315,x] = F[69,x]+F[80,x]
F[316,x] = F[317,x]+F[76,x]
F[317,x] = F[304,x]*F[41,x]
F[318,x] = F[319,x]
F[319,x] = F[0,x]*F[22,x]*F[279,x]*F[41,x]
F[320,x] = F[109,x]*F[41,x]
F[321,x] = F[322,x]
F[322,x] = F[233,x]*F[41,x]*F[78,x]
F[323,x] = F[324,x]
F[324,x] = -F[337,x]+F[325,x]
F[325,x] = 1/F[41,x]*F[326,x]
F[326,x] = F[327,x]
F[327,x] = -F[330,x]+F[328,x]
F[328,x] = 1/F[41,x]*F[329,x]
F[329,x] = F[15,x]
F[330,x] = F[288,x]+F[331,x]
F[331,x] = F[332,x]
F[332,x] = F[333,x]*F[41,x]
F[333,x] = F[334,x]+F[335,x]
F[334,x] = F[4,x]*F[95,x]
F[335,x] = F[336,x]
F[336,x] = F[120,x]*F[41,x]*F[46,x]
F[337,x] = F[177,x]*F[46,x]
F[338,x] = F[171,x]*F[177,x]
F[339,x] = F[340,x]
F[340,x] = F[171,x]*F[41,x]*F[79,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{60}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{3}+2 x^{2} F_{11} \left(x \right)^{2}+x^{2} F_{11}\! \left(x \right)+x F_{11} \left(x \right)^{2}+2 x F_{11}\! \left(x \right)+x
F_{12}\! \left(x \right) = x^{2}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{16}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{41}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{52}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{51}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x^{2} F_{22} \left(x \right)^{3}-x^{2} F_{22} \left(x \right)^{2}+x F_{22} \left(x \right)^{2}+1
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right) F_{25}\! \left(x \right) F_{41}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{41}\! \left(x \right) F_{46}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{33}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = x
F_{42}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right) F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{22}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{25}\! \left(x \right) F_{41}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{5}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{41}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{27}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{41}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{339}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{178}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{169}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{0}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{15}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{80}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{10}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{41}\! \left(x \right) F_{76}\! \left(x \right) F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{80}\! \left(x \right) = F_{16}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{41}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{160}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{155}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{150}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{41}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{148}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{22}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{140}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{131}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{0}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{2}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{41}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{129}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{127}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{41}\! \left(x \right) F_{48}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{15}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{125}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{2}\! \left(x \right)
F_{109}\! \left(x \right) = F_{0}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{41}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{122}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{41}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{109}\! \left(x \right) F_{94}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{109}\! \left(x \right) F_{120}\! \left(x \right) F_{22}\! \left(x \right) F_{41}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{22}\! \left(x \right) F_{41}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = \frac{F_{124}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{124}\! \left(x \right) = F_{96}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{102}\! \left(x \right) F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{104}\! \left(x \right) F_{41}\! \left(x \right)
F_{129}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{92}\! \left(x \right)
F_{130}\! \left(x \right) = F_{4}\! \left(x \right)+F_{99}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{41}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{138}\! \left(x \right)
F_{136}\! \left(x \right) = F_{109}\! \left(x \right) F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{2}\! \left(x \right)+F_{96}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right) F_{90}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{144}\! \left(x \right)
F_{141}\! \left(x \right) = F_{100}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right) F_{55}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{0}\! \left(x \right) F_{146}\! \left(x \right) F_{41}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{102}\! \left(x \right) F_{29}\! \left(x \right) F_{41}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{25}\! \left(x \right) F_{41}\! \left(x \right) F_{90}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{41}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{0}\! \left(x \right) F_{29}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{158}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{41}\! \left(x \right) F_{86}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{151}\! \left(x \right) F_{41}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{41}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{165}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{79} \left(x \right)^{2} F_{22}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{94}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{79}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{32}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right) F_{79}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{177}\! \left(x \right) F_{41}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{175}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{46}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{171}\! \left(x \right) F_{41}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{172}\! \left(x \right) F_{41}\! \left(x \right)
F_{177}\! \left(x \right) = F_{0}\! \left(x \right)+F_{100}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{41}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{195}\! \left(x \right)
F_{181}\! \left(x \right) = F_{102}\! \left(x \right) F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{188}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{46}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{22}\! \left(x \right) F_{67}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{173}\! \left(x \right) F_{25}\! \left(x \right) F_{41}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{41}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{182}\! \left(x \right) F_{25}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{22}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{172}\! \left(x \right) F_{41}\! \left(x \right)
F_{195}\! \left(x \right) = \frac{F_{196}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right) F_{41}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = -F_{338}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = \frac{F_{201}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right) F_{41}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{323}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right) F_{210}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{46}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{56}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{41}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{212}\! \left(x \right)
F_{211}\! \left(x \right) = F_{0}\! \left(x \right) F_{78}\! \left(x \right)
F_{212}\! \left(x \right) = -F_{321}\! \left(x \right)+F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right)
F_{215}\! \left(x \right) = \frac{F_{216}\! \left(x \right)}{F_{172}\! \left(x \right) F_{41}\! \left(x \right)}
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)
F_{217}\! \left(x \right) = -F_{227}\! \left(x \right)+F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)+F_{224}\! \left(x \right)
F_{219}\! \left(x \right) = F_{202}\! \left(x \right)+F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)+F_{222}\! \left(x \right)
F_{221}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{102}\! \left(x \right) F_{41}\! \left(x \right) F_{46}\! \left(x \right)
F_{224}\! \left(x \right) = -F_{202}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = \frac{F_{226}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{226}\! \left(x \right) = F_{68}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)+F_{230}\! \left(x \right)
F_{228}\! \left(x \right) = F_{0}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{173}\! \left(x \right)+F_{4}\! \left(x \right)
F_{230}\! \left(x \right) = -F_{231}\! \left(x \right)+F_{224}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{172}\! \left(x \right) F_{233}\! \left(x \right) F_{41}\! \left(x \right)
F_{233}\! \left(x \right) = F_{104}\! \left(x \right)+F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = -F_{320}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right) F_{41}\! \left(x \right)
F_{237}\! \left(x \right) = \frac{F_{238}\! \left(x \right)}{F_{243}\! \left(x \right) F_{41}\! \left(x \right)}
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = -F_{318}\! \left(x \right)+F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{274}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right) F_{273}\! \left(x \right) F_{41}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right) F_{41}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)+F_{249}\! \left(x \right)
F_{246}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{1}\! \left(x \right)+F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{247}\! \left(x \right) F_{41}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{251}\! \left(x \right) F_{259}\! \left(x \right) F_{41}\! \left(x \right)
F_{251}\! \left(x \right) = F_{247}\! \left(x \right)+F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{41}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)+F_{255}\! \left(x \right)+F_{258}\! \left(x \right)
F_{254}\! \left(x \right) = 0
F_{255}\! \left(x \right) = F_{256}\! \left(x \right) F_{41}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{247}\! \left(x \right) F_{41}\! \left(x \right)
F_{258}\! \left(x \right) = F_{252}\! \left(x \right) F_{41}\! \left(x \right)
F_{259}\! \left(x \right) = F_{247}\! \left(x \right)+F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)+F_{76}\! \left(x \right)
F_{261}\! \left(x \right) = F_{254}\! \left(x \right)+F_{262}\! \left(x \right)+F_{272}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{41}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)+F_{265}\! \left(x \right)
F_{264}\! \left(x \right) = F_{253}\! \left(x \right)+F_{256}\! \left(x \right)
F_{265}\! \left(x \right) = F_{261}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = 2 F_{254}\! \left(x \right)+F_{267}\! \left(x \right)+F_{268}\! \left(x \right)
F_{267}\! \left(x \right) = F_{261}\! \left(x \right) F_{41}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right) F_{41}\! \left(x \right)
F_{269}\! \left(x \right) = F_{266}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{41}\! \left(x \right) F_{76}\! \left(x \right)
F_{272}\! \left(x \right) = F_{260}\! \left(x \right) F_{41}\! \left(x \right)
F_{273}\! \left(x \right) = F_{104}\! \left(x \right)+F_{109}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right) F_{279}\! \left(x \right) F_{41}\! \left(x \right)
F_{276}\! \left(x \right) = F_{243}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right)
F_{279}\! \left(x \right) = \frac{F_{280}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{280}\! \left(x \right) = F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = -F_{296}\! \left(x \right)+F_{282}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = -F_{289}\! \left(x \right)+F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = \frac{F_{285}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{129}\! \left(x \right)
F_{287}\! \left(x \right) = F_{142}\! \left(x \right)+F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)+F_{294}\! \left(x \right)
F_{290}\! \left(x \right) = \frac{F_{291}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)
F_{292}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{98}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right)
F_{295}\! \left(x \right) = F_{109}\! \left(x \right) F_{146}\! \left(x \right) F_{41}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right) F_{302}\! \left(x \right) F_{41}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right) F_{41}\! \left(x \right)
F_{300}\! \left(x \right) = \frac{F_{301}\! \left(x \right)}{F_{22}\! \left(x \right) F_{41}\! \left(x \right)}
F_{301}\! \left(x \right) = F_{146}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)+F_{306}\! \left(x \right)
F_{303}\! \left(x \right) = F_{1}\! \left(x \right)+F_{304}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)
F_{305}\! \left(x \right) = F_{251}\! \left(x \right) F_{41}\! \left(x \right)
F_{306}\! \left(x \right) = \frac{F_{307}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{307}\! \left(x \right) = -F_{316}\! \left(x \right)+F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = -F_{311}\! \left(x \right)+F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = \frac{F_{310}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{310}\! \left(x \right) = F_{15}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right) F_{41}\! \left(x \right)
F_{313}\! \left(x \right) = \frac{F_{314}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{69}\! \left(x \right)+F_{80}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right)+F_{76}\! \left(x \right)
F_{317}\! \left(x \right) = F_{304}\! \left(x \right) F_{41}\! \left(x \right)
F_{318}\! \left(x \right) = F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{279}\! \left(x \right) F_{41}\! \left(x \right)
F_{320}\! \left(x \right) = F_{109}\! \left(x \right) F_{41}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = F_{233}\! \left(x \right) F_{41}\! \left(x \right) F_{78}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = -F_{337}\! \left(x \right)+F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = \frac{F_{326}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = -F_{330}\! \left(x \right)+F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = \frac{F_{329}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{329}\! \left(x \right) = F_{15}\! \left(x \right)
F_{330}\! \left(x \right) = F_{288}\! \left(x \right)+F_{331}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right) F_{41}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right)+F_{335}\! \left(x \right)
F_{334}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{335}\! \left(x \right) = F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{120}\! \left(x \right) F_{41}\! \left(x \right) F_{46}\! \left(x \right)
F_{337}\! \left(x \right) = F_{177}\! \left(x \right) F_{46}\! \left(x \right)
F_{338}\! \left(x \right) = F_{171}\! \left(x \right) F_{177}\! \left(x \right)
F_{339}\! \left(x \right) = F_{340}\! \left(x \right)
F_{340}\! \left(x \right) = F_{171}\! \left(x \right) F_{41}\! \left(x \right) F_{79}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_41(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_41(x)*F_7(x))
Eq(F_7(x), F_60(x) + F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x**2*(F_11(x) + 1)**3 - x*(x - 1)*(F_11(x) + 1)**2)
Eq(F_12(x), x**2)
Eq(F_13(x), F_14(x) + F_16(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), -F_2(x) + F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_41(x))
Eq(F_18(x), F_19(x) + F_52(x))
Eq(F_19(x), F_20(x) + F_51(x))
Eq(F_20(x), F_21(x) + F_23(x))
Eq(F_21(x), F_2(x)*F_22(x))
Eq(F_22(x), x**2*F_22(x)**3 - x*(x - 1)*F_22(x)**2 + 1)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_19(x)*F_25(x)*F_41(x))
Eq(F_25(x), F_26(x)/(F_41(x)*F_46(x)))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x)*F_41(x))
Eq(F_29(x), F_30(x)/F_41(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), -F_22(x) + F_32(x))
Eq(F_32(x), F_33(x)/F_0(x))
Eq(F_33(x), F_34(x) - F_42(x))
Eq(F_34(x), F_35(x)/F_41(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x) + F_37(x))
Eq(F_37(x), -F_2(x) + F_38(x))
Eq(F_38(x), -F_22(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_41(x))
Eq(F_40(x), F_2(x))
Eq(F_41(x), x)
Eq(F_42(x), F_43(x) - F_45(x))
Eq(F_43(x), F_44(x)/F_41(x))
Eq(F_44(x), F_37(x))
Eq(F_45(x), F_2(x)*F_32(x))
Eq(F_46(x), F_47(x) + F_51(x))
Eq(F_47(x), F_20(x) + F_48(x))
Eq(F_48(x), F_22(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_25(x)*F_41(x)*F_48(x))
Eq(F_51(x), F_22(x)*F_5(x))
Eq(F_52(x), F_53(x) + F_56(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_55(x))
Eq(F_55(x), F_11(x) + F_21(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_41(x)*F_58(x))
Eq(F_58(x), F_27(x) + F_59(x))
Eq(F_59(x), F_14(x)*F_22(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_41(x)*F_62(x))
Eq(F_62(x), F_339(x) + F_63(x))
Eq(F_63(x), F_178(x) + F_64(x))
Eq(F_64(x), F_169(x) + F_65(x))
Eq(F_65(x), F_0(x)*F_66(x))
Eq(F_66(x), F_4(x) + F_67(x))
Eq(F_67(x), F_14(x) + F_68(x))
Eq(F_68(x), -F_14(x) + F_69(x))
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_41(x))
Eq(F_71(x), F_15(x))
Eq(F_72(x), F_73(x) + F_80(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_10(x) + F_75(x))
Eq(F_75(x), F_41(x)*F_76(x)*F_79(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_41(x)*F_78(x)*F_79(x))
Eq(F_78(x), F_1(x) + F_76(x))
Eq(F_79(x), F_1(x) + F_41(x))
Eq(F_80(x), F_16(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_41(x)*F_83(x))
Eq(F_83(x), F_160(x) + F_84(x))
Eq(F_84(x), F_155(x) + F_85(x))
Eq(F_85(x), F_150(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_41(x)*F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_41(x)*F_78(x)*F_79(x)*F_90(x))
Eq(F_90(x), F_148(x) + F_91(x))
Eq(F_91(x), F_22(x)*F_92(x))
Eq(F_92(x), F_140(x) + F_93(x))
Eq(F_93(x), F_131(x) + F_94(x))
Eq(F_94(x), F_0(x) + F_95(x))
Eq(F_95(x), F_2(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_41(x)*F_98(x))
Eq(F_98(x), F_129(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_127(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_41(x))
Eq(F_102(x), F_103(x)/(F_41(x)*F_48(x)))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x) - F_107(x))
Eq(F_105(x), F_106(x)/F_41(x))
Eq(F_106(x), F_15(x))
Eq(F_107(x), F_108(x) + F_125(x))
Eq(F_108(x), F_109(x)*F_2(x))
Eq(F_109(x), F_0(x) + F_110(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_41(x))
Eq(F_112(x), F_113(x) + F_122(x))
Eq(F_113(x), F_109(x) + F_114(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_41(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_109(x)*F_94(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_109(x)*F_120(x)*F_22(x)*F_41(x))
Eq(F_120(x), F_121(x)/(F_22(x)*F_41(x)))
Eq(F_121(x), F_122(x))
Eq(F_122(x), -F_114(x) + F_123(x))
Eq(F_123(x), F_124(x)/F_41(x))
Eq(F_124(x), F_96(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_102(x)*F_19(x)*F_41(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_104(x)*F_41(x))
Eq(F_129(x), -F_130(x) + F_92(x))
Eq(F_130(x), F_4(x) + F_99(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_0(x)*F_2(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_41(x))
Eq(F_135(x), F_136(x) + F_138(x))
Eq(F_136(x), F_109(x)*F_137(x))
Eq(F_137(x), F_2(x) + F_96(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_102(x)*F_41(x)*F_90(x))
Eq(F_140(x), F_141(x) + F_144(x))
Eq(F_141(x), F_100(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_102(x)*F_41(x)*F_55(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_0(x)*F_146(x)*F_41(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_102(x)*F_29(x)*F_41(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_25(x)*F_41(x)*F_90(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x)*F_41(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_0(x)*F_29(x)*F_41(x)*F_78(x)*F_79(x))
Eq(F_155(x), F_156(x) + F_158(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_41(x)*F_86(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_151(x)*F_41(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_162(x)*F_41(x))
Eq(F_162(x), F_163(x) + F_165(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_22(x)*F_41(x)*F_78(x)*F_79(x)**2*F_94(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_79(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_32(x)*F_41(x)*F_78(x)*F_79(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_171(x)*F_177(x)*F_41(x))
Eq(F_171(x), F_172(x) + F_175(x))
Eq(F_172(x), F_173(x) + F_46(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_171(x)*F_41(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_172(x)*F_41(x))
Eq(F_177(x), F_0(x) + F_100(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_180(x)*F_41(x))
Eq(F_180(x), F_181(x) + F_195(x))
Eq(F_181(x), F_102(x)*F_182(x))
Eq(F_182(x), F_183(x) + F_188(x))
Eq(F_183(x), F_184(x) + F_46(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_22(x)*F_67(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_173(x)*F_25(x)*F_41(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_190(x)*F_41(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_182(x)*F_25(x))
Eq(F_192(x), F_193(x)*F_22(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_172(x)*F_41(x))
Eq(F_195(x), F_196(x)/F_41(x))
Eq(F_196(x), F_197(x))
Eq(F_197(x), F_198(x)*F_41(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x) - F_338(x))
Eq(F_200(x), F_201(x)/F_41(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_204(x)*F_41(x))
Eq(F_204(x), F_205(x) + F_323(x))
Eq(F_205(x), F_206(x)*F_210(x))
Eq(F_206(x), F_207(x) + F_46(x))
Eq(F_207(x), F_208(x) + F_56(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_0(x)*F_22(x)*F_41(x))
Eq(F_210(x), F_211(x) + F_212(x))
Eq(F_211(x), F_0(x)*F_78(x))
Eq(F_212(x), F_213(x) - F_321(x))
Eq(F_213(x), F_214(x))
Eq(F_214(x), F_215(x)*F_41(x)*F_78(x))
Eq(F_215(x), F_216(x)/(F_172(x)*F_41(x)))
Eq(F_216(x), F_217(x))
Eq(F_217(x), F_218(x) - F_227(x))
Eq(F_218(x), F_219(x) + F_224(x))
Eq(F_219(x), F_202(x) + F_220(x))
Eq(F_220(x), F_221(x) + F_222(x))
Eq(F_221(x), F_0(x)*F_4(x))
Eq(F_222(x), F_223(x))
Eq(F_223(x), F_102(x)*F_41(x)*F_46(x))
Eq(F_224(x), -F_202(x) + F_225(x))
Eq(F_225(x), F_226(x)/F_41(x))
Eq(F_226(x), F_68(x))
Eq(F_227(x), F_228(x) + F_230(x))
Eq(F_228(x), F_0(x)*F_229(x))
Eq(F_229(x), F_173(x) + F_4(x))
Eq(F_230(x), F_224(x) - F_231(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_172(x)*F_233(x)*F_41(x))
Eq(F_233(x), F_104(x) + F_234(x))
Eq(F_234(x), F_235(x) - F_320(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_237(x)*F_41(x))
Eq(F_237(x), F_238(x)/(F_243(x)*F_41(x)))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_240(x) - F_318(x))
Eq(F_240(x), F_241(x) + F_274(x))
Eq(F_241(x), F_242(x))
Eq(F_242(x), F_243(x)*F_273(x)*F_41(x))
Eq(F_243(x), F_244(x))
Eq(F_244(x), F_245(x)*F_41(x))
Eq(F_245(x), F_246(x) + F_249(x))
Eq(F_246(x), F_0(x)*F_22(x)*F_247(x))
Eq(F_247(x), F_1(x) + F_248(x))
Eq(F_248(x), F_247(x)*F_41(x))
Eq(F_249(x), F_250(x))
Eq(F_250(x), F_0(x)*F_22(x)*F_251(x)*F_259(x)*F_41(x))
Eq(F_251(x), F_247(x) + F_252(x))
Eq(F_252(x), F_253(x) + F_41(x))
Eq(F_253(x), F_254(x) + F_255(x) + F_258(x))
Eq(F_254(x), 0)
Eq(F_255(x), F_256(x)*F_41(x))
Eq(F_256(x), F_257(x))
Eq(F_257(x), F_247(x)*F_41(x))
Eq(F_258(x), F_252(x)*F_41(x))
Eq(F_259(x), F_247(x) + F_260(x))
Eq(F_260(x), F_261(x) + F_76(x))
Eq(F_261(x), F_254(x) + F_262(x) + F_272(x))
Eq(F_262(x), F_263(x)*F_41(x))
Eq(F_263(x), F_264(x) + F_265(x))
Eq(F_264(x), F_253(x) + F_256(x))
Eq(F_265(x), F_261(x) + F_266(x))
Eq(F_266(x), 2*F_254(x) + F_267(x) + F_268(x))
Eq(F_267(x), F_261(x)*F_41(x))
Eq(F_268(x), F_269(x)*F_41(x))
Eq(F_269(x), F_266(x) + F_270(x))
Eq(F_270(x), F_271(x))
Eq(F_271(x), F_41(x)*F_76(x))
Eq(F_272(x), F_260(x)*F_41(x))
Eq(F_273(x), F_104(x) + F_109(x))
Eq(F_274(x), F_275(x))
Eq(F_275(x), F_276(x)*F_279(x)*F_41(x))
Eq(F_276(x), F_243(x) + F_277(x))
Eq(F_277(x), F_278(x))
Eq(F_278(x), F_0(x)*F_22(x))
Eq(F_279(x), F_280(x)/F_41(x))
Eq(F_280(x), F_281(x))
Eq(F_281(x), F_282(x) - F_296(x))
Eq(F_282(x), F_283(x))
Eq(F_283(x), F_284(x) - F_289(x))
Eq(F_284(x), F_285(x)/F_41(x))
Eq(F_285(x), F_286(x))
Eq(F_286(x), F_129(x) - F_287(x))
Eq(F_287(x), F_142(x) + F_288(x))
Eq(F_288(x), F_0(x)*F_2(x))
Eq(F_289(x), F_290(x) + F_294(x))
Eq(F_290(x), F_291(x)/F_41(x))
Eq(F_291(x), F_292(x))
Eq(F_292(x), -F_288(x) + F_293(x))
Eq(F_293(x), -F_140(x) + F_98(x))
Eq(F_294(x), F_295(x))
Eq(F_295(x), F_109(x)*F_146(x)*F_41(x))
Eq(F_296(x), F_297(x))
Eq(F_297(x), F_298(x)*F_302(x)*F_41(x))
Eq(F_298(x), F_299(x))
Eq(F_299(x), F_300(x)*F_41(x))
Eq(F_300(x), F_301(x)/(F_22(x)*F_41(x)))
Eq(F_301(x), F_146(x))
Eq(F_302(x), F_303(x) + F_306(x))
Eq(F_303(x), F_1(x) + F_304(x))
Eq(F_304(x), F_305(x))
Eq(F_305(x), F_251(x)*F_41(x))
Eq(F_306(x), F_307(x)/F_41(x))
Eq(F_307(x), F_308(x) - F_316(x))
Eq(F_308(x), F_309(x) - F_311(x))
Eq(F_309(x), F_310(x)/F_41(x))
Eq(F_310(x), F_15(x))
Eq(F_311(x), F_312(x))
Eq(F_312(x), F_313(x)*F_41(x))
Eq(F_313(x), F_314(x)/F_41(x))
Eq(F_314(x), F_315(x))
Eq(F_315(x), F_69(x) + F_80(x))
Eq(F_316(x), F_317(x) + F_76(x))
Eq(F_317(x), F_304(x)*F_41(x))
Eq(F_318(x), F_319(x))
Eq(F_319(x), F_0(x)*F_22(x)*F_279(x)*F_41(x))
Eq(F_320(x), F_109(x)*F_41(x))
Eq(F_321(x), F_322(x))
Eq(F_322(x), F_233(x)*F_41(x)*F_78(x))
Eq(F_323(x), F_324(x))
Eq(F_324(x), F_325(x) - F_337(x))
Eq(F_325(x), F_326(x)/F_41(x))
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_328(x) - F_330(x))
Eq(F_328(x), F_329(x)/F_41(x))
Eq(F_329(x), F_15(x))
Eq(F_330(x), F_288(x) + F_331(x))
Eq(F_331(x), F_332(x))
Eq(F_332(x), F_333(x)*F_41(x))
Eq(F_333(x), F_334(x) + F_335(x))
Eq(F_334(x), F_4(x)*F_95(x))
Eq(F_335(x), F_336(x))
Eq(F_336(x), F_120(x)*F_41(x)*F_46(x))
Eq(F_337(x), F_177(x)*F_46(x))
Eq(F_338(x), F_171(x)*F_177(x))
Eq(F_339(x), F_340(x))
Eq(F_340(x), F_171(x)*F_41(x)*F_79(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": 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